test models and mortar stuff

src/core.jl

@@ -58,13 +58,11 @@ include("equations.jl")
 include("dirichlet.jl")
 include("heat.jl")
 include("elasticity.jl")
-include("linear_elasticity.jl")
 
 ### ASSEMBLY + SOLVE ###
 include("assembly.jl")
 include("solver_utils.jl")
 include("solvers.jl")
-include("directsolver.jl") # parallel sparse direct solver for non-linear problems
 
 ### MORTAR STUFF ###
 include("mortar.jl")  # mortar projection

src/mortar.jl

@@ -40,6 +40,10 @@ function get_unknown_field_name(::Type{Mortar})
     return "reaction force"
 end
 
+function get_formulation_type(problem::Problem{Mortar})
+    return :incremental
+end
+
 macro debug(msg)
     haskey(ENV, "DEBUG") || return
     return msg

src/mortar_2d.jl

@@ -1,12 +1,12 @@
 # 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 2d
+# Mortar projection calculation for 2d, in initial configuration X
 
 """ Find projection from slave nodes to master element, i.e. find xi2 from
 master element corresponding to the xi1.
 """
-function project_from_slave_to_master{S,M}(slave::Element{S}, master::Element{M}, xi1::Vector, time::Float64=0.0; max_iterations=5, tol=1.0e-9)
+function project_from_slave_to_master{S,M}(slave::Element{S}, master::Element{M}, xi1::Vector, time::Real; max_iterations=5, tol=1.0e-9)
 
     # slave side geometry and normal direction at xi1
     X1 = slave("geometry", xi1, time)
@@ -29,7 +29,7 @@ function project_from_slave_to_master{S,M}(slave::Element{S}, master::Element{M}
 
     # equation to solve
     R(xi2) = det([X2(xi2)-X1  N1]')
-    dR(xi2) = det([dX2(xi2) N1]')
+    dR(xi2) = det([dX2(xi2)  N1]')
 
     # solve using Newton iterations
     xi2 = 0.0
@@ -50,7 +50,7 @@ end
 
 """ Find projection from master surface to slave point, i.e. find xi1 from slave
 element corresponding to the xi2. """
-function project_from_master_to_slave{S,M}(slave::Element{S}, master::Element{M}, xi2::Vector, time::Float64=0.0; max_iterations=5, tol=1.0e-9)
+function project_from_master_to_slave{S,M}(slave::Element{S}, master::Element{M}, xi2::Vector, time::Real; max_iterations=5, tol=1.0e-9)
 
     # slave side geometry and normal direction at xi1
 
@@ -91,7 +91,120 @@ function project_from_master_to_slave{S,M}(slave::Element{S}, master::Element{M}
     for i=1:max_iterations
         dxi1 = -R(xi1) / dR(xi1)
         xi1 += dxi1
-        #info("dxi1 = $dxi1, xi1 = $xi1, norm(dxi1) = $(norm(dxi1))")
+        if norm(dxi1) < tol
+            return Float64[xi1]
+        end
+    end
+
+    println("slave element geometry")
+    dump(slave("geometry", time).data)
+    println("master element geometry")
+    dump(master("geometry", time).data)
+    error("find projection from master to slave: did not converge")
+end
+
+# for deformed state
+
+""" Find projection from slave nodes to master element, i.e. find xi2 from
+master element corresponding to the xi1.
+"""
+function project_from_slave_to_master{S,M}(slave::Element{S}, master::Element{M}, xi1::Vector, time::Real, ::Type{Val{:deformed}}; max_iterations=5, tol=1.0e-9)
+
+    # slave side geometry and normal direction at xi1
+    x1 = slave("geometry", xi1, time)
+    if haskey(slave, "displacement")
+        x1 += slave("displacement", xi1, time)
+    end
+    N1 = slave("normal-tangential coordinates", xi1, time)[:,1]
+
+    # master side geometry at xi2
+    master_basis(xi2) = get_basis(M, [xi2])
+    master_dbasis(xi2) = get_dbasis(M, [xi2])
+    master_geometry = master("geometry")(time)
+    if haskey(master, "displacement")
+        master_geometry += master("displacement")(time)
+    end
+
+    function x2(xi2)
+        N = master_basis(xi2)
+        return sum([N[i]*master_geometry[i] for i=1:length(N)])
+    end
+
+    function dx2(xi2)
+        dN = master_dbasis(xi2)
+        return sum([dN[i]*master_geometry[i] for i=1:length(dN)])
+    end
+
+    # equation to solve
+    R(xi2) = det([x2(xi2)-x1  N1]')
+    dR(xi2) = det([dx2(xi2)  N1]')
+
+    # solve using Newton iterations
+    xi2 = 0.0
+    for i=1:max_iterations
+        dxi2 = -R(xi2) / dR(xi2)
+        xi2 += dxi2
+        if norm(dxi2) < tol
+            return Float64[xi2]
+        end
+    end
+
+    println("slave element geometry")
+    dump(slave("geometry", time).data)
+    println("master element geometry")
+    dump(master("geometry", time).data)
+    error("find projection from slave to master: did not converge")
+end
+
+""" Find projection from master surface to slave point, i.e. find xi1 from slave
+element corresponding to the xi2. """
+function project_from_master_to_slave{S,M}(slave::Element{S}, master::Element{M}, xi2::Vector, time::Real, ::Type{Val{:deformed}}; max_iterations=5, tol=1.0e-9)
+
+    # slave side geometry and normal direction at xi1
+
+    slave_geometry = slave("geometry")(time)
+    if haskey(slave, "displacement")
+        slave_geometry += slave("displacement")(time)
+    end
+    slave_normals = slave("normal-tangential coordinates")(time)
+    slave_basis(xi) = get_basis(S, [xi])
+    slave_dbasis(xi) = get_dbasis(S, [xi])
+
+    function x1(xi1)
+        N = slave_basis(xi1)
+        return sum([N[i]*slave_geometry[i] for i=1:length(N)])
+    end
+
+    function dx1(xi1)
+        dN = slave_dbasis(xi1)
+        return sum([dN[i]*slave_geometry[i] for i=1:length(dN)])
+    end
+
+    function N1(xi1)
+        N = slave_basis(xi1)
+        return sum([N[i]*slave_normals[i] for i=1:length(N)])[:,1]
+    end
+
+    function dN1(xi1)
+        dN = slave_dbasis(xi1)
+        return sum([dN[i]*slave_normals[i] for i=1:length(dN)])[:,1]
+    end
+
+    # master side geometry at xi2
+    x2 = master("geometry", xi2, time)
+    if haskey(master, "displacement")
+        x2 += master("displacement", xi2, time)
+    end
+
+    # equation to solve
+    R(xi1) = det([x1(xi1)-x2  N1(xi1)]')
+    dR(xi1) = det([dx1(xi1) N1(xi1)]') + det([x1(xi1)-x2 dN1(xi1)]')
+
+    # go!
+    xi1 = 0.0
+    for i=1:max_iterations
+        dxi1 = -R(xi1) / dR(xi1)
+        xi1 += dxi1
         if norm(dxi1) < tol
             return Float64[xi1]
         end
@@ -110,6 +223,8 @@ end
 # quadratic not tested yet
 typealias MortarElements2D Union{Seg2}
 
+""" Assemble 2d mortar contribution. Mortar matrices are assembled at initial
+configuration X, so this works for tie contact and small sliding contact. """
 function assemble!{E<:MortarElements2D}(assembly::Assembly, problem::Problem{Mortar},
                                         slave_element::Element{E}, time::Real)
 
@@ -145,9 +260,7 @@ function assemble!{E<:MortarElements2D}(assembly::Assembly, problem::Problem{Mor
     la = Q2'*la
 
     G = zeros(2*nnodes)
-    u = zeros(2*nnodes)
-    c = zeros(2*nnodes)
-
+    g = zeros(2*nnodes)
     local_assembly = Assembly()
 
     for master_element in slave_element["master elements"]
@@ -169,8 +282,8 @@ function assemble!{E<:MortarElements2D}(assembly::Assembly, problem::Problem{Mor
         end
 
         master_dofs = get_gdofs(master_element, field_dim)
-        xi1a = project_from_master_to_slave(slave_element, master_element, [-1.0])
-        xi1b = project_from_master_to_slave(slave_element, master_element, [ 1.0])
+        xi1a = project_from_master_to_slave(slave_element, master_element, [-1.0], time)
+        xi1b = project_from_master_to_slave(slave_element, master_element, [ 1.0], time)
         xi1 = clamp([xi1a xi1b], -1.0, 1.0)
         l = 1/2*abs(xi1[2]-xi1[1])
         isapprox(l, 0.0) && continue # no contribution
@@ -215,7 +328,7 @@ function assemble!{E<:MortarElements2D}(assembly::Assembly, problem::Problem{Mor
             # integration point on slave side segment
             xi_slave = 1/2*(1-ip.xi)*xi1[1] + 1/2*(1+ip.xi)*xi1[2]
             # projected integration point to master side element
-            xi_master = project_from_slave_to_master(slave_element, master_element, xi_slave)
+            xi_master = project_from_slave_to_master(slave_element, master_element, xi_slave, time)
             N1 = slave_element(xi_slave, time)
             N2 = master_element(xi_master, time)
             M = w*kron(Ae*N1', N2)
@@ -224,14 +337,11 @@ function assemble!{E<:MortarElements2D}(assembly::Assembly, problem::Problem{Mor
             end
         end
 
-        # Calculate normal-tangential constraints
+        # Calculate normal-tangential constraints and weighted gap
         C2S2 = Q2'*C1S2
         C2M2 = Q2'*C1M2
-
-        # initial weighted gap (capital G for "undeformed")
         G += -(C2S2*X1 - C2M2*X2)
-        # change in weighted gap caused by deformation
-        u += -(C2S2*u1 - C2M2*u2)
+        g += -(C2S2*x1 - C2M2*x2)
 
         # Add contributions
         add!(local_assembly.C1, slave_dofs, slave_dofs, C1S2)
@@ -241,38 +351,37 @@ function assemble!{E<:MortarElements2D}(assembly::Assembly, problem::Problem{Mor
 
     end # all master elements are done
 
-    add!(local_assembly.g, slave_dofs, G)
-
     # if only equality constraints, i.e., mesh tying problem, we're done for this element.
     if !props.contact
         append!(assembly, local_assembly)
         return
     end
 
+    add!(local_assembly.g, slave_dofs, G)
+
+    lan = la[1:field_dim:end]
+    lat = la[2:field_dim:end]
+    gn = g[1:field_dim:end]
+    gt = g[2:field_dim:end]
+
+    # normal condition
+    cn = 1.0 # complemementarity parameter
+    Cn = lan - max(0, lan - cn*gn)
+    inactive_nodes = find(lan - cn*gn .<= 0)
+    active_nodes = find(lan - cn*gn .> 0)
+
+    # if all nodes inactive, nothing to contribute.
+    if length(active_nodes) == 0
+        return
+    end
+
+    # manipulate local assembly (remove rows from it based on active set)
+    # before adding it to global assembly
     C1 = sparse(local_assembly.C1)
     C2 = sparse(local_assembly.C2)
     D = spzeros(size(C2)...)
     g = sparse(local_assembly.g)
 
-    # complementarity condition
-    lan = la[1:field_dim:end]
-    lat = la[2:field_dim:end]
-    Gn = G[1:field_dim:end]
-    un = u[1:field_dim:end]
-    cn = lan - (Gn + un)
-    #Cn = lan - max(0, lan - (Gn+un))
-
-    # normal condition
-    inactive_nodes = find(cn .<= 0)
-    active_nodes = find(cn .> 0)
-    #inactive_nodes = find(Cn .>= 0)
-    #active_nodes = find(Cn .== 0)
-
-    # inactive element
-    if length(active_nodes) == 0
-        return
-    end
-
     node_ids = get_connectivity(slave_element)
 
     # normal constraint: remove inactive nodes
@@ -281,32 +390,19 @@ function assemble!{E<:MortarElements2D}(assembly::Assembly, problem::Problem{Mor
             j in props.always_in_contact && continue
         end
         gdofs = [2*(j-1)+1, 2*(j-1)+2]
+        # λⱼ = 0 ∀ j ∈ S
         C1[gdofs,:] = 0
         C2[gdofs,:] = 0
         D[gdofs,:] = 0
-        g[gdofs] = 0
+        g[gdofs,:] = 0
     end
 
-    # frictional contact, see Gitterle2010
-    mu = 0.3
-    ct = lat + c[2:field_dim:end]
-
-    C = max(mu*cn, abs(ct)).*lat - mu*max(0, cn).*ct
-    stick_nodes = find(abs(ct) - mu*cn .< 0)
-    slip_nodes = find(abs(ct) - mu*cn .>= 0)
-    stick_nodes = setdiff(stick_nodes, inactive_nodes)
-    slip_nodes = setdiff(slip_nodes, inactive_nodes)
-
     for (i, j) in enumerate(node_ids[active_nodes])
         gdofs = [2*(j-1)+1, 2*(j-1)+2]
         #D[gdofs[2],gdofs] = C2[gdofs[2],gdofs]
-        D[gdofs[2],gdofs] = Q[i][:,2]'
+        D[gdofs[2],gdofs] = Q[i][:,2]
         C2[gdofs[2],:] = 0
-        if props.friction
-            g[gdofs[2]] = C[i]
-        else
-            g[gdofs[2]] = 0.0
-        end
+        g[gdofs[2],:] = 0
     end
 
     local_assembly.C1 = C1
@@ -316,14 +412,85 @@ function assemble!{E<:MortarElements2D}(assembly::Assembly, problem::Problem{Mor
     append!(assembly, local_assembly)
 
     if props.store_debug_info
-        slave_element["G"] = G
         slave_element["g"] = g
         slave_element["c"] = c
         slave_element["C1"] = C1
         slave_element["C2"] = C2
-        slave_element["D"] = D2
+        slave_element["D"] = D
         slave_element["active nodes"] = active_nodes
     end
 
 end
 
+
+function calculate_gap_vector{E<:MortarElements2D}(
+    problem::Problem{Mortar}, slave_element::Element{E},
+    time::Real)
+
+    # slave element must have a set of master elements
+    haskey(slave_element, "master elements") || return
+    props = problem.properties
+
+    # get dimension and name of PARENT field
+    field_dim = problem.dimension
+    field_name = problem.parent_field_name
+
+    nnodes = size(slave_element, 2)
+    gap = zeros(2*nnodes)
+
+    for master_element in slave_element["master elements"]
+
+        xi1a = project_from_master_to_slave(slave_element, master_element, [-1.0], time, Val{:deformed})
+        xi1b = project_from_master_to_slave(slave_element, master_element, [ 1.0], time, Val{:deformed})
+        xi1 = clamp([xi1a xi1b], -1.0, 1.0)
+        l = 1/2*abs(xi1[2]-xi1[1])
+        isapprox(l, 0.0) && continue # no contribution
+
+        # Calculate biorthogonal basis
+        Ae = zeros(nnodes, nnodes)
+        De = zeros(nnodes, nnodes)
+        Me = zeros(nnodes, nnodes)
+        for ip in get_integration_points(slave_element, Val{5})
+            J = get_jacobian(slave_element, ip, time, Val{:deformed})
+            w = ip.weight*norm(J)*l
+            xi = 1/2*(1-ip.xi)*xi1[1] + 1/2*(1+ip.xi)*xi1[2]
+            N = slave_element(xi, time)
+            De += w*diagm(vec(N))
+            Me += w*N'*N
+        end
+        Ae = De*inv(Me)
+
+        # Calculate weighted gap
+        for ip in get_integration_points(slave_element, Val{5})
+            J = get_jacobian(slave_element, ip, time, Val{:deformed})
+            w = ip.weight*norm(J)*l
+            # integration point on slave side segment
+            xi_slave = 1/2*(1-ip.xi)*xi1[1] + 1/2*(1+ip.xi)*xi1[2]
+            # projected integration point to master side element
+            xi_master = project_from_slave_to_master(slave_element, master_element, xi_slave, time, Val{:deformed})
+            X1 = slave_element("geometry", xi_slave, time)
+            u1 = zeros(2*nnodes)
+            if haskey(slave_element, "displacement")
+                u1 = slave_element("displacement", xi_slave, time)
+            end
+            x1 = X1 + u1
+            X2 = master_element("geometry", xi_master, time)
+            u2 = zeros(2*nnodes)
+            if haskey(master_element, "displacement")
+                u2 = master_element("displacement", xi_master, time)
+            end
+            x2 = X2 + u2
+            Q = slave_element("normal-tangential coordinates", xi_slave, time)
+            g = -Q'*(x1-x2)
+            N1 = slave_element(xi_slave, time)
+            Phi = vec(Ae*N1')
+            gap[1:field_dim:end] += w*g[1]*Phi
+            gap[2:field_dim:end] += w*g[2]*Phi
+        end
+
+    end # all master elements are done
+
+    return gap
+
+end
+

src/problems.jl

@@ -169,12 +169,11 @@ function update_assembly!(problem, u, la)
     if get_formulation_type(problem) == :incremental
         info("incremental formulation, adding increment to solution vector")
         assembly.u += u
-        assembly.la += la
     else
         info("total formulation, replacing solution vector with new values")
         assembly.u = u
-        assembly.la = la
     end
+    assembly.la = la
 
     # calculate change of norm
     assembly.u_norm_change = norm(assembly.u - assembly.u_prev)