From 65eb014de909fccf4b375e5a2eaa27658976c5ec Mon Sep 17 00:00:00 2001
From: Jukka Aho <jukka.aho@kapsi.fi>
Date: Tue, 23 Feb 2016 11:32:53 +0200
Subject: [PATCH] first attemps to make properly linearized version of mortar
 projection for finite sliding. not working at the moment, it has convergence
 issues.

---
 .../MESH_UPPER_BLOCK_SMALLER.med              | Bin 0 -> 32586 bytes
 .../2d_curved_interface/PUNCH_AND_BLOCK.med   | Bin 0 -> 86639 bytes
 .../2d_curved_interface/UPPER_SMALLER.med     | Bin 0 -> 24974 bytes
 geometry/2d_curved_interface/model.hdf        | Bin 440211 -> 780701 bytes
 geometry/2d_finite_sliding_test/TWOBLOCKS.med | Bin 0 -> 13293 bytes
 geometry/2d_finite_sliding_test/model.hdf     | Bin 0 -> 277040 bytes
 src/elements.jl                               |  29 +
 src/fields.jl                                 |   9 +
 src/lagrange.jl                               |   8 +
 src/mortar.jl                                 | 720 +-----------------
 src/mortar_2d.jl                              |   5 +-
 src/mortar_2d_autodiff.jl                     | 674 ++++++++++++++++
 src/mortar_3d.jl                              | 643 ++++++++++++++++
 src/mortar_forwarddiff_pe.jl                  | 446 +++++++++++
 src/problems.jl                               |  20 +-
 src/solvers.jl                                |  21 +-
 src/sparse.jl                                 |  25 +-
 src/xdmf.jl                                   |   4 +-
 18 files changed, 1865 insertions(+), 739 deletions(-)
 create mode 100644 geometry/2d_curved_interface/MESH_UPPER_BLOCK_SMALLER.med
 create mode 100644 geometry/2d_curved_interface/PUNCH_AND_BLOCK.med
 create mode 100644 geometry/2d_curved_interface/UPPER_SMALLER.med
 create mode 100644 geometry/2d_finite_sliding_test/TWOBLOCKS.med
 create mode 100644 geometry/2d_finite_sliding_test/model.hdf
 create mode 100644 src/mortar_2d_autodiff.jl
 create mode 100644 src/mortar_3d.jl
 create mode 100644 src/mortar_forwarddiff_pe.jl

diff --git a/geometry/2d_curved_interface/MESH_UPPER_BLOCK_SMALLER.med b/geometry/2d_curved_interface/MESH_UPPER_BLOCK_SMALLER.med
new file mode 100644
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diff --git a/geometry/2d_curved_interface/PUNCH_AND_BLOCK.med b/geometry/2d_curved_interface/PUNCH_AND_BLOCK.med
new file mode 100644
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HcmV?d00001

diff --git a/src/elements.jl b/src/elements.jl
index 608cfc8..4d59834 100644
--- a/src/elements.jl
+++ b/src/elements.jl
@@ -132,6 +132,35 @@ function call{E}(element::Element{E}, xi::VecOrIP, time::Float64=0.0)
     return get_basis(element, xi)
 end
 
+""" Given a list of elementa and nodes, find a subset of elements
+containing nodes.
+"""
+function find_elements(elements, nodes)
+    s = Set{Element}()
+    for element in elements
+        conn = get_connectivity(element)
+        for j in nodes
+            if j in conn
+                push!(s, element)
+                break
+            end
+        end
+    end
+    return collect(s)
+end
+
+function get_gdofs(element::Element)
+    return get_gdofs(element, 1)
+end
+
+function get_dbasis{E}(element::Element{E}, ip::IntegrationPoint)
+    return get_dbasis(E, ip.xi)
+end
+
+function get_basis{E, T<:Real}(element::Element{E}, xi::T)
+    return get_basis(E, xi)
+end
+
 """ Return dual basis transformation matrix Ae. """
 function get_dualbasis(element::Element, time::Real)
     if length(element.A) == 0
diff --git a/src/fields.jl b/src/fields.jl
index 66e8b52..38857e0 100644
--- a/src/fields.jl
+++ b/src/fields.jl
@@ -216,6 +216,15 @@ function Base.(:*){T<:Real}(c::T, field::DVTI)
     return DVTI(c*field.data)
 end
 
+""" Multiply DVTI field with another vector T. Vector length
+must match to the field length and this can be used mainly
+for interpolation purposes, i.e., u = ∑ Nᵢuᵢ
+"""
+function Base.(:*)(T::Vector, f::DVTI)
+    @assert length(T) == length(f)
+    return sum([T[i]*f[i] for i=1:length(f)])
+end
+
 function Base.vec(field::DVTI)
     return [field.data...;]
 end
diff --git a/src/lagrange.jl b/src/lagrange.jl
index 98b278a..4a33f8c 100644
--- a/src/lagrange.jl
+++ b/src/lagrange.jl
@@ -140,3 +140,11 @@ end
     (xi) -> [    1.0,   xi[1],       xi[2],       xi[3],     xi[1]^2,
              xi[2]^2, xi[3]^2, xi[1]*xi[2], xi[2]*xi[3], xi[3]*xi[1]])
 
+
+# some helpers to make accessing 1d basis functions more easily
+function get_basis{T<:Real, E<:Union{Seg2,Seg3}}(::Type{E}, xi::T)
+    get_basis(E, [xi])
+end
+function get_dbasis{T<:Real, E<:Union{Seg2,Seg3}}(::Type{E}, xi::T)
+    get_dbasis(E, [xi])
+end
diff --git a/src/mortar.jl b/src/mortar.jl
index c2aee87..e1c8246 100644
--- a/src/mortar.jl
+++ b/src/mortar.jl
@@ -19,7 +19,7 @@ b) Remove inactive inequality constraints in assembly level. This is done in
 
 """
 type Mortar <: BoundaryProblem
-    formulation :: Symbol # :total or :incremental
+    formulation :: Symbol # :total, :incremental, :autodiff
     dual_basis :: Bool
     inequality_constraints :: Bool # Launch PDASS to solve inequality constraints
     normal_condition :: Symbol # Tie or Contact
@@ -31,10 +31,11 @@ type Mortar <: BoundaryProblem
     always_in_slip :: Vector{Int64} # nodes in this list always in slip
     contact :: Bool
     friction :: Bool
+    gap_sign :: Int # gap sign convention
 end
 
 function Mortar()
-    Mortar(:total, true, false, :Tie, :Stick, Inf, false, [], [], [], false, false)
+    Mortar(:total, true, false, :Tie, :Stick, Inf, false, [], [], [], false, false, -1)
 end
 
 function get_unknown_field_name(::Type{Mortar})
@@ -51,719 +52,8 @@ macro debug(msg)
 end
 
 include("mortar_2d.jl")
-
-
-### Mortar projection calculation for 3d cases
-
-"""
-Construct auxiliary plane for surface.
-
-Parameters
-----------
-x::Array{Float64, 2}
-    Node coordinates
-ximp::Array{Float64, 1}
-    Element mid-point in dimensionless mother element coordinates ξ
-normals::Array{Float64, 2}
-    Normal directions in nodes
-
-Returns
--------
-x0, Q
-    x0::Array{Float64, 1} - origo of auxiliary plane
-    Q::Array{Float64, 2} - orthogonal basis, first vector is normal direction
-    and two rest vectors create orthonormal right-handed basis.
-
-Examples
---------
-Calculate auxiliary plane given nodal coordinates, midpoint of mother element,
-node normals and suitable function space:
-
-julia> xquad = [
-...     -2.5   2.5  2.0  -2.0
-...     -2.0  -2.0  2.3   2.0
-...      1.0   0.7  0.0   1.0]
-julia> m_midpoint = [0.0, 0.0]
-julia> normals = [
-...     0.05989060  0.0590504  0.225612   0.2445800
-...    -0.00748633  0.1670810  0.182034  -0.0305725
-...     0.99817700  0.9841730  0.957059   0.9691470]
-julia> basis(xi) = [
-...     (1-xi[1])(1-xi[2])/4
-...     (1+xi[1])(1-xi[2])/4
-...     (1+xi[1])(1+xi[2])/4
-...     (1-xi[1])(1+xi[2])/4]'
-julia> x0, Q = create_auxiliary_plane(xquad, mmidpoint, normals, basis)
-julia> x0
-3-element Array{Float64,1}:
- 0.0
- 0.075
- 0.675
-julia> Q
-3x3 Array{Float64,2}:
- 0.148586    0.988899    0.0
- 0.0784519  -0.0117877   0.996848
- 0.985783   -0.148118   -0.0793325
-
-Notes
------
-- Midpoint in mother element typically (0, 0) for quadrangles and (1/3, 1/3)
-  for triangles.
-- Uses Gram-Schmidt process to find orthogonal basis
-- [1](http://www.math.umn.edu/~olver/aims_/qr.pdf)
-- [2](http://www.ecs.umass.edu/ece/ece313/Online_help/gram.pdf)
-- [3](http://www.terathon.com/code/tangent.html)
-
-"""
-# function create_auxiliary_plane(x, ximp, normals, basis)
-function create_auxiliary_plane{E}(element::Element{E}, time::Real)
-#   proj(u, v) = dot(v, u) / dot(u, u) * u
-#    xi = [1.0/3.0, 1.0/3.0]
-
-    xi = get_reference_element_midpoint(E)
-    x0 = element("geometry", xi, time)
-    ntbasis = element("normal-tangential coordinates", xi, time)
-    return x0, ntbasis
-#=
-    n = element("normal-tangential coordinates", xi, time)[:, 1]
-    n /= norm(n)
-    # gram-schmidt
-    u1 = n
-    j = indmax(abs(u1))
-    v2 = zeros(3)
-    v2[mod(j,3)+1] = 1.0
-    u2 = v2 - proj(u1, v2)
-    u3 = cross(u1, u2)
-    t1 = u2/norm(u2)
-    t2 = u3/norm(u3)
-    new_basis = [n t1 t2]
-    return x0, new_basis
-=#
-end
-
-"""
-Project point q onto a plane given by a point p and normal n.
-
-Parameters
-----------
-q::Array{Float64, 2}
-    point to project (row vector)
-x0::Array{Float64, 2}
-    origo of plane
-n::Array{Float64, 2}
-    normal vector of plane
-
-Returns
--------
-y::Array{Float64, 2}
-    projected point
-
-Examples
---------
-julia> p = [-0.5 -1.0 4.0]'
-julia> x0 = [0.0 0.075 0.675]'
-julia> n = [0.1485860 0.0784519 0.9857830]'
-julia> project_node_to_auxiliary_plane(p, x0, n)
-3-element Array{Float64,1}:
-  0.963455
- -1.2447
-  0.925247
-
-Notes
------
-[1](http://stackoverflow.com/questions/8942950/how-do-i-find-the-orthogonal-projection-of-a-point-onto-a-plane)
-
-"""
-function project_point_to_auxiliary_plane(p::Vector, x0::Vector, Q::Matrix)
-    n = Q[:,1]
-    ph = p - dot(p-x0, n)*n
-    qproj = Q'*(ph-x0)
-    if !isapprox(qproj[1], 0.0; atol=1.0e-12)
-        info("project_point_to_auxiliary_plane(): point not projected correctly.")
-        info("p: $p")
-        info("x0: $x0")
-        info("Q: \n$Q")
-        info("qproj: $qproj")
-        error("Failed to project point to auxiliary plane.")
-    end
-    return qproj[2:3]
-end
-
-"""
-Find edge intersections of two planar arbitrary shape polygons.
-
-Parameters
-----------
-S::Array{Float64,2}
-M::Array{Float64,2}
-
-Matrices with size (2, n) where n is number of vertices of each polygon.
-
-Returns
--------
-P::Array{Float64,2}
-    Intersection points of polygons
-n::Array{Float64,2}
-    Neighbour info matrix with size (ns, mn). This keeps information which
-    edges of polygons are intersecting. See further explanation in example
-    below.
-
-Examples
---------
-Find intersection points of two triangles:
-
-julia> S = [0 0; 3 0; 0 3]'
-julia> M = [-1 1; 2 -1/2; 1 3/2]'
-julia> P, n = get_edge_intersections(S, M)
-julia> P
-2x4 Array{Float64,2}:
- 1.0  1.75  0.0  0.0
- 0.0  0.0   0.5  1.25
-julia> n
-3x3 Array{Int64,2}:
- 1  1  0
- 0  0  0
- 1  0  1)
-
-So intersection points are: (1.00, 0.00), (1.75, 0.00), (0.00, 0.50), (0.00, 1.25).
-"Neighbour matrix" can be interpreted as following:
-
-    1 1 0 <--> First edge of S intersects edges 1 and 2 of M
-    0 0 0 <--> Second edge of S doesn't intersect at all
-    1 0 1 <--> Third edge of S intersects with edges 1 and 3 of M
-
-"""
-function get_edge_intersections(S::Matrix, M::Matrix)
-    ns = size(S, 2)
-    nm = size(M, 2)
-    P = zeros(2, 0)
-    n = zeros(Int64, ns, nm)
-    k = 0
-    for i=1:ns
-        for j=1:nm
-            b = M[:,j]-S[:,i]
-            A = [S[:,mod(i,ns)+1]-S[:,i]  -M[:,mod(j,nm)+1]+M[:,j]]
-            if rank(A) == 2
-                r = A\b
-                if (r[1]>=0) & (r[1]<=1) & (r[2]>=0) & (r[2]<=1)  # intersection found
-                    k += 1
-                    f = S[:,i]+r[1]*(S[:,mod(i,ns)+1] - S[:,i])
-                    f = f''
-                    P = hcat(P, f)
-                    n[i, j] = 1
-                end
-            end
-        end
-    end
-    return P, n
-end
-
-
-"""
-Find any points laying inside or border of triangle.
-
-Parameters
-----------
-Y::Array{Float64, 2}
-    Triangle coordinates in 2×3 matrix
-X::Array{Float64, 2}
-    List of points to test in 2×n matrix
-
-Returns
--------
-P::Array{Float64, 2}
-    List of points in triangle in 2×m matrix, where m is number of points inside triangle
-
-Examples
---------
-julia> S = [0.0 0.0; 3.0 0.0; 0.0 3.0]'  # triangle corner points
-julia> pts = [-1.0 1.0; 2.0 -0.5; 1.0 1.5; 0.5 1.5]'  # points to tests
-julia> points_in_triangle(S, pts)
-2x2 Array{Float64,2}:
- 1.0  0.5
- 1.5  1.5
-"""
-function get_points_inside_triangle(Y::Matrix, X::Matrix)
-    @assert size(Y, 2) == 3  # "Point in TRIANGLE..."
-    P = zeros(2, 0)
-    v0 = Y[:,2] - Y[:,1]
-    v1 = Y[:,3] - Y[:,1] # find interior points of X in Y
-    d00 = (v0'*v0)[1]
-    d01 = (v0'*v1)[1]
-    d11 = (v1'*v1)[1]  # using baricentric coordinates
-    id = 1/(d00*d11 - d01*d01)
-    for i=1:size(X, 2)
-        v2 = X[:,i] - Y[:,1]
-        d02 = (v0'*v2)[1]
-        d12 = (v1'*v2)[1]
-        u = (d11*d02-d01*d12)*id
-        v = (d00*d12-d01*d02)*id
-        if (u>=0) & (v>=0) & (u+v<=1)  # also include nodes on the boundary
-            P = hcat(P, X[:,i]'')
-        end
-    end
-    return P
-end
-
-"""
-Determine is point P inside or on boudary of polygon X.
-
-http://paulbourke.net/geometry/polygonmesh/#insidepoly
-"""
-function is_point_inside_convex_polygon(P, X)
-    x, y = P
-    for i=1:length(X)
-        x0, y0 = X[i]
-        x1, y1 = X[mod(i, length(X))+1]
-        if (y-y0)*(x1-x0) - (x-x0)*(y1-y0) < 0
-            return false
-        end
-    end
-    return true
-end
-
-function get_points_inside_convex_polygon(pts, X)
-    # TODO: Make more readable
-    X2 = [X[:,i] for i=1:size(X,2)]
-    c = filter(P->is_point_inside_convex_polygon(P, X2), [pts[:,i] for i=1:size(pts, 2)])
-    return length(c) == 0 ? zeros(2, 0) : hcat(c...)
-end
-
-""" Return unique objects with some given tolerance. This is used in next function
-    because traditional unique() command returns row vectors as non-unique if they
-    differs only a "little".
-"""
-function uniquetol(P, dim::Int; args...)
-    @assert dim == 2
-    items = Vector{Float64}[P[:,i] for i=1:size(P,dim)]
-    new_items = Vector{Float64}[]
-    for item in items
-        has_found = false
-        for new_item in new_items
-            if isapprox(item, new_item; args...)
-                has_found = true
-                break
-            end
-        end
-        if !has_found
-            push!(new_items, item)
-        end
-    end
-    return reshape([new_items...;], length(new_items[]), length(new_items))
-end
-
-
-"""
-Make polygon clipping of shapes S and M.
-
-Parameters
-----------
-S::Array{Float64, 2}
-M::Array{Float64, 2}
-    Shapes to clip. Needs to be triangles at the moment.
-
-Returns
--------
-Array{Float64, 2}, Array{Float64, 2}
-- Polygon vertices in 2×n matrix, sorted in counter-clockwise order.
-- 3×3 "neighbouring" matrix, see example.
-
-Examples
---------
-julia> S = [0 0; 3 0; 0 3]'
-julia> M = [-1 1; 2 -1/2; 2 2]'
-julia> P, n = clip_polygon(S, M)
-julia> P
-2x6 Array{Float64,2}:
- 0.0  1.0  2.0  2.0  1.25  0.0
- 0.5  0.0  0.0  1.0  1.75  1.33333,
-julia> n
-3x3 Array{Int64,2}:
- 1  0  1 <- first edge of M ([-1 1; 2 -1/2]') intersects with edges 1 and 3 of S ([0 0; 3 0]' and [0 3; 0 0]')
- 1  1  0 <- second edge of M ([2 -1/2; 2 2]') intersects with edges 1 and 2 of S
- 0  1  1 <- third edge of M ([2 2; -1 1]') intersects with edgse 2 and 3 of S
-
-"""
-function clip_polygon(S::Matrix, M::Matrix)
-    P1, neighbours = get_edge_intersections(M, S)
-    #P2 = get_points_inside_triangle(M, S)
-    #P3 = get_points_inside_triangle(S, M)
-    P2 = get_points_inside_convex_polygon(M, S)
-    P3 = get_points_inside_convex_polygon(S, M)
-#   info("polygon clipping: P1 = $P1")
-#   info("polygon clipping: P2 = $P2")
-#   info("polygon clipping: P3 = $P3")
-#   info("hcat P = $P")
-    P = hcat(P1, P2, P3)
-    if length(P) == 0
-        return nothing, nothing
-    end
-    P = uniquetol(P, 2)
-    meanval = mean(P, 2)
-    tmp = P .- meanval
-    angles = atan2(tmp[2,:], tmp[1,:])
-    angles = reshape(angles, length(angles))
-    order = sortperm(angles)
-    return P[:, order], neighbours
-end
-
-
-"""
-Calculate polygon geometric center point
-
-Parameters
-----------
-P::Array{Float64, 2}
-    Polygon vertices in 2×n matrix
-
-Returns
--------
-Array{Float63, 2}
-    Center point
-
-Examples
---------
-julia> P
-2x6 Array{Float64,2}:
- 0.0  1.0  2.0  2.0  1.25  0.0
- 0.5  0.0  0.0  1.0  1.75  1.33333,
-julia> C = get_polygon_cp(P)
-2x1 Array{Float64,2}:
- 1.039740
- 0.804701
-
-"""
-function calculate_polygon_centerpoint(P::Matrix)
-    n = size(P, 2)
-    A = 0.0
-    for i=1:n
-        A += 1/2*(P[1,i]*P[2,mod(i,n)+1] - P[1,mod(i,n)+1]*P[2,i])
-    end
-    Cx = 0.0
-    Cy = 0.0
-    for i=1:n
-        inext = mod(i, n)+1
-        Cx += 1/(6*A)*(P[1,i] + P[1,inext])*(P[1,i]*P[2,inext] - P[1,inext]*P[2,i])
-        Cy += 1/(6*A)*(P[2,i] + P[2,inext])*(P[1,i]*P[2,inext] - P[1,inext]*P[2,i])
-    end
-    return Float64[Cx, Cy]
-end
-
-"""
-Project point from auxiliary plane to parametric surface given by (ξ₁, ξ₂)
-
-Parameters
-----------
-p::Array{Float64,1}
-    point in auxiliary plane, in (n,t1,t2) coordinate system
-x0::Array{Float64,1}
-    origo of auxiliary plane cs
-Q::Array{Float64,2}
-    basis of auxiliary plane cs
-x::Array{Float64,2}
-    surface node coords
-basis::Array{Float64,2}
-    surface basis functions
-dbasis::Array{Float64,2}
-    partial derivatives of surface basis functions
-
-Returns
--------
-Array{Float64,2}
-    solution vector (d, ξ₁, ξ₂) where d is distance to surface
-
-Examples
---------
-Define surface with node points, basis + dbasis
-
-julia> xquad = [
-...     -2.5 -2.0 1.0
-...      2.5 -2.0 0.7
-...      2.0  2.3 0.0
-...     -2.0  2.0 1.0]'
-julia> basis(xi) = [
-...     (1-xi[1])(1-xi[2])/4
-...     (1+xi[1])(1-xi[2])/4
-...     (1+xi[1])(1+xi[2])/4
-...     (1-xi[1])(1+xi[2])/4]
-julia> dbasis(xi) = [
-...     -(1-xi[2])/4    -(1-xi[1])/4
-...      (1-xi[2])/4    -(1+xi[1])/4
-...      (1+xi[2])/4     (1+xi[1])/4
-...     -(1+xi[2])/4     (1-xi[1])/4]
-
-We aim to find point p, which we first project to auxiliary plane defined as following
-julia> p = [-2.5 -2.0 1.0]'
-julia> x0 = [0.0 0.075 0.675]'
-julia> Q = [
-...     0.1485860   0.9888990   0.0000000
-...     0.0784519  -0.0117877   0.9968480
-...     0.9857830  -0.1481180  -0.0793325]
-
-Our projected point is therefore
-julia> n = Q[:,1] # first component is normal direction
-julia> ph = project_node_to_auxiliary_plane(p, x0, n)
-julia> ph = Q'(ph-x0)
-julia> ph
-3x1 Array{Float64,2}:
-  1.33264e-7
- -2.49593
- -2.09424
-
-Our point ph is now in auxiliary plane in n,t1,t2 coordinate system. Next we
-project it back to surface defined by xquad*basis
-
-julia> theta = project_point_from_plane_to_surface(ph, x0, Q, xquad, basis, dbasis)
-julia> theta
-3x1 Array{Float64,2}:
- -0.213874
- -0.999999
- -1.0
-
-We see that our ξ₁ = ξ₂ = -1 so we found first point of xquad
-[-2.5 -2.0 1.0]' correctly.
-
-julia> xquad*basis(theta[2:3])
-3-element Array{Float64,1}:
- -2.5
- -2.0
-  1.0
-
-"""
-function project_point_from_plane_to_surface{E}(p::Vector, x0::Vector, Q::Matrix, element::Element{E}, time::Real; max_iterations::Int=10, iter_tol::Float64=1.0e-9)
-    basis(xi) = get_basis(E, xi)
-    dbasis(xi) = get_dbasis(E, xi)
-    x = element("geometry", time)
-    ph = Q*[0; p] + x0
-    theta = Float64[0.0, 0.0, 0.0]
-    n = Q[:,1]
-    for i=1:max_iterations
-        b = ph + theta[1]*n - basis(theta[2:3])*x
-        J = [n -dbasis(theta[2:3])*x]
-        dtheta = J \ -b
-        theta += dtheta
-        if norm(dtheta) < iter_tol
-            return theta
-        end
-    end
-    begin
-        info("projecting point from auxiliary plane back to surface didn't go very well.")
-        info("element type: $E")
-        info("element connectivity: $(get_connectivity(element))")
-        info("auxiliary plane: x0 = $x0, Q = $Q")
-        info("point coordinates on plane: $p")
-        info("element geometry: $x")
-        info("ph: $ph")
-        info("normal direction: $n")
-        info("parameter vector before giving up: $theta")
-    end
-    error("project_point_to_surface: did not converge in $max_iterations iterations!")
-end
-
-typealias MortarElements3D Union{Tri3, Quad4}
-
-function assemble!{E<:MortarElements3D}(assembly::Assembly, problem::Problem{Mortar},
-                                        slave_element::Element{E}, time::Real)
-    haskey(slave_element, "master elements") || return
-    field_dim = get_unknown_field_dimension(problem)
-    field_name = get_parent_field_name(problem)
-    slave_dofs = get_gdofs(slave_element, field_dim)
-
-    props = problem.properties
-    if props.formulation == :Standard && props.normal_condition == :Contact
-        error("for contact choose Dual formulation.""")
-    end
-
-    # create auxiliary plane and project slave nodes to it
-    # x0 = origo, Q = local basis
-    x0, Q = create_auxiliary_plane(slave_element, time)
-
-    # 1. project slave nodes to auxiliary plane
-    Sl = Vector{Float64}[]
-    for p in slave_element("geometry", time)
-        push!(Sl, project_point_to_auxiliary_plane(p, x0, Q))
-    end
-    S = hcat(Sl...)
-
-    for master_element in slave_element["master elements"]
-
-        # if distance between elements is "far enough" cannot expect contact
-        if (props.normal_condition == :Contact) || props.inequality_constraints
-            slave_midpoint = slave_element("geometry", [0.0, 0.0], time)
-            master_midpoint = master_element("geometry", [0.0, 0.0], time)
-            if norm(slave_midpoint - master_midpoint) > props.minimum_distance
-                continue
-            end
-        end
-
-        master_dofs = get_gdofs(master_element, field_dim)
-
-        # 2. project master nodes to auxiliary plane
-        M = Vector{Float64}[]
-        for p in master_element("geometry", time)
-            push!(M, project_point_to_auxiliary_plane(p, x0, Q))
-        end
-        M = hcat(M...)
-
-        # 3. create polygon clipping on auxiliary plane
-        P = nothing
-        neighbours = nothing
-        try
-            P, neighbours = clip_polygon(S, M)
-        catch
-            info("polygon clipping failed")
-            info("S = ")
-            dump(S)
-            info("M = ")
-            dump(M)
-            info("original Sl = ")
-            info(Sl)
-            error("cannot continue")
-        end
-        isa(P, Void) && continue # no clipping
-
-        # shared edge but no shared volume. skipping
-        size(P, 2) < 3 && continue
-
-        C = calculate_polygon_centerpoint(P)
-        npts = size(P, 2) # number of vertices in polygon
-
-        # loop vertices and create temporary integrate cells
-        # TODO: basically when npts == 3 or npts == 4 we could integrate without splitting to cells.
-        nnodes = size(slave_element, 2)
-        C1S3 = zeros(3*nnodes, 3*nnodes)
-        C1M3 = zeros(3*nnodes, 3*nnodes)
-
-        for pnt=1:npts # integration of mortar matrices begin
-            cell = Field(Vector{Float64}[C, P[:,pnt], P[:,mod(pnt,npts)+1]])
-
-            # calculate slave side projection matrix D
-            # construct dual basis
-            Ae = zeros(nnodes, nnodes)
-            De = zeros(nnodes, nnodes)
-            Me = zeros(nnodes, nnodes)
-            if problem.properties.formulation == :Dual # Construct dual basis
-                for ip in get_integration_points(Tri3, Val{5})
-                    N = get_basis(Tri3, ip.xi)
-                    xi = vec(N*cell)
-                    theta = project_point_from_plane_to_surface(xi, x0, Q, slave_element, time)
-                    xi_slave = theta[2:3]
-                    N1 = slave_element(xi_slave, time)
-                    # jacobian determinant on integration cell
-                    dNC = get_dbasis(Tri3, ip.xi)
-                    JC = sum([kron(dNC[:,j], cell[j]') for j=1:length(cell)])
-                    wC = ip.weight*det(JC)
-                    De += wC*diagm(vec(N1))
-                    Me += wC*N1'*N1
-                end
-                Ae = De*inv(Me)
-            end
-            for i=1:field_dim
-                C1S3[i:field_dim:end,i:field_dim:end] += De
-            end
-
-            # Calculate master side projection matrix M
-            for ip in get_integration_points(Tri3, Val{5})
-                # gauss point in auxiliary plane
-                #N = get_basis(E, ip.xi)
-                N = get_basis(Tri3, ip.xi)
-                xi = vec(N*cell)  # xi defined in auxilary plane
-
-                # find projection of gauss point to master and slave elements
-                theta1 = project_point_from_plane_to_surface(xi, x0, Q, slave_element, time)
-                theta2 = project_point_from_plane_to_surface(xi, x0, Q, master_element, time)
-                xi_slave = theta1[2:3]
-                xi_master = theta2[2:3]
-
-                # evaluate shape functions values in gauss point and add contribution to matrices
-                N1 = slave_element(xi_slave, time)
-                N2 = master_element(xi_master, time)
-
-                # jacobian determinant on integration cell
-                dNC = get_dbasis(Tri3, ip.xi)
-                JC = sum([kron(dNC[:,j], cell[j]') for j=1:length(cell)])
-                wC = ip.weight*det(JC)
-
-                # extend matrices according to the problem dimension (3)
-                @assert length(slave_dofs) == length(master_dofs)
-                Me = wC*Ae*N1'*N2
-                for k=1:field_dim
-                    C1M3[k:field_dim:end,k:field_dim:end] += Me
-                end
-            end
-        end  # integration of mortar matrices done.
-
-        # constraints in normal-tangential direction and initial weighted gap
-        X1 = vec(slave_element("geometry", time))
-        X2 = vec(master_element("geometry", time))
-        Q_ = slave_element("normal-tangential coordinates", time)
-        Z = zeros(3, 3)
-        if nnodes == 3
-            Q3 = [Q Z Z; Z Q Z; Z Z Q]
-        elseif nnodes == 4
-            Q3 = [Q Z Z Z; Z Q Z Z; Z Z Q Z; Z Z Z Q]
-        end
-        D3 = zeros(3*nnodes, 3*nnodes)
-        C2S3 = Q3'*C1S3
-        C2M3 = Q3'*C1M3
-        G = -(C2S3*X1 - C2M3*X2)
-
-        # complementarity condition
-        if haskey(slave_element, "displacement")
-            u1 = vec(slave_element("displacement", time))
-        else
-            u1 = zeros(3*nnodes)
-        end
-        if haskey(master_element, "displacement")
-            u2 = vec(master_element("displacement", time))
-        else
-            u2 = zeros(3*nnodes)
-        end
-        x1 = X1 + u1
-        x2 = X2 + u2
-        if  haskey(slave_element, "reaction force")
-            la = vec(slave_element("reaction force", time))
-        else
-            la = zeros(3*nnodes)
-        end
-        g = -(C2S3*x1 - C2M3*x2)
-        c = Q3'*la - g
-        inactive_nodes = find(c[1:field_dim:end] .<= 0)
-        active_nodes = find(c[1:field_dim:end] .> 0)
-
-        # normal constraint: remove inactive nodes if normal condition is set to contact
-        if problem.properties.normal_condition == :Contact
-            for j in inactive_nodes
-                dofs = [3*(j-1)+1, 3*(j-1)+2, 3*(j-1)+3]
-                G[dofs] = 0
-                C1S3[dofs,:] = 0
-                C1M3[dofs,:] = 0
-                C2S3[dofs,:] = 0
-                C2M3[dofs,:] = 0
-            end
-        end
-
-        # tangential constraint: stick or slip
-        if problem.properties.tangential_condition == :Slip
-            D3 = copy(C2S3)
-            D3[1:field_dim:end, :] = 0
-            C2S3[2:field_dim:end, :] = 0
-            C2M3[2:field_dim:end, :] = 0
-            C2S3[3:field_dim:end, :] = 0
-            C2M3[3:field_dim:end, :] = 0
-        end
-
-        # add contributions
-        add!(assembly.C1, slave_dofs, slave_dofs, C1S3)
-        add!(assembly.C1, slave_dofs, master_dofs, -C1M3)
-        add!(assembly.C2, slave_dofs, slave_dofs, C2S3)
-        add!(assembly.C2, slave_dofs, master_dofs, -C2M3)
-        add!(assembly.D, slave_dofs, slave_dofs, D3)
-        add!(assembly.c, slave_dofs, c)
-        add!(assembly.g, slave_dofs, G)
-    end
-end
-
+include("mortar_2d_autodiff.jl")
+include("mortar_3d.jl")
 
 """ Remove inactive inequality constraints by using primal-dual active set strategy. """
 function boundary_assembly_posthook!(solver::Solver, problem::Problem{Mortar}, C1, C2, D, g)
diff --git a/src/mortar_2d.jl b/src/mortar_2d.jl
index 64845eb..74da3dc 100644
--- a/src/mortar_2d.jl
+++ b/src/mortar_2d.jl
@@ -217,7 +217,6 @@ function project_from_master_to_slave{S,M}(slave::Element{S}, master::Element{M}
     error("find projection from master to slave: did not converge")
 end
 
-
 # Mortar assembly 2d
 
 # quadratic not tested yet
@@ -546,8 +545,8 @@ function assemble!{E<:MortarElements2D}(assembly::Assembly, problem::Problem{Mor
         # Calculate normal-tangential constraints and weighted gap
         C2S2 = Q2'*C1S2
         C2M2 = Q2'*C1M2
-        G += -(C2S2*X1 - C2M2*X2)
-        g += -(C2S2*x1 - C2M2*x2)
+        G += props.gap_sign*(C2S2*X1 - C2M2*X2)
+        g += props.gap_sign*(C2S2*x1 - C2M2*x2)
 
         # Add contributions
         add!(local_assembly.C1, slave_dofs, slave_dofs, C1S2)
diff --git a/src/mortar_2d_autodiff.jl b/src/mortar_2d_autodiff.jl
new file mode 100644
index 0000000..b4d2cbb
--- /dev/null
+++ b/src/mortar_2d_autodiff.jl
@@ -0,0 +1,674 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+""" Find segment from slave element corresponding to master element nodes.
+x1_, n1_
+slave element geometry and normal direction
+
+x2_ master element nodes to project onto slave
+"""
+function project_from_master_to_slave{E<:MortarElements2D}(
+    slave_element::Element{E}, x1_::DVTI, n1_::DVTI, x2::Vector;
+    tol=1.0e-10, max_iterations=20)
+
+    function x1(xi1)
+        N = get_basis(E, xi1)
+        return vec(N)*x1_
+    end
+
+    function dx1(xi1)
+        dN = get_dbasis(E, xi1)
+        return vec(dN)*x1_
+    end
+
+    function n1(xi1)
+        N = get_basis(E, xi1)
+        return vec(N)*n1_
+    end
+
+    function dn1(xi1)
+        dN = get_dbasis(E, xi1)
+        return vec(dN)*n1_
+    end
+
+    cross2(a, b) = cross([a; 0], [b; 0])[3]
+    R(xi1) = cross2(x1(xi1)-x2, n1(xi1))
+    dR(xi1) = cross2(dx1(xi1), n1(xi1)) + cross2(x1(xi1)-x2, dn1(xi1))
+    xi1 = 0.0
+    dxi1 = 0.0
+    for i=1:max_iterations
+        dxi1 = -R(xi1)/dR(xi1)
+        xi1 += dxi1
+        if norm(dxi1) < tol
+            return xi1
+        end
+    end
+
+    info("x1 = $(ForwardDiff.get_value(x1_.data))")
+    info("n1 = $(ForwardDiff.get_value(n1_.data))")
+    info("x2 = $(ForwardDiff.get_value(x2))")
+    info("xi1 = $(ForwardDiff.get_value(xi1)), dxi1 = $(ForwardDiff.get_value(dxi1))")
+    info("-R(xi1) = $(ForwardDiff.get_value(-R(xi1)))")
+    info("dR(xi1) = $(ForwardDiff.get_value(dR(xi1)))")
+    error("find projection from master to slave: did not converge")
+
+end
+
+function project_from_slave_to_master{E<:MortarElements2D}(
+    master_element::Element{E}, x1::Vector, n1::Vector, x2_::DVTI;
+    tol=1.0e-10, max_iterations=20)
+
+    function x2(xi2)
+        N = get_basis(E, xi2)
+        return vec(N)*x2_
+    end
+
+    function dx2(xi2)
+        dN = get_dbasis(E, xi2)
+        return vec(dN)*x2_
+    end
+
+    cross2(a, b) = cross([a; 0], [b; 0])[3]
+    R(xi2) = cross2(x2(xi2)-x1, n1)
+    dR(xi2) = cross2(dx2(xi2), n1)
+    xi2 = 0.0
+    dxi2 = 0.0
+    for i=1:max_iterations
+        dxi2 = -R(xi2) / dR(xi2)
+        xi2 += dxi2
+        if norm(dxi2) < tol
+            return xi2
+        end
+    end
+
+    error("find projection from slave to master: did not converge, last val: $xi2 and $dxi2")
+    
+end
+
+
+function assemble!{E<:MortarElements2D}(assembly::Assembly, problem::Problem{Mortar}, slave_element::Element{E}, time::Real,
+    ::Type{Val{:forwarddiff_old}})
+    haskey(slave_element, "master elements") || return
+    props = problem.properties
+    field_dim = get_unknown_field_dimension(problem)
+    field_name = get_parent_field_name(problem)
+    slave_dofs = get_gdofs(slave_element, field_dim)
+    nnodes = size(slave_element, 2)
+    X1 = slave_element("geometry", time)
+    #u1 = slave_element("displacement", time)
+    #x1 = X1 + u1
+    slave_element_nodes = get_connectivity(slave_element)
+    adjacent_elements = find_elements(get_elements(problem), slave_element_nodes)
+    adjacent_nodes = get_nodes(adjacent_elements) # including also nodes from adjacent elements
+    Q = [0.0 -1.0; 1.0 0.0]
+
+    X = spzeros(10000, 1)
+    for element in get_elements(problem)
+        conn = get_connectivity(element)
+        geom = element("geometry", time)
+        for (c, g) in zip(conn, geom)
+            dofs = [field_dim*(c-1)+1, field_dim*(c-1)+2]
+            X[dofs] = g
+        end
+    end
+
+    # here x does not mean deformed configuration
+    x = [problem.assembly.u; problem.assembly.la]
+    if length(x) == 0
+        info("mortar_2d_autodiff: length(x) == 0")
+        # resize solution vectors according to initial configuration of this problem
+        X = vec(full(sparse(findnz(X)...)))
+        x = zeros(length(X)*2)
+    else
+        # resize initial configuration to match real dimension
+        I, J, V = findnz(X)
+        X = vec(full(sparse(I, J, V, length(problem.assembly.u), 1)))
+    end
+    ndofs = round(Int, length(x)/2)
+    # at the end we should have 
+#   info("mortar_2d_autodiff: size of x = $(size(x))")
+#   info("mortar_2d_autodiff: size of X = $(size(X))")
+#   info("mortar_2d_autodiff: ndofs = $ndofs")
+
+    """ Calculate normal vector for slave element nodes in current configuration. """
+    function calculate_normals(u::Matrix)
+        normals = zeros(u)
+        # 1. update nodal normals
+        for element in adjacent_elements
+            conn = get_connectivity(element)
+            gdofs = get_gdofs(element, field_dim)
+            X_el = element("geometry", time)
+            u_el = Field(Vector[u[:, i] for i in conn])
+            x_el = X_el + u_el
+            for ip in get_integration_points(element, Val{3})
+                dN = get_dbasis(element, ip)
+                N = element(ip, time)
+                t = sum([kron(dN[:,i], x_el[i]') for i=1:length(x_el)])
+                normals[:, conn] += ip.weight*Q*t'*N
+            end
+        end
+        slave_normals = Field(Vector[normals[:,i]/norm(normals[:,i]) for i in slave_element_nodes])
+        return slave_normals
+    end
+
+    function calculate_mortar_projection(u::Matrix, n1::DVTI)
+        B = SparseMatrixCOO{Real}([], [], [])
+
+        u1 = Field([u[:,i] for i in slave_element_nodes])
+        x1 = X1 + u1
+
+        for master_element in slave_element["master elements"]
+            X2 = master_element("geometry", time)
+            master_element_nodes = get_connectivity(master_element)
+            u2 = Field([u[:,i] for i in master_element_nodes])
+            x2 = X2 + u2
+            #info("master element coordinate 1 = $(ForwardDiff.get_value(x2[1]))")
+            #info("master element coordinate 2 = $(ForwardDiff.get_value(x2[2]))")
+
+            # calculate segmentation: we care only about endpoints
+            # note: these are quadratic/cubic functions, analytical solution possible
+            xi1a = project_from_master_to_slave(slave_element, x1, n1, x2[1])
+            xi1b = project_from_master_to_slave(slave_element, x1, n1, x2[end])
+            xi1 = clamp([xi1a; xi1b], -1.0, 1.0)
+            l = 1/2*abs(xi1[2]-xi1[1])
+            isapprox(l, 0.0) && continue # no contribution
+
+            # integrate slave side
+            D = zeros(nnodes, nnodes)
+            Me = zeros(nnodes, nnodes)
+            for ip in get_integration_points(slave_element, Val{5})
+                dN = get_dbasis(slave_element, ip)
+                # jacobian of slave element in deformed state
+                j = sum([kron(dN[:,i], x1[i]') for i=1:length(x1)])
+                w = ip.weight*norm(j)*l
+                xi_s = dot([1/2*(1-ip.xi); 1/2*(1+ip.xi)], xi1)
+                N = get_basis(slave_element, xi_s)
+                D += w*diagm(vec(N))
+                Me += w*N'*N
+            end
+            Ae = D*inv(Me)
+
+            # integrate master side
+            M = zeros(nnodes, nnodes)
+            for ip in get_integration_points(slave_element, Val{5})
+                dN = get_dbasis(slave_element, ip)
+                # jacobian of slave element in deformed state
+                j = sum([kron(dN[:,i], x1[i]') for i=1:length(x1)])
+                w = ip.weight*norm(j)*l
+                xi_g = dot([1/2*(1-ip.xi); 1/2*(1+ip.xi)], xi1)
+                N1 = get_basis(slave_element, xi_g)
+                x_g = vec(N1)*x1
+                n_g = vec(N1)*n1
+                #info("slave gauss point coordinates $(ForwardDiff.get_value(x_g))")
+                #info("slave gauss point normal direction $(ForwardDiff.get_value(n_g))")
+                xi_m = project_from_slave_to_master(master_element, x_g, n_g, x2)
+                N2 = get_basis(master_element, xi_m)
+                M += w*kron(Ae*N1', N2)
+            end
+
+            slave_dofs = get_gdofs(slave_element, field_dim)
+            master_dofs = get_gdofs(master_element, field_dim)
+            for i=1:field_dim
+                add!(B, slave_dofs[i:field_dim:end], slave_dofs[i:field_dim:end], D)
+                add!(B, slave_dofs[i:field_dim:end], master_dofs[i:field_dim:end], -M)
+            end
+
+        end
+
+        return B
+    end
+
+    function calculate_contact_rhs(x::Vector)
+        ndofs = round(Int, length(x)/2)
+        u = x[1:ndofs]
+        la = x[ndofs+1:end]
+#       info("calculate_contact_rhs: size of u = $(size(u))")
+#       info("calculate_contact_rhs: size of X = $(size(X))")
+#       info("calculate_contact_rhs: size of la = $(size(la))")
+#       info("calculate_contact_rhs: ndofs = $ndofs")
+        u2 = reshape(u, field_dim, round(Int, length(u)/field_dim))
+
+        normals = calculate_normals(u2)
+        B = calculate_mortar_projection(u2, normals)
+        B = sparse(B, ndofs, ndofs)
+        fc = B' * la # contact force residual for r = fint + fc - fext = 0
+
+        N = SparseMatrixCOO{Real}([], [], [])
+        T = SparseMatrixCOO{Real}([], [], [])
+        for (i, j) in enumerate(slave_element_nodes)
+            dofs = [2*(j-1)+1, 2*(j-1)+2]
+            add!(N, dofs, [dofs[1]], reshape(normals[i], 2, 1))
+            add!(T, dofs, [dofs[2]], reshape(Q'*normals[i], 2, 1))
+        end
+        N = sparse(N, ndofs, ndofs)
+        T = sparse(T, ndofs, ndofs)
+        gn = -N*B*(X+u)
+        gt = -T*B*(X+u)
+#       gn = -N*B*u
+        lan = N*la
+        lat = T*la
+        cn = 1.0e3
+        C = lan - max(0, lan - cn*gn) + lat
+        # C = lan - gn + lat - gt <-- ihan viturallensa
+        # C = gn+gt <-- not working
+        # C = B*(X+u)
+        # C = B*u <- pitää kiinni, "tie".
+        # C = N*B*u + T*la <- palikat menee väärään suuntaan
+        # C = -N*B*(X+u) + T*la <- toimii suht hyvin mut kääntyy väärään suuntaan (t-suunnassa)
+        # C = -N*B*(X+u) - T*la <- sama
+        # C = -N*B*(X+u) - T*B*la <- sama
+        # C = N*la + T*la - max(0, N*la + N*B*(X+u))
+        cond = lan[1:field_dim:end] - cn*gn[1:field_dim:end]
+        all_nodes = slave_element_nodes
+        inactive_nodes = find(cond .<= 0)
+        active_nodes = find(cond .> 0)
+        inactive_nodes = setdiff(all_nodes, inactive_nodes)
+        active_nodes = setdiff(all_nodes, active_nodes)
+        info("S = $all_nodes, I = $inactive_nodes, A = $active_nodes")
+        info("lambda = $(ForwardDiff.get_value(lan[slave_dofs]))")
+        info("gn = $(ForwardDiff.get_value(gn[slave_dofs]))")
+        #for j in active_nodes
+        #    dofs = [field_dim*(j-1)+1, field_dim*(j-1)+2]
+        #    C[dofs] = 0
+        #end
+        
+#       C = -(N+T)*B*(X+u)
+#       C = -B*(X+u)
+
+        return [fc; C]
+
+    end
+
+    A, allresults = ForwardDiff.jacobian(calculate_contact_rhs, x, ForwardDiff.AllResults)
+    b = -ForwardDiff.value(allresults)
+    A = sparse(A)
+    b = sparse(b)
+    K = A[1:ndofs,1:ndofs]
+    C1 = A[1:ndofs,ndofs+1:end]'
+    C2 = A[ndofs+1:end,1:ndofs]
+    D = A[ndofs+1:end,ndofs+1:end]
+    f = b[1:ndofs]
+    g = b[ndofs+1:end]
+    C2[2:field_dim:end] = 0
+    g[2:field_dim:end] = 0
+
+#   C2[2:field_dim:end] = 0
+#   g[2:field_dim:end] = 0
+#   inactives = find(g[1:field_dim:end] .<= 0)
+#   actives = find(g[1:field_dim:end] .> 0)
+#   inactives = setdiff(slave_element_nodes, inactives)
+#   actives = setdiff(slave_element_nodes, actives)
+#   info("all nodes = $slave_element_nodes, inactives = $inactives, actives = $actives")
+#   info("g = $g")
+
+#   for j in inactives
+    #    dofs = [field_dim*(j-1)+1, field_dim*(j-1)+2]
+    #    K[dofs,:] = 0
+    #    C1[dofs,:] = 0
+    #    C2[dofs,:] = 0
+    #    D[dofs,:] = 0
+    #    g[dofs,:] = 0
+    #end
+    #for j in actives
+    #    dofs = [field_dim*(j-1)+1, field_dim*(j-1)+2]
+    #    C2[dofs[1],:] = 0
+    #end
+    add!(assembly.K, K)
+    add!(assembly.C1, C1)
+    add!(assembly.C2, C2)
+    add!(assembly.D, D)
+    add!(assembly.f, f)
+    add!(assembly.g, g)
+end
+
+
+function assemble!{E<:MortarElements2D}(assembly::Assembly,
+    problem::Problem{Mortar}, slave_element::Element{E},
+    time::Real, ::Type{Val{:forwarddiff_old2}})
+    haskey(slave_element, "master elements") || return
+    props = problem.properties
+    field_dim = get_unknown_field_dimension(problem)
+    field_name = get_parent_field_name(problem)
+
+    function calculate_interface(x::Vector)
+
+        ndofs = round(Int, length(x)/2)
+        nnodes = round(Int, ndofs/field_dim)
+        u = reshape(x[1:ndofs], field_dim, nnodes)
+        la = reshape(x[ndofs+1:end], field_dim, nnodes)
+        fc = zeros(u)
+        C = zeros(la)
+        
+        slave_element_nodes = get_connectivity(slave_element)
+        X1 = slave_element("geometry", time)
+        u1 = Field(Vector[u[:,i] for i in slave_element_nodes])
+        la1 = Field(Vector[la[:,i] for i in slave_element_nodes])
+        x1 = X1 + u1
+
+        # 1. update nodal normals for this element. average nodes from adjacent elements
+        adjacent_elements = find_elements(get_elements(problem), slave_element_nodes)
+        adjacent_nodes = get_nodes(adjacent_elements) # including also nodes from adjacent elements
+        Q = [0.0 -1.0; 1.0 0.0]
+        normals = zeros(u)
+        for element in adjacent_elements
+            conn = get_connectivity(element)
+            gdofs = get_gdofs(element, field_dim)
+            X_el = element("geometry", time)
+            u_el = Field(Vector[u[:, i] for i in conn])
+            x_el = X_el + u_el
+            for ip in get_integration_points(element, Val{3})
+                dN = get_dbasis(element, ip)
+                N = element(ip, time)
+                t = sum([kron(dN[:,i], x_el[i]') for i=1:length(x_el)])
+                normals[:, conn] += ip.weight*Q*t'*N
+            end
+        end
+        # --> slave side normals in deformed state
+        n1 = Field(Vector[normals[:,i]/norm(normals[:,i]) for i in slave_element_nodes])
+
+        for master_element in slave_element["master elements"]
+
+            master_element_nodes = get_connectivity(master_element)
+            X2 = master_element("geometry", time)
+            u2 = Field(Vector[u[:,i] for i in master_element_nodes])
+            x2 = X2 + u2
+
+            # calculate segmentation: we care only about endpoints
+            # note: these are quadratic/cubic functions, analytical solution possible
+            xi1a = project_from_master_to_slave(slave_element, x1, n1, x2[1])
+            xi1b = project_from_master_to_slave(slave_element, x1, n1, x2[end])
+            xi1 = clamp([xi1a; xi1b], -1.0, 1.0)
+            l = 1/2*abs(xi1[2]-xi1[1])
+            isapprox(l, 0.0) && continue # no contribution in this master element
+
+            nnodes = size(slave_element, 2)
+            De = zeros(nnodes, nnodes)
+            Me = zeros(nnodes, nnodes)
+            for ip in get_integration_points(slave_element, Val{5})
+                # jacobian of slave element in deformed state
+                dN = get_dbasis(slave_element, ip)
+                j = sum([kron(dN[:,i], x1[i]') for i=1:length(x1)])
+                w = ip.weight*norm(j)*l
+                xi_s = dot([1/2*(1-ip.xi); 1/2*(1+ip.xi)], xi1)
+                N1 = get_basis(slave_element, xi_s)
+                De += w*diagm(vec(N1))
+                Me += w*N1'*N1
+            end
+            Ae = De*inv(Me)
+
+            slave_dofs = get_gdofs(slave_element, field_dim)
+            master_dofs = get_gdofs(master_element, field_dim)
+
+            for ip in get_integration_points(slave_element, Val{5})
+                # jacobian of slave element in deformed state
+                dN = get_dbasis(slave_element, ip)
+                j = sum([kron(dN[:,i], x1[i]') for i=1:length(x1)])
+                w = ip.weight*norm(j)*l
+
+                # project gauss point from slave element to master element
+                xi_s = dot([1/2*(1-ip.xi); 1/2*(1+ip.xi)], xi1)
+                N1 = vec(get_basis(slave_element, xi_s))
+                x_s = N1*x1 # coordinate in gauss point
+                n_s = N1*n1 # normal direction in gauss point
+                t_s = Q'*n_s # tangent direction in gauss point
+                R_s = [n_s t_s]
+                xi_m = project_from_slave_to_master(master_element, x_s, n_s, x2)
+                N2 = vec(get_basis(master_element, xi_m))
+                x_m = N2*x2
+                Phi = Ae*N1
+
+                u_s = N1*u1
+                u_m = N2*u2
+
+                la_s = Phi*la1 # traction force in gauss point
+                #lan = dot(n_s, la_s) # normal component
+                #lat = dot(t_s, la_s) # tangential component
+                la_nt = R_s*la_s
+                g = x_s-x_m
+                gn = props.gap_sign*dot(n_s, g) # normal gap
+                #gu = dot(n_s, u_s - u_m) # normal displacement gap
+                #gt = dot(t_s, x_s - x_m) # tangential gap
+
+                fc[:,slave_element_nodes] += w*la_s*N1'
+                fc[:,master_element_nodes] -= w*la_s*N2'
+                C[1,slave_element_nodes] += w*gn*Phi'
+                #C[2,slave_element_nodes] += w*la_nt[2]*Phi'
+                #C[2,slave_element_nodes] += w*la_nt[2,:]*Phi'
+                #C[2,slave_element_nodes] += w*dot(t_s, u_s - u_m)*Phi' # <-- for tie
+
+                #R += w*R_s
+
+            end
+
+        end # master elements done
+
+        for (i, j) in enumerate(slave_element_nodes)
+            n = n1[i]
+            t = Q'*n
+            R = [n t]
+            la_nt = R*la[:,j]
+            C[2,j] += la_nt[2]
+        end
+
+        return vec([fc C])
+
+    end
+
+    # x doesn't mean deformed configuration here
+    x = [problem.assembly.u; problem.assembly.la]
+    ndofs = round(Int, length(x)/2)
+    #if ndofs == 0
+    #    info("INITIALIZING THINGS")
+    #    problem.assembly.u = zeros(16)
+    #    problem.assembly.la = zeros(16)
+    #    x = [problem.assembly.u; problem.assembly.la]
+    #    ndofs = round(Int, length(x)/2)
+    #end
+
+    A, allresults = ForwardDiff.jacobian(calculate_interface, x, ForwardDiff.AllResults)
+    b = -ForwardDiff.value(allresults)
+    #b = -calculate_interface(x)
+    #info("PE = $(ForwardDiff.value(allresults))")
+    A = sparse(A)
+    b = sparse(b)
+    SparseMatrix.droptol!(A, 1.0e-12)
+    SparseMatrix.droptol!(b, 1.0e-12)
+    #println(A)
+    K = A[1:ndofs,1:ndofs]
+    C1 = transpose(A[1:ndofs,ndofs+1:end])
+    C2 = A[ndofs+1:end,1:ndofs]
+    D = A[ndofs+1:end,ndofs+1:end]
+    f = b[1:ndofs]
+    g = b[ndofs+1:end]
+    add!(assembly.K, K)
+    add!(assembly.C1, C1)
+    add!(assembly.C2, C2)
+    add!(assembly.D, D)
+    add!(assembly.f, f)
+    add!(assembly.g, g)
+
+    return
+
+end
+
+
+function assemble!{E<:MortarElements2D}(assembly::Assembly,
+    problem::Problem{Mortar}, slave_element::Element{E},
+    time::Real, ::Type{Val{:forwarddiff}})
+    haskey(slave_element, "master elements") || return
+    props = problem.properties
+    field_dim = get_unknown_field_dimension(problem)
+    field_name = get_parent_field_name(problem)
+
+    function calculate_interface(x::Vector)
+
+        ndofs = round(Int, length(x)/2)
+        nnodes = round(Int, ndofs/field_dim)
+        u = reshape(x[1:ndofs], field_dim, nnodes)
+        la = reshape(x[ndofs+1:end], field_dim, nnodes)
+        fc = zeros(u)
+        C = zeros(la)
+        
+        slave_element_nodes = get_connectivity(slave_element)
+        X1 = slave_element("geometry", time)
+        u1 = Field(Vector[u[:,i] for i in slave_element_nodes])
+        la1 = Field(Vector[la[:,i] for i in slave_element_nodes])
+        x1 = X1 + u1
+
+        # 1. update nodal normals for this element. average nodes from adjacent elements
+        adjacent_elements = find_elements(get_elements(problem), slave_element_nodes)
+        adjacent_nodes = get_nodes(adjacent_elements) # including also nodes from adjacent elements
+        Q = [0.0 -1.0; 1.0 0.0]
+        normals = zeros(u)
+        for element in adjacent_elements
+            conn = get_connectivity(element)
+            gdofs = get_gdofs(element, field_dim)
+            X_el = element("geometry", time)
+            u_el = Field(Vector[u[:, i] for i in conn])
+            x_el = X_el + u_el
+            for ip in get_integration_points(element, Val{3})
+                dN = get_dbasis(element, ip)
+                N = element(ip, time)
+                t = sum([kron(dN[:,i], x_el[i]') for i=1:length(x_el)])
+                normals[:, conn] += ip.weight*Q*t'*N
+            end
+        end
+        # --> slave side normals in deformed state
+        n1 = Field(Vector[ForwardDiff.get_value(normals[:,i]/norm(normals[:,i])) for i in slave_element_nodes])
+
+
+        nnodes = size(slave_element, 2)
+        lan_tot = zeros(nnodes) # normal pressure
+        gap_tot = zeros(nnodes) # weighted normal gap
+
+        for master_element in slave_element["master elements"]
+
+            master_element_nodes = get_connectivity(master_element)
+            X2 = master_element("geometry", time)
+            u2 = Field(Vector[u[:,i] for i in master_element_nodes])
+            x2 = X2 + u2
+
+            # calculate segmentation: we care only about endpoints
+            # note: these are quadratic/cubic functions, analytical solution possible
+            xi1a = project_from_master_to_slave(slave_element, x1, n1, x2[1])
+            xi1b = project_from_master_to_slave(slave_element, x1, n1, x2[end])
+            xi1 = clamp([xi1a; xi1b], -1.0, 1.0)
+            l = 1/2*abs(xi1[2]-xi1[1])
+            isapprox(l, 0.0) && continue # no contribution in this master element
+
+            De = zeros(nnodes, nnodes)
+            Me = zeros(nnodes, nnodes)
+            for ip in get_integration_points(slave_element, Val{5})
+                # jacobian of slave element in deformed state
+                dN = get_dbasis(slave_element, ip)
+                j = sum([kron(dN[:,i], x1[i]') for i=1:length(x1)])
+                w = ip.weight*norm(j)*l
+                xi_s = dot([1/2*(1-ip.xi); 1/2*(1+ip.xi)], xi1)
+                N1 = get_basis(slave_element, xi_s)
+                De += w*diagm(vec(N1))
+                Me += w*N1'*N1
+            end
+            Ae = De*inv(Me)
+
+            slave_dofs = get_gdofs(slave_element, field_dim)
+            master_dofs = get_gdofs(master_element, field_dim)
+
+            for ip in get_integration_points(slave_element, Val{5})
+                # jacobian of slave element in deformed state
+                dN = get_dbasis(slave_element, ip)
+                j = sum([kron(dN[:,i], x1[i]') for i=1:length(x1)])
+                w = ip.weight*norm(j)*l
+
+                # project gauss point from slave element to master element
+                xi_s = dot([1/2*(1-ip.xi); 1/2*(1+ip.xi)], xi1)
+                N1 = vec(get_basis(slave_element, xi_s))
+                x_s = N1*x1 # coordinate in gauss point
+                n_s = N1*n1 # normal direction in gauss point
+                t_s = Q'*n_s # tangent direction in gauss point
+                R_s = [n_s t_s]
+                xi_m = project_from_slave_to_master(master_element, x_s, n_s, x2)
+                N2 = vec(get_basis(master_element, xi_m))
+                x_m = N2*x2
+                Phi = Ae*N1
+
+                u_s = N1*u1
+                u_m = N2*u2
+
+                la_s = Phi*la1 # traction force in gauss point
+                la_nt = R_s*la_s
+                gn = -dot(n_s, x_s - x_m) # normal gap
+
+                fc[:,slave_element_nodes] += w*la_s*N1'
+                fc[:,master_element_nodes] -= w*la_s*N2'
+                #C[1,slave_element_nodes] += w*gn*Phi'
+                
+                lan_tot += w*la_nt[1]*Phi
+                gap_tot += w*gn*Phi
+
+            end
+
+        end # master elements done
+
+#       ncf = lan_tot - max(0, lan_tot - gap_tot)
+#       info("pressure in nodes: $(ForwardDiff.get_value(lan_tot))")
+#       info("weighted gap in nodes: $(ForwardDiff.get_value(gap_tot))")
+#       info("ncf: $(ForwardDiff.get_value(ncf))")
+#       cond = +lan_tot + gap_tot
+#       cond = +lan_tot - gap_tot # singular
+#       cond = -lan_tot + gap_tot
+#       cond = -lan_tot - gap_tot
+
+        for (i, j) in enumerate(slave_element_nodes)
+            n = n1[i]
+            t = Q'*n
+            R = [n t]
+            la_nt = R*la[:,j]
+            info("node $j, n=$(ForwardDiff.get_value(n)) lan = $(ForwardDiff.get_value(la_nt[1])) gap = $(ForwardDiff.get_value(gap_tot[i]))")
+
+#           if -lan_tot[i] + gap_tot[i] < 0
+            if -la_nt[1] + gap_tot[i] < 0
+            #if j in [31, 32, 33, 34, 35, 36]
+                info("set node $j active")
+                C[1,j] -= gap_tot[i]
+#               C[1,j] += la_nt[1] - max(0, la_nt[1] - gap_tot[i])
+                C[2,j] += la_nt[2]
+            else
+                info("set node $j inactive")
+                C[1,j] += la1[i][1]
+                C[2,j] += la1[i][2]
+            end
+        end
+
+        return vec([fc C])
+
+    end
+
+    # x doesn't mean deformed configuration here
+    x = [problem.assembly.u; problem.assembly.la]
+    ndofs = round(Int, length(x)/2)
+    A, allresults = ForwardDiff.jacobian(calculate_interface, x, ForwardDiff.AllResults)
+    b = -ForwardDiff.value(allresults)
+    #b = -calculate_interface(x)
+    #info("PE = $(ForwardDiff.value(allresults))")
+    A = sparse(A)
+    b = sparse(b)
+    SparseMatrix.droptol!(A, 1.0e-12)
+    SparseMatrix.droptol!(b, 1.0e-12)
+    #println(A)
+    K = A[1:ndofs,1:ndofs]
+    C1 = transpose(A[1:ndofs,ndofs+1:end])
+    C2 = A[ndofs+1:end,1:ndofs]
+    D = A[ndofs+1:end,ndofs+1:end]
+    f = b[1:ndofs]
+    g = b[ndofs+1:end]
+    add!(assembly.K, K)
+    add!(assembly.C1, C1)
+    add!(assembly.C2, C2)
+    add!(assembly.D, D)
+    add!(assembly.f, f)
+    add!(assembly.g, g)
+
+    return
+
+end
+
diff --git a/src/mortar_3d.jl b/src/mortar_3d.jl
new file mode 100644
index 0000000..b4194e4
--- /dev/null
+++ b/src/mortar_3d.jl
@@ -0,0 +1,643 @@
+# This file is a part of JuliaFEM.
+# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
+
+# Mortar projection calculation for 3d cases
+
+""" Construct auxiliary plane for surface. """
+function create_auxiliary_plane{E}(element::Element{E}, time::Real)
+    xi = get_reference_element_midpoint(E)
+    x0 = element("geometry", xi, time)
+    ntbasis = element("normal-tangential coordinates", xi, time)
+    return x0, ntbasis
+end
+
+
+"""
+Project point q onto a plane given by a point p and normal n.
+
+Parameters
+----------
+q::Array{Float64, 2}
+    point to project (row vector)
+x0::Array{Float64, 2}
+    origo of plane
+n::Array{Float64, 2}
+    normal vector of plane
+
+Returns
+-------
+y::Array{Float64, 2}
+    projected point
+
+Examples
+--------
+julia> p = [-0.5 -1.0 4.0]'
+julia> x0 = [0.0 0.075 0.675]'
+julia> n = [0.1485860 0.0784519 0.9857830]'
+julia> project_node_to_auxiliary_plane(p, x0, n)
+3-element Array{Float64,1}:
+  0.963455
+ -1.2447
+  0.925247
+
+Notes
+-----
+[1](http://stackoverflow.com/questions/8942950/how-do-i-find-the-orthogonal-projection-of-a-point-onto-a-plane)
+
+"""
+function project_point_to_auxiliary_plane(p::Vector, x0::Vector, Q::Matrix)
+    n = Q[:,1]
+    ph = p - dot(p-x0, n)*n
+    qproj = Q'*(ph-x0)
+    if !isapprox(qproj[1], 0.0; atol=1.0e-12)
+        info("project_point_to_auxiliary_plane(): point not projected correctly.")
+        info("p: $p")
+        info("x0: $x0")
+        info("Q: \n$Q")
+        info("qproj: $qproj")
+        error("Failed to project point to auxiliary plane.")
+    end
+    return qproj[2:3]
+end
+
+"""
+Find edge intersections of two planar arbitrary shape polygons.
+
+Parameters
+----------
+S::Array{Float64,2}
+M::Array{Float64,2}
+
+Matrices with size (2, n) where n is number of vertices of each polygon.
+
+Returns
+-------
+P::Array{Float64,2}
+    Intersection points of polygons
+n::Array{Float64,2}
+    Neighbour info matrix with size (ns, mn). This keeps information which
+    edges of polygons are intersecting. See further explanation in example
+    below.
+
+Examples
+--------
+Find intersection points of two triangles:
+
+julia> S = [0 0; 3 0; 0 3]'
+julia> M = [-1 1; 2 -1/2; 1 3/2]'
+julia> P, n = get_edge_intersections(S, M)
+julia> P
+2x4 Array{Float64,2}:
+ 1.0  1.75  0.0  0.0
+ 0.0  0.0   0.5  1.25
+julia> n
+3x3 Array{Int64,2}:
+ 1  1  0
+ 0  0  0
+ 1  0  1)
+
+So intersection points are: (1.00, 0.00), (1.75, 0.00), (0.00, 0.50), (0.00, 1.25).
+"Neighbour matrix" can be interpreted as following:
+
+    1 1 0 <--> First edge of S intersects edges 1 and 2 of M
+    0 0 0 <--> Second edge of S doesn't intersect at all
+    1 0 1 <--> Third edge of S intersects with edges 1 and 3 of M
+
+"""
+function get_edge_intersections(S::Matrix, M::Matrix)
+    ns = size(S, 2)
+    nm = size(M, 2)
+    P = zeros(2, 0)
+    n = zeros(Int64, ns, nm)
+    k = 0
+    for i=1:ns
+        for j=1:nm
+            b = M[:,j]-S[:,i]
+            A = [S[:,mod(i,ns)+1]-S[:,i]  -M[:,mod(j,nm)+1]+M[:,j]]
+            if rank(A) == 2
+                r = A\b
+                if (r[1]>=0) & (r[1]<=1) & (r[2]>=0) & (r[2]<=1)  # intersection found
+                    k += 1
+                    f = S[:,i]+r[1]*(S[:,mod(i,ns)+1] - S[:,i])
+                    f = f''
+                    P = hcat(P, f)
+                    n[i, j] = 1
+                end
+            end
+        end
+    end
+    return P, n
+end
+
+
+"""
+Find any points laying inside or border of triangle.
+
+Parameters
+----------
+Y::Array{Float64, 2}
+    Triangle coordinates in 2×3 matrix
+X::Array{Float64, 2}
+    List of points to test in 2×n matrix
+
+Returns
+-------
+P::Array{Float64, 2}
+    List of points in triangle in 2×m matrix, where m is number of points inside triangle
+
+Examples
+--------
+julia> S = [0.0 0.0; 3.0 0.0; 0.0 3.0]'  # triangle corner points
+julia> pts = [-1.0 1.0; 2.0 -0.5; 1.0 1.5; 0.5 1.5]'  # points to tests
+julia> points_in_triangle(S, pts)
+2x2 Array{Float64,2}:
+ 1.0  0.5
+ 1.5  1.5
+"""
+function get_points_inside_triangle(Y::Matrix, X::Matrix)
+    @assert size(Y, 2) == 3  # "Point in TRIANGLE..."
+    P = zeros(2, 0)
+    v0 = Y[:,2] - Y[:,1]
+    v1 = Y[:,3] - Y[:,1] # find interior points of X in Y
+    d00 = (v0'*v0)[1]
+    d01 = (v0'*v1)[1]
+    d11 = (v1'*v1)[1]  # using baricentric coordinates
+    id = 1/(d00*d11 - d01*d01)
+    for i=1:size(X, 2)
+        v2 = X[:,i] - Y[:,1]
+        d02 = (v0'*v2)[1]
+        d12 = (v1'*v2)[1]
+        u = (d11*d02-d01*d12)*id
+        v = (d00*d12-d01*d02)*id
+        if (u>=0) & (v>=0) & (u+v<=1)  # also include nodes on the boundary
+            P = hcat(P, X[:,i]'')
+        end
+    end
+    return P
+end
+
+"""
+Determine is point P inside or on boudary of polygon X.
+
+http://paulbourke.net/geometry/polygonmesh/#insidepoly
+"""
+function is_point_inside_convex_polygon(P, X)
+    x, y = P
+    for i=1:length(X)
+        x0, y0 = X[i]
+        x1, y1 = X[mod(i, length(X))+1]
+        if (y-y0)*(x1-x0) - (x-x0)*(y1-y0) < 0
+            return false
+        end
+    end
+    return true
+end
+
+function get_points_inside_convex_polygon(pts, X)
+    # TODO: Make more readable
+    X2 = [X[:,i] for i=1:size(X,2)]
+    c = filter(P->is_point_inside_convex_polygon(P, X2), [pts[:,i] for i=1:size(pts, 2)])
+    return length(c) == 0 ? zeros(2, 0) : hcat(c...)
+end
+
+""" Return unique objects with some given tolerance. This is used in next function
+    because traditional unique() command returns row vectors as non-unique if they
+    differs only a "little".
+"""
+function uniquetol(P, dim::Int; args...)
+    @assert dim == 2
+    items = Vector{Float64}[P[:,i] for i=1:size(P,dim)]
+    new_items = Vector{Float64}[]
+    for item in items
+        has_found = false
+        for new_item in new_items
+            if isapprox(item, new_item; args...)
+                has_found = true
+                break
+            end
+        end
+        if !has_found
+            push!(new_items, item)
+        end
+    end
+    return reshape([new_items...;], length(new_items[]), length(new_items))
+end
+
+
+"""
+Make polygon clipping of shapes S and M.
+
+Parameters
+----------
+S::Array{Float64, 2}
+M::Array{Float64, 2}
+    Shapes to clip. Needs to be triangles at the moment.
+
+Returns
+-------
+Array{Float64, 2}, Array{Float64, 2}
+- Polygon vertices in 2×n matrix, sorted in counter-clockwise order.
+- 3×3 "neighbouring" matrix, see example.
+
+Examples
+--------
+julia> S = [0 0; 3 0; 0 3]'
+julia> M = [-1 1; 2 -1/2; 2 2]'
+julia> P, n = clip_polygon(S, M)
+julia> P
+2x6 Array{Float64,2}:
+ 0.0  1.0  2.0  2.0  1.25  0.0
+ 0.5  0.0  0.0  1.0  1.75  1.33333,
+julia> n
+3x3 Array{Int64,2}:
+ 1  0  1 <- first edge of M ([-1 1; 2 -1/2]') intersects with edges 1 and 3 of S ([0 0; 3 0]' and [0 3; 0 0]')
+ 1  1  0 <- second edge of M ([2 -1/2; 2 2]') intersects with edges 1 and 2 of S
+ 0  1  1 <- third edge of M ([2 2; -1 1]') intersects with edgse 2 and 3 of S
+
+"""
+function clip_polygon(S::Matrix, M::Matrix)
+    P1, neighbours = get_edge_intersections(M, S)
+    #P2 = get_points_inside_triangle(M, S)
+    #P3 = get_points_inside_triangle(S, M)
+    P2 = get_points_inside_convex_polygon(M, S)
+    P3 = get_points_inside_convex_polygon(S, M)
+#   info("polygon clipping: P1 = $P1")
+#   info("polygon clipping: P2 = $P2")
+#   info("polygon clipping: P3 = $P3")
+#   info("hcat P = $P")
+    P = hcat(P1, P2, P3)
+    if length(P) == 0
+        return nothing, nothing
+    end
+    P = uniquetol(P, 2)
+    meanval = mean(P, 2)
+    tmp = P .- meanval
+    angles = atan2(tmp[2,:], tmp[1,:])
+    angles = reshape(angles, length(angles))
+    order = sortperm(angles)
+    return P[:, order], neighbours
+end
+
+
+"""
+Calculate polygon geometric center point
+
+Parameters
+----------
+P::Array{Float64, 2}
+    Polygon vertices in 2×n matrix
+
+Returns
+-------
+Array{Float63, 2}
+    Center point
+
+Examples
+--------
+julia> P
+2x6 Array{Float64,2}:
+ 0.0  1.0  2.0  2.0  1.25  0.0
+ 0.5  0.0  0.0  1.0  1.75  1.33333,
+julia> C = get_polygon_cp(P)
+2x1 Array{Float64,2}:
+ 1.039740
+ 0.804701
+
+"""
+function calculate_polygon_centerpoint(P::Matrix)
+    n = size(P, 2)
+    A = 0.0
+    for i=1:n
+        A += 1/2*(P[1,i]*P[2,mod(i,n)+1] - P[1,mod(i,n)+1]*P[2,i])
+    end
+    Cx = 0.0
+    Cy = 0.0
+    for i=1:n
+        inext = mod(i, n)+1
+        Cx += 1/(6*A)*(P[1,i] + P[1,inext])*(P[1,i]*P[2,inext] - P[1,inext]*P[2,i])
+        Cy += 1/(6*A)*(P[2,i] + P[2,inext])*(P[1,i]*P[2,inext] - P[1,inext]*P[2,i])
+    end
+    return Float64[Cx, Cy]
+end
+
+"""
+Project point from auxiliary plane to parametric surface given by (ξ₁, ξ₂)
+
+Parameters
+----------
+p::Array{Float64,1}
+    point in auxiliary plane, in (n,t1,t2) coordinate system
+x0::Array{Float64,1}
+    origo of auxiliary plane cs
+Q::Array{Float64,2}
+    basis of auxiliary plane cs
+x::Array{Float64,2}
+    surface node coords
+basis::Array{Float64,2}
+    surface basis functions
+dbasis::Array{Float64,2}
+    partial derivatives of surface basis functions
+
+Returns
+-------
+Array{Float64,2}
+    solution vector (d, ξ₁, ξ₂) where d is distance to surface
+
+Examples
+--------
+Define surface with node points, basis + dbasis
+
+julia> xquad = [
+...     -2.5 -2.0 1.0
+...      2.5 -2.0 0.7
+...      2.0  2.3 0.0
+...     -2.0  2.0 1.0]'
+julia> basis(xi) = [
+...     (1-xi[1])(1-xi[2])/4
+...     (1+xi[1])(1-xi[2])/4
+...     (1+xi[1])(1+xi[2])/4
+...     (1-xi[1])(1+xi[2])/4]
+julia> dbasis(xi) = [
+...     -(1-xi[2])/4    -(1-xi[1])/4
+...      (1-xi[2])/4    -(1+xi[1])/4
+...      (1+xi[2])/4     (1+xi[1])/4
+...     -(1+xi[2])/4     (1-xi[1])/4]
+
+We aim to find point p, which we first project to auxiliary plane defined as following
+julia> p = [-2.5 -2.0 1.0]'
+julia> x0 = [0.0 0.075 0.675]'
+julia> Q = [
+...     0.1485860   0.9888990   0.0000000
+...     0.0784519  -0.0117877   0.9968480
+...     0.9857830  -0.1481180  -0.0793325]
+
+Our projected point is therefore
+julia> n = Q[:,1] # first component is normal direction
+julia> ph = project_node_to_auxiliary_plane(p, x0, n)
+julia> ph = Q'(ph-x0)
+julia> ph
+3x1 Array{Float64,2}:
+  1.33264e-7
+ -2.49593
+ -2.09424
+
+Our point ph is now in auxiliary plane in n,t1,t2 coordinate system. Next we
+project it back to surface defined by xquad*basis
+
+julia> theta = project_point_from_plane_to_surface(ph, x0, Q, xquad, basis, dbasis)
+julia> theta
+3x1 Array{Float64,2}:
+ -0.213874
+ -0.999999
+ -1.0
+
+We see that our ξ₁ = ξ₂ = -1 so we found first point of xquad
+[-2.5 -2.0 1.0]' correctly.
+
+julia> xquad*basis(theta[2:3])
+3-element Array{Float64,1}:
+ -2.5
+ -2.0
+  1.0
+
+"""
+function project_point_from_plane_to_surface{E}(p::Vector, x0::Vector, Q::Matrix, element::Element{E}, time::Real; max_iterations::Int=10, iter_tol::Float64=1.0e-9)
+    basis(xi) = get_basis(E, xi)
+    dbasis(xi) = get_dbasis(E, xi)
+    x = element("geometry", time)
+    ph = Q*[0; p] + x0
+    theta = Float64[0.0, 0.0, 0.0]
+    n = Q[:,1]
+    for i=1:max_iterations
+        b = ph + theta[1]*n - basis(theta[2:3])*x
+        J = [n -dbasis(theta[2:3])*x]
+        dtheta = J \ -b
+        theta += dtheta
+        if norm(dtheta) < iter_tol
+            return theta
+        end
+    end
+    begin
+        info("projecting point from auxiliary plane back to surface didn't go very well.")
+        info("element type: $E")
+        info("element connectivity: $(get_connectivity(element))")
+        info("auxiliary plane: x0 = $x0, Q = $Q")
+        info("point coordinates on plane: $p")
+        info("element geometry: $x")
+        info("ph: $ph")
+        info("normal direction: $n")
+        info("parameter vector before giving up: $theta")
+    end
+    error("project_point_to_surface: did not converge in $max_iterations iterations!")
+end
+
+typealias MortarElements3D Union{Tri3, Quad4}
+
+function assemble!{E<:MortarElements3D}(assembly::Assembly, problem::Problem{Mortar},
+                                        slave_element::Element{E}, time::Real, ::Type{Val{:total}})
+    assemble!(assembly, problem, slave_element, time, Val{problem.properties.formulation})
+end
+
+function assemble!{E<:MortarElements3D}(assembly::Assembly, problem::Problem{Mortar},
+                                        slave_element::Element{E}, time::Real, ::Type{Val{:total}})
+    haskey(slave_element, "master elements") || return
+    field_dim = get_unknown_field_dimension(problem)
+    field_name = get_parent_field_name(problem)
+    slave_dofs = get_gdofs(slave_element, field_dim)
+
+    props = problem.properties
+    if props.formulation == :Standard && props.normal_condition == :Contact
+        error("for contact choose Dual formulation.""")
+    end
+
+    # create auxiliary plane and project slave nodes to it
+    # x0 = origo, Q = local basis
+    x0, Q = create_auxiliary_plane(slave_element, time)
+
+    # 1. project slave nodes to auxiliary plane
+    Sl = Vector{Float64}[]
+    for p in slave_element("geometry", time)
+        push!(Sl, project_point_to_auxiliary_plane(p, x0, Q))
+    end
+    S = hcat(Sl...)
+
+    for master_element in slave_element["master elements"]
+
+        # if distance between elements is "far enough" cannot expect contact
+        if (props.normal_condition == :Contact) || props.inequality_constraints
+            slave_midpoint = slave_element("geometry", [0.0, 0.0], time)
+            master_midpoint = master_element("geometry", [0.0, 0.0], time)
+            if norm(slave_midpoint - master_midpoint) > props.minimum_distance
+                continue
+            end
+        end
+
+        master_dofs = get_gdofs(master_element, field_dim)
+
+        # 2. project master nodes to auxiliary plane
+        M = Vector{Float64}[]
+        for p in master_element("geometry", time)
+            push!(M, project_point_to_auxiliary_plane(p, x0, Q))
+        end
+        M = hcat(M...)
+
+        # 3. create polygon clipping on auxiliary plane
+        P = nothing
+        neighbours = nothing
+        try
+            P, neighbours = clip_polygon(S, M)
+        catch
+            info("polygon clipping failed")
+            info("S = ")
+            dump(S)
+            info("M = ")
+            dump(M)
+            info("original Sl = ")
+            info(Sl)
+            error("cannot continue")
+        end
+        isa(P, Void) && continue # no clipping
+
+        # shared edge but no shared volume. skipping
+        size(P, 2) < 3 && continue
+
+        C = calculate_polygon_centerpoint(P)
+        npts = size(P, 2) # number of vertices in polygon
+
+        # loop vertices and create temporary integrate cells
+        # TODO: basically when npts == 3 or npts == 4 we could integrate without splitting to cells.
+        nnodes = size(slave_element, 2)
+        C1S3 = zeros(3*nnodes, 3*nnodes)
+        C1M3 = zeros(3*nnodes, 3*nnodes)
+
+        for pnt=1:npts # integration of mortar matrices begin
+            cell = Field(Vector{Float64}[C, P[:,pnt], P[:,mod(pnt,npts)+1]])
+
+            # calculate slave side projection matrix D
+            # construct dual basis
+            Ae = zeros(nnodes, nnodes)
+            De = zeros(nnodes, nnodes)
+            Me = zeros(nnodes, nnodes)
+            if problem.properties.formulation == :Dual # Construct dual basis
+                for ip in get_integration_points(Tri3, Val{5})
+                    N = get_basis(Tri3, ip.xi)
+                    xi = vec(N*cell)
+                    theta = project_point_from_plane_to_surface(xi, x0, Q, slave_element, time)
+                    xi_slave = theta[2:3]
+                    N1 = slave_element(xi_slave, time)
+                    # jacobian determinant on integration cell
+                    dNC = get_dbasis(Tri3, ip.xi)
+                    JC = sum([kron(dNC[:,j], cell[j]') for j=1:length(cell)])
+                    wC = ip.weight*det(JC)
+                    De += wC*diagm(vec(N1))
+                    Me += wC*N1'*N1
+                end
+                Ae = De*inv(Me)
+            end
+            for i=1:field_dim
+                C1S3[i:field_dim:end,i:field_dim:end] += De
+            end
+
+            # Calculate master side projection matrix M
+            for ip in get_integration_points(Tri3, Val{5})
+                # gauss point in auxiliary plane
+                #N = get_basis(E, ip.xi)
+                N = get_basis(Tri3, ip.xi)
+                xi = vec(N*cell)  # xi defined in auxilary plane
+
+                # find projection of gauss point to master and slave elements
+                theta1 = project_point_from_plane_to_surface(xi, x0, Q, slave_element, time)
+                theta2 = project_point_from_plane_to_surface(xi, x0, Q, master_element, time)
+                xi_slave = theta1[2:3]
+                xi_master = theta2[2:3]
+
+                # evaluate shape functions values in gauss point and add contribution to matrices
+                N1 = slave_element(xi_slave, time)
+                N2 = master_element(xi_master, time)
+
+                # jacobian determinant on integration cell
+                dNC = get_dbasis(Tri3, ip.xi)
+                JC = sum([kron(dNC[:,j], cell[j]') for j=1:length(cell)])
+                wC = ip.weight*det(JC)
+
+                # extend matrices according to the problem dimension (3)
+                @assert length(slave_dofs) == length(master_dofs)
+                Me = wC*Ae*N1'*N2
+                for k=1:field_dim
+                    C1M3[k:field_dim:end,k:field_dim:end] += Me
+                end
+            end
+        end  # integration of mortar matrices done.
+
+        # constraints in normal-tangential direction and initial weighted gap
+        X1 = vec(slave_element("geometry", time))
+        X2 = vec(master_element("geometry", time))
+        Q_ = slave_element("normal-tangential coordinates", time)
+        Z = zeros(3, 3)
+        if nnodes == 3
+            Q3 = [Q Z Z; Z Q Z; Z Z Q]
+        elseif nnodes == 4
+            Q3 = [Q Z Z Z; Z Q Z Z; Z Z Q Z; Z Z Z Q]
+        end
+        D3 = zeros(3*nnodes, 3*nnodes)
+        C2S3 = Q3'*C1S3
+        C2M3 = Q3'*C1M3
+        G = -(C2S3*X1 - C2M3*X2)
+
+        # complementarity condition
+        if haskey(slave_element, "displacement")
+            u1 = vec(slave_element("displacement", time))
+        else
+            u1 = zeros(3*nnodes)
+        end
+        if haskey(master_element, "displacement")
+            u2 = vec(master_element("displacement", time))
+        else
+            u2 = zeros(3*nnodes)
+        end
+        x1 = X1 + u1
+        x2 = X2 + u2
+        if  haskey(slave_element, "reaction force")
+            la = vec(slave_element("reaction force", time))
+        else
+            la = zeros(3*nnodes)
+        end
+        g = -(C2S3*x1 - C2M3*x2)
+        c = Q3'*la - g
+        inactive_nodes = find(c[1:field_dim:end] .<= 0)
+        active_nodes = find(c[1:field_dim:end] .> 0)
+
+        # normal constraint: remove inactive nodes if normal condition is set to contact
+        if problem.properties.normal_condition == :Contact
+            for j in inactive_nodes
+                dofs = [3*(j-1)+1, 3*(j-1)+2, 3*(j-1)+3]
+                G[dofs] = 0
+                C1S3[dofs,:] = 0
+                C1M3[dofs,:] = 0
+                C2S3[dofs,:] = 0
+                C2M3[dofs,:] = 0
+            end
+        end
+
+        # tangential constraint: stick or slip
+        if problem.properties.tangential_condition == :Slip
+            D3 = copy(C2S3)
+            D3[1:field_dim:end, :] = 0
+            C2S3[2:field_dim:end, :] = 0
+            C2M3[2:field_dim:end, :] = 0
+            C2S3[3:field_dim:end, :] = 0
+            C2M3[3:field_dim:end, :] = 0
+        end
+
+        # add contributions
+        add!(assembly.C1, slave_dofs, slave_dofs, C1S3)
+        add!(assembly.C1, slave_dofs, master_dofs, -C1M3)
+        add!(assembly.C2, slave_dofs, slave_dofs, C2S3)
+        add!(assembly.C2, slave_dofs, master_dofs, -C2M3)
+        add!(assembly.D, slave_dofs, slave_dofs, D3)
+        add!(assembly.c, slave_dofs, c)
+        add!(assembly.g, slave_dofs, G)
+    end
+end
+
+
diff --git a/src/mortar_forwarddiff_pe.jl b/src/mortar_forwarddiff_pe.jl
new file mode 100644
index 0000000..f0117a8
--- /dev/null
+++ b/src/mortar_forwarddiff_pe.jl
@@ -0,0 +1,446 @@
+using JuliaFEM.Core: MortarElements2D, DVTI, Assembly
+
+import JuliaFEM.Core: project_from_master_to_slave, project_from_slave_to_master, assemble!,
+get_unknown_field_dimension, get_parent_field_name, get_gdofs, find_elements, get_nodes, Field,
+get_integration_points, get_basis, get_dbasis, add!
+
+""" Find segment from slave element corresponding to master element nodes.
+x1_, n1_
+slave element geometry and normal direction
+
+x2_ master element nodes to project onto slave
+"""
+function project_from_master_to_slave{E<:MortarElements2D}(
+    slave_element::Element{E}, x1_::DVTI, n1_::DVTI, x2::Vector)
+
+    function x1(xi1)
+        N = get_basis(E, xi1)
+        return vec(N)*x1_
+    end
+
+    function dx1(xi1)
+        dN = get_dbasis(E, xi1)
+        return vec(dN)*x1_
+    end
+
+    function n1(xi1)
+        N = get_basis(E, xi1)
+        return vec(N)*n1_
+    end
+
+    function dn1(xi1)
+        dN = get_dbasis(E, xi1)
+        return vec(dN)*n1_
+    end
+
+    cross2(a, b) = cross([a; 0], [b; 0])[3]
+    R(xi1) = cross2(x1(xi1)-x2, n1(xi1))
+    dR(xi1) = cross2(dx1(xi1), n1(xi1)) + cross2(x1(xi1)-x2, dn1(xi1))
+    xi1 = 0.0
+    for i=1:5
+        dxi1 = -R(xi1)/dR(xi1)
+        xi1 += dxi1
+        if norm(dxi1) < 1.0e-10
+            return xi1
+        end
+    end
+
+    error("find projection from master to slave: did not converge")
+
+end
+
+function project_from_slave_to_master{E<:MortarElements2D}(
+    master_element::Element{E}, x1::Vector, n1::Vector, x2_::DVTI)
+
+    function x2(xi2)
+        N = get_basis(E, xi2)
+        return vec(N)*x2_
+    end
+
+    function dx2(xi2)
+        dN = get_dbasis(E, xi2)
+        return vec(dN)*x2_
+    end
+
+    cross2(a, b) = cross([a; 0], [b; 0])[3]
+    R(xi2) = cross2(x2(xi2)-x1, n1)
+    dR(xi2) = cross2(dx2(xi2), n1)
+    xi2 = 0.0
+    dxi2 = 0.0
+    for i=1:5
+        dxi2 = -R(xi2) / dR(xi2)
+        xi2 += dxi2
+        if norm(dxi2) < 1.0e-10
+            return xi2
+        end
+    end
+
+    error("find projection from slave to master: did not converge, last val: $xi2 and $dxi2")
+    
+end
+
+
+function assemble!{E<:MortarElements2D}(assembly::Assembly,
+    problem::Problem{Mortar}, slave_element::Element{E},
+    time::Real, ::Type{Val{:forwarddiff}})
+    haskey(slave_element, "master elements") || return
+    props = problem.properties
+    field_dim = get_unknown_field_dimension(problem)
+    field_name = get_parent_field_name(problem)
+
+    function calculate_interface(u::Matrix, la::Matrix)
+
+        X1 = slave_element("geometry", time)
+        slave_element_nodes = get_connectivity(slave_element)
+        u1 = Field(Vector[u[:,i] for i in slave_element_nodes])
+        la1 = Field(Vector[la[:,i] for i in slave_element_nodes])
+        x1 = X1 + u1
+
+        adjacent_elements = find_elements(get_elements(problem), slave_element_nodes)
+        adjacent_nodes = get_nodes(adjacent_elements) # including also nodes from adjacent elements
+        Q = [0.0 -1.0; 1.0 0.0]
+        # 1. update nodal normals for this element
+        normals = zeros(u)
+        for element in adjacent_elements
+            conn = get_connectivity(element)
+            gdofs = get_gdofs(element, field_dim)
+            X_el = element("geometry", time)
+            u_el = Field(Vector[u[:, i] for i in conn])
+            x_el = X_el + u_el
+            for ip in get_integration_points(element, Val{3})
+                dN = get_dbasis(element, ip)
+                N = element(ip, time)
+                t = sum([kron(dN[:,i], x_el[i]') for i=1:length(x_el)])
+                normals[:, conn] += ip.weight*Q*t'*N
+            end
+        end
+        # --> slave side normals in deformed state
+        n1 = Field(Vector[normals[:,i]/norm(normals[:,i]) for i in slave_element_nodes])
+
+        fc = SparseMatrixCOO{Real}([], [], []) # interface virtual work
+        C = SparseMatrixCOO{Real}([], [], []) # constraints
+        B = SparseMatrixCOO{Real}([], [], [])
+
+        #info("u1.data = ", ForwardDiff.get_value(u1.data))
+        info("normal calculations done. looping master elements.")
+        for master_element in slave_element["master elements"]
+            X2 = master_element("geometry", time)
+            master_element_nodes = get_connectivity(master_element)
+            u2 = Field(Vector[u[:,i] for i in master_element_nodes])
+            x2 = X2 + u2
+            info("master element ready.")
+
+            # calculate segmentation: we care only about endpoints
+            # note: these are quadratic/cubic functions, analytical solution possible
+            info("calculating segmentation.")
+            xi1a = project_from_master_to_slave(slave_element, x1, n1, x2[1])
+            xi1b = project_from_master_to_slave(slave_element, x1, n1, x2[end])
+            xi1 = clamp([xi1a; xi1b], -1.0, 1.0)
+            l = 1/2*abs(xi1[2]-xi1[1])
+            isapprox(l, 0.0) && continue # no contribution
+            info("xi1 = $xi1")
+
+            info("create bi-orthogonal basis")
+            nnodes = size(slave_element, 2)
+            De = zeros(nnodes, nnodes)
+            Me = zeros(nnodes, nnodes)
+            for ip in get_integration_points(slave_element, Val{5})
+                # jacobian of slave element in deformed state
+                dN = get_dbasis(slave_element, ip)
+                j = sum([kron(dN[:,i], x1[i]') for i=1:length(x1)])
+                w = ip.weight*norm(j)*l
+                xi_s = dot([1/2*(1-ip.xi); 1/2*(1+ip.xi)], xi1)
+                N1 = get_basis(slave_element, xi_s)
+                De += w*diagm(vec(N1))
+                Me += w*N1'*N1
+            end
+            Ae = De*inv(Me)
+            info("bi-orthogonal basis done. integrating fc.")
+
+            slave_dofs = get_gdofs(slave_element, field_dim)
+            master_dofs = get_gdofs(master_element, field_dim)
+
+            info("integrate fc")
+            D = zeros(nnodes, nnodes)
+            M = zeros(nnodes, nnodes)
+            gn = zeros(nnodes)
+            lan = zeros(nnodes)
+            lat = zeros(nnodes)
+
+            for ip in get_integration_points(slave_element, Val{5})
+                # jacobian of slave element in deformed state
+                dN = get_dbasis(slave_element, ip)
+                j = sum([kron(dN[:,i], x1[i]') for i=1:length(x1)])
+                w = ip.weight*norm(j)*l
+                xi_s = dot([1/2*(1-ip.xi); 1/2*(1+ip.xi)], xi1)
+                N1 = get_basis(slave_element, xi_s)
+                # project gauss point to master element to evaluate shape function there
+                x_s = vec(N1)*x1 # coordinate in gauss point
+                n_s = vec(N1)*n1 # normal direction in gauss point
+                xi_m = project_from_slave_to_master(master_element, x_s, n_s, x2)
+                N2 = get_basis(master_element, xi_m)
+                x_m = vec(N2)*x2
+                Phi = vec(Ae*N1')
+                la_s = Phi*la1 # traction force in gauss point
+                u_s = vec(N1)*u1
+                u_m = vec(N2)*u2
+                #info("la_s = $(ForwardDiff.get_value(la_s))")
+                SM = [slave_dofs; master_dofs]
+                #N1N2 = [N1 -N2]
+                #info("all_dofs = $(SM)")
+                #info("shape functions = $(ForwardDiff.get_value(N1N2))")
+                #for i=1:field_dim
+                #    #info("add to slave dofs $(slave_dofs[i:field_dim:end])")
+                #    #info("add to master dofs $(master_dofs[i:field_dim:end])")
+                #    add!(fc, slave_dofs[i:field_dim:end], [1, 1], -w*la_s[i]*N1)
+                #    add!(fc, master_dofs[i:field_dim:end], [1, 1], +w*la_s[i]*N2)
+                    #add!(fc, slave_dofs[i:field_dim:end], [1, 1], w*la_s'*u_s[i])
+                    #add!(fc, master_dofs[i:field_dim:end], [1, 1], -w*la_s'*u_m[i])
+                #    add!(fc, master_dofs[i:field_dim:end], [1, 1], -w*la_s[i]*u_m)
+                #end
+                #add!(fc, [slave_dofs; master_dofs], [1, 1, 1, 1, 1, 1, 1, 1], w*la_s*[u_s' -u_m'])
+                D += w*kron(Ae*N1', N1)
+                M += w*kron(Ae*N1', N2)
+                gn += -w*dot(n_s, x_s-x_m)*Phi
+                lan += w*dot(n_s, la_s)*Phi
+                t_s = Q'*n_s
+                lat += w*dot(t_s, la_s)*Phi
+            end
+
+            #D2 = zeros(2*nnodes, 2*nnodes)
+            #M2 = zeros(2*nnodes, 2*nnodes)
+            #for i=1:field_dim
+            #    D2[i:field_dim:end, i:field_dim:end] += D
+            #    M2[i:field_dim:end, i:field_dim:end] += M
+            #end
+            #info("size of D2 = $(size(D2))")
+            #fco = [D2 -M2]*vec(la1)
+            #fco = [D -M]*la[:,slave_element_nodes]
+            #info("fco = $(ForwardDiff.get_value(fco))")
+            #add!(fc, [slave_dofs; master_dofs], [1, 1, 1, 1], fco)
+
+            for i=1:field_dim
+                add!(B, slave_dofs[i:field_dim:end], slave_dofs[i:field_dim:end], D)
+                add!(B, slave_dofs[i:field_dim:end], master_dofs[i:field_dim:end], -M)
+            end
+            info("gn = $gn")
+            #Cj = lan - max(0, lan - gn) + lat
+            add!(C, slave_dofs[1:field_dim:end], [1, 1], gn')
+
+        end # master elements done
+
+        ndofs = prod(size(la))
+        N = SparseMatrixCOO{Real}([], [], [])
+        T = SparseMatrixCOO{Real}([], [], [])
+        for (i, j) in enumerate(slave_element_nodes)
+            dofs = [2*(j-1)+1, 2*(j-1)+2]
+            add!(N, [dofs[1]], dofs, reshape(n1[i], 1, 2))
+            add!(T, [dofs[2]], dofs, reshape(Q'*n1[i], 1, 2))
+        end
+        N = sparse(N, ndofs, ndofs)
+        T = sparse(T, ndofs, ndofs)
+        B = sparse(B, ndofs, ndofs)
+        fc = B'*vec(la)
+        #println(sparse(fc))
+        #fc = sparse(fc, ndofs, 1)
+        #println(fc)
+        #dump(full(fc))
+        #C = sparse(C, ndofs, 1)
+        C = N*B*vec(u) + T*vec(la)
+        return fc, C
+
+    end
+
+
+    function calculate_interface_PE(x::Vector)
+
+        ndofs = round(Int, length(x)/2)
+        nnodes = round(Int, ndofs/field_dim)
+        u = reshape(x[1:ndofs], field_dim, nnodes)
+        la = reshape(x[ndofs+1:end], field_dim, nnodes)
+        #fixed_la = ForwardDiff.get_value(la)
+        #fixed_u = ForwardDiff.get_value(u)
+        #u = ForwardDiff.get_value(u)
+
+        X1 = slave_element("geometry", time)
+        slave_element_nodes = get_connectivity(slave_element)
+        u1 = Field(Vector[u[:,i] for i in slave_element_nodes])
+        la1 = Field(Vector[la[:,i] for i in slave_element_nodes])
+        #fixed_la1 = Field(Vector[fixed_la[:,i] for i in slave_element_nodes])
+        x1 = X1 + u1
+
+        # 1. update nodal normals for this element
+        adjacent_elements = find_elements(get_elements(problem), slave_element_nodes)
+        adjacent_nodes = get_nodes(adjacent_elements) # including also nodes from adjacent elements
+        Q = [0.0 -1.0; 1.0 0.0]
+        normals = zeros(u)
+        for element in adjacent_elements
+            conn = get_connectivity(element)
+            gdofs = get_gdofs(element, field_dim)
+            X_el = element("geometry", time)
+            u_el = Field(Vector[u[:, i] for i in conn])
+            x_el = X_el + u_el
+            for ip in get_integration_points(element, Val{3})
+                dN = get_dbasis(element, ip)
+                N = element(ip, time)
+                t = sum([kron(dN[:,i], x_el[i]') for i=1:length(x_el)])
+                normals[:, conn] += ip.weight*Q*t'*N
+            end
+        end
+        # --> slave side normals in deformed state
+        n1 = Field(Vector[normals[:,i]/norm(normals[:,i]) for i in slave_element_nodes])
+
+        Wco = 0.0
+        Wla = 0.0
+
+        for master_element in slave_element["master elements"]
+            X2 = master_element("geometry", time)
+            master_element_nodes = get_connectivity(master_element)
+            u2 = Field(Vector[u[:,i] for i in master_element_nodes])
+            x2 = X2 + u2
+
+            # calculate segmentation: we care only about endpoints
+            # note: these are quadratic/cubic functions, analytical solution possible
+            xi1a = project_from_master_to_slave(slave_element, x1, n1, x2[1])
+            xi1b = project_from_master_to_slave(slave_element, x1, n1, x2[end])
+            xi1 = clamp([xi1a; xi1b], -1.0, 1.0)
+            l = 1/2*abs(xi1[2]-xi1[1])
+            isapprox(l, 0.0) && continue # no contribution
+
+            nnodes = size(slave_element, 2)
+            De = zeros(nnodes, nnodes)
+            Me = zeros(nnodes, nnodes)
+            for ip in get_integration_points(slave_element, Val{5})
+                # jacobian of slave element in deformed state
+                dN = get_dbasis(slave_element, ip)
+                j = sum([kron(dN[:,i], x1[i]') for i=1:length(x1)])
+                w = ip.weight*norm(j)*l
+                xi_s = dot([1/2*(1-ip.xi); 1/2*(1+ip.xi)], xi1)
+                N1 = get_basis(slave_element, xi_s)
+                De += w*diagm(vec(N1))
+                Me += w*N1'*N1
+            end
+            Ae = De*inv(Me)
+
+            for ip in get_integration_points(slave_element, Val{5})
+                # jacobian of slave element in deformed state
+                dN = get_dbasis(slave_element, ip)
+                j = sum([kron(dN[:,i], x1[i]') for i=1:length(x1)])
+                w = ip.weight*norm(j)*l
+                xi_s = dot([1/2*(1-ip.xi); 1/2*(1+ip.xi)], xi1)
+                N1 = vec(get_basis(slave_element, xi_s))
+
+                # project gauss point to master element to evaluate shape function there
+                x_s = N1*x1 # coordinate in gauss point
+                n_s = N1*n1 # normal direction in gauss point
+                t_s = Q'*n_s
+                xi_m = project_from_slave_to_master(master_element, x_s, n_s, x2)
+                N2 = vec(get_basis(master_element, xi_m))
+                x_m = N2*x2
+                Phi = Ae*N1
+
+                gn = -dot(n_s, x_s - x_m)
+                gt = dot(t_s, x_s - x_m)
+                lan = dot(n_s, Phi*la1)
+                lat = dot(t_s, Phi*la1)
+                u_s = N1*u1
+                u_m = N2*u2
+                gu = dot(n_s, u_s - u_m)
+
+                Wco += w*dot(Phi*la1, N1*u1 - N2*u2)
+                #Wla += w*(lan*gn + lat*gt)
+                #gn = min(0, gn)
+                Wla += 1/2*w*1e6*gn*gn
+                #info("gn = $(ForwardDiff.get_value(gn))")
+                #Wla += w*dot(dot(n_s, Phi*la1), dot(n_s, N1*u1 - N2*u2))
+            end
+
+        end
+        return Wco, Wla
+    end
+
+
+    function calculate_contact_rhs(x::Vector)
+        ndofs = round(Int, length(x)/2)
+        nnodes = round(Int, ndofs/field_dim)
+        u = reshape(x[1:ndofs], field_dim, nnodes)
+        la = reshape(x[ndofs+1:end], field_dim, nnodes)
+        fc, C = calculate_interface(u, la)
+        info("interface vector calculated.")
+        return vec(full([fc; C]))
+    end
+
+    # x doesn't mean deformed configuration here
+    x = [problem.assembly.u; problem.assembly.la]
+    ndofs = round(Int, length(x)/2)
+    if ndofs == 0
+        info("INITIALIZING THINGS")
+        problem.assembly.u = zeros(16)
+        problem.assembly.la = zeros(16)
+        x = [problem.assembly.u; problem.assembly.la]
+        ndofs = round(Int, length(x)/2)
+    end
+
+    function add_fco!()
+        get_PI(x::Vector) = calculate_interface_PE(x)[1]
+        A, allresults = ForwardDiff.hessian(get_PI, x, ForwardDiff.AllResults)
+        b = -ForwardDiff.gradient(allresults)
+        info("PE = $(ForwardDiff.value(allresults))")
+        A = sparse(A)
+        b = sparse(b)
+        SparseMatrix.droptol!(A, 1.0e-12)
+        SparseMatrix.droptol!(b, 1.0e-12)
+        K = A[1:ndofs,1:ndofs]
+        C1 = transpose(A[1:ndofs,ndofs+1:end])
+        C2 = A[ndofs+1:end,1:ndofs]
+        D = A[ndofs+1:end,ndofs+1:end]
+        f = b[1:ndofs]
+        g = b[ndofs+1:end]
+        add!(assembly.K, K)
+        add!(assembly.C1, C1)
+        add!(assembly.C2, C2)
+        add!(assembly.D, D)
+        add!(assembly.f, f)
+        add!(assembly.g, g)
+    end
+    #add_fco!()
+
+    function add_wla!()
+        get_PI(x::Vector) = calculate_interface_PE(x)[2]
+        A, allresults = ForwardDiff.hessian(get_PI, x, ForwardDiff.AllResults)
+        b = -ForwardDiff.gradient(allresults)
+        info("PE = $(ForwardDiff.value(allresults))")
+        A = sparse(A)
+        b = sparse(b)
+        SparseMatrix.droptol!(A, 1.0e-12)
+        SparseMatrix.droptol!(b, 1.0e-12)
+        #info("A")
+        #println(full(A))
+        K = A[1:ndofs,1:ndofs]
+        C1 = transpose(A[1:ndofs,ndofs+1:end])
+        C2 = A[ndofs+1:end,1:ndofs]
+        D = A[ndofs+1:end,ndofs+1:end]
+        f = b[1:ndofs]
+        g = b[ndofs+1:end]
+
+        add!(assembly.K, K)
+        add!(assembly.C1, C1)
+        add!(assembly.C2, C2)
+        add!(assembly.D, D)
+        add!(assembly.f, f)
+        add!(assembly.g, g)
+    end
+    add_wla!()
+
+    return
+
+end
+
+mesh, body1, body2, bc_top, bc_bottom, contact = divided_block_problem()
+bc_top.properties.formulation = :incremental
+bc_bottom.properties.formulation = :incremental
+contact.properties.formulation = :forwarddiff
+contact.assembly.u = zeros(16)
+contact.assembly.la = zeros(16)
+assemble!(contact.assembly, contact, contact.elements[1], 0.0, Val{:forwarddiff})
+
diff --git a/src/problems.jl b/src/problems.jl
index 2cd5371..3097436 100644
--- a/src/problems.jl
+++ b/src/problems.jl
@@ -166,16 +166,22 @@ function update_assembly!(problem, u, la)
     # copy current solutions to previous ones and add/replace new solution
     assembly.u_prev = copy(assembly.u)
     assembly.la_prev = copy(assembly.la)
-    if get_formulation_type(problem) == :incremental
-        info("$(problem.name): incremental formulation, adding increment to solution vector")
-        #info("solution vector:")
-        #dump(round(u, 3)')
-        assembly.u += u
-    else
+    if get_formulation_type(problem) == :total
         info("$(problem.name): total formulation, replacing solution vector with new values")
         assembly.u = u
+        assembly.la = la
+    elseif get_formulation_type(problem) == :incremental
+        info("$(problem.name): incremental formulation, adding increment to solution vector")
+        assembly.u += u
+        assembly.la = la
+    elseif get_formulation_type(problem) == :forwarddiff
+        info("$(problem.name): forwarddiff formulation, adding increment to solution vector")
+        assembly.u += u
+        assembly.la += la
+    else
+        info("$(problem.name): unknown formulation type, don't know what to do with results")
+        error("serious failure with problem formulation: $(get_formulation_type(problem))")
     end
-    assembly.la = la
 
     # calculate change of norm
     assembly.u_norm_change = norm(assembly.u - assembly.u_prev)
diff --git a/src/solvers.jl b/src/solvers.jl
index 22aa4af..31a172a 100644
--- a/src/solvers.jl
+++ b/src/solvers.jl
@@ -141,9 +141,11 @@ type Solver
     name :: ASCIIString # some descriptive name for problem
     time :: Real        # current time
     iteration :: Int    # iteration counter
+    norms :: Vector{Tuple} # solution norms for convergence studies
     ndofs :: Int        # total dimension of global stiffness matrix, i.e., dim*nnodes
     problems :: Vector{Problem}
     is_linear_system :: Bool # setting this to true makes assumption of one step convergence
+    nonlinear_system_min_iterations :: Int64
     nonlinear_system_max_iterations :: Int64
     nonlinear_system_convergence_tolerance :: Float64
     nonlinear_system_error_if_no_convergence :: Bool
@@ -155,9 +157,11 @@ function Solver(name::ASCIIString="default solver", time::Real=0.0)
         name,
         time,
         0,     # iteration #
+        [],    # solution norms in (norm(u), norm(la)) tuples
         0,     # ndofs
         [],    # array of problems
         false, # is_linear_system
+        1,     # min nonlinear iterations
         10,    # max nonlinear iterations
         5.0e-5, # nonlinear iteration convergence tolerance
         true,  # throw error if no convergence
@@ -277,12 +281,14 @@ crosspoints.
 function get_boundary_assembly(solver::Solver)
     ndofs = solver.ndofs
     @assert ndofs != 0
+    Kc = spzeros(ndofs, ndofs)
     C1 = spzeros(ndofs, ndofs)
     C2 = spzeros(ndofs, ndofs)
     D = spzeros(ndofs, ndofs)
     g = spzeros(ndofs, 1)
     for problem in get_boundary_problems(solver)
         assembly = problem.assembly
+        Kc_ = sparse(assembly.K, ndofs, ndofs)
         C1_ = sparse(assembly.C1, ndofs, ndofs)
         C2_ = sparse(assembly.C2, ndofs, ndofs)
         D_ = sparse(assembly.D, ndofs, ndofs)
@@ -297,12 +303,13 @@ function get_boundary_assembly(solver::Solver)
             handle_overconstraint_error!(problem, overconstrained_nodes,
                 overconstrained_dofs, C1, C1_, C2, C2_, D, D_, g, g_)
         end
+        Kc += Kc_
         C1 += C1_
         C2 += C2_
         D += D_
         g += g_
     end
-    return C1, C2, D, g
+    return Kc, C1, C2, D, g
 end
 
 
@@ -316,10 +323,10 @@ function solve_linear_system(solver::Solver, ::Type{Val{:DirectLinearSolver}})
     K, f = get_field_assembly(solver)
 
     # assemble boundary problems
-    C1, C2, D, g = get_boundary_assembly(solver)
+    Kc, C1, C2, D, g = get_boundary_assembly(solver)
 
     # construct global system Ax=b and solve using lu factorization
-    A = [K C1'; C2 D]
+    A = [K+Kc C1'; C2 D]
     b = [f; g]
 
     nz = get_nonzero_rows(A)
@@ -379,6 +386,7 @@ end
 """ Main solver loop.
 """
 function call(solver::Solver)
+
     # 1. initialize each problem so that we can start nonlinear iterations
     for problem in solver.problems
         initialize!(problem, solver.time)
@@ -394,6 +402,7 @@ function call(solver::Solver)
 
         # 2.2 call solver for linearized system (default: direct lu factorization)
         u, la = solve_linear_system(solver, Val{solver.linear_system_solver})
+        push!(solver.norms, (norm(u), norm(la)))
 
         # 2.3 update solution back to elements
         for problem in solver.problems
@@ -404,7 +413,11 @@ function call(solver::Solver)
         # 2.4 check convergence
         if has_converged(solver)
             info("Converged in $(solver.iteration) iterations.")
-            return true
+            if solver.iteration < solver.nonlinear_system_min_iterations
+                info("Converged but continuing")
+            else
+                return true
+            end
         end
     end
 
diff --git a/src/sparse.jl b/src/sparse.jl
index ac9527f..37250d3 100644
--- a/src/sparse.jl
+++ b/src/sparse.jl
@@ -4,18 +4,22 @@
 # Sparse utils to make assembly of local and global matrices easier.
 # Unoptimized but should do all necessary stuff for at start.
 
-type SparseMatrixCOO
+type SparseMatrixCOO{T<:Real}
     I :: Vector{Int}
     J :: Vector{Int}
-    V :: Vector{Float64}
+    V :: Vector{T}
 end
 
 typealias SparseMatrixIJV SparseMatrixCOO
 
 function SparseMatrixCOO()
-    SparseMatrixCOO([], [], [])
+    SparseMatrixCOO{Float64}([], [], [])
 end
 
+#function SparseMatrixCOO{T}()
+#    SparseMatrixCOO{T}([], [], [])
+#end
+
 function Base.convert(::Type{SparseMatrixCOO}, A::SparseMatrixCSC)
     return SparseMatrixCOO(findnz(A)...)
 end
@@ -80,7 +84,7 @@ function Base.(:+)(A::SparseMatrixIJV, B::SparseMatrixIJV)
     return C
 end
 
-function Base.full(A::SparseMatrixIJV, args...)
+function Base.full(A::SparseMatrixCOO, args...)
     return full(sparse(A.I, A.J, A.V, args...))
 end
 
@@ -94,7 +98,7 @@ Example
 >>> S = [3, 4]
 >>> M = [6, 7, 8]
 >>> data = Float64[5 6 7; 8 9 10]
->>> A = SparseMatrixIJV()
+>>> A = SparseMatrixCOO()
 >>> add!(A, S, M, data)
 >>> full(A)
 4x8 Array{Float64,2}:
@@ -104,7 +108,7 @@ Example
  0.0  0.0  0.0  0.0  0.0  8.0  9.0  10.0
 
 """
-function add!(A::SparseMatrixIJV, dofs1::Vector{Int}, dofs2::Vector{Int}, data::Matrix{Float64})
+function add!(A::SparseMatrixCOO, dofs1::Vector{Int}, dofs2::Vector{Int}, data::Matrix)
     n, m = size(data)
     for j=1:m
         for i=1:n
@@ -112,11 +116,16 @@ function add!(A::SparseMatrixIJV, dofs1::Vector{Int}, dofs2::Vector{Int}, data::
             push!(A.J, dofs2[j])
         end
     end
-#   append!(A.I, repeat(dofs1, outer=[m]))
-#   append!(A.J, repeat(dofs2, inner=[n]))
     append!(A.V, vec(data))
 end
 
+""" Add sparse matrix of CSC to COO. """
+function add!(A::SparseMatrixCOO, B::SparseMatrixCSC)
+    I, J, V = findnz(B)
+    C = SparseMatrixCOO(I, J, V)
+    append!(A, C)
+end
+
 """ Add new data to COO Sparse vector. """
 function add!(A::SparseMatrixCOO, dofs::Vector{Int}, data::Array{Float64}, dim::Int=1)
     if length(dofs) != length(data)
diff --git a/src/xdmf.jl b/src/xdmf.jl
index b6db5f2..578b9c9 100644
--- a/src/xdmf.jl
+++ b/src/xdmf.jl
@@ -73,11 +73,11 @@ function xdmf_new_grid(temporal_collection; time=0)
     return grid
 end
 
-function xdmf_new_mesh!(grid, nodes, elements)
+function xdmf_new_mesh!(grid, nodes, elements; datatype="XYZ")
 
     # 1. write nodes
     geometry = new_child(grid, "Geometry")
-    set_attribute(geometry, "Type", "XYZ")
+    set_attribute(geometry, "Type", datatype)
     dataitem = new_child(geometry, "DataItem")
     set_attribute(dataitem, "DataType", "Float")
     ndim = sum([length(node) for node in nodes])