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Adding plastic material with linear elasticity

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This commit is contained in:
Olli Väinölä
2015-12-18 10:04:16 +02:00
parent 899638fe00
commit 8a47ee53cf
5 changed files with 112 additions and 18 deletions
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src/elasticity.jl
-1
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@@ -81,7 +81,6 @@ function get_residual_vector{P<:ElasticityProblem}(problem::Problem{P}, element:
# strain
E = 1/2*(F'*F - I)
# stress
S = lambda*trace(E)*I + 2*mu*E
src/elasticplastic.jl
+4 -12
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@@ -58,16 +58,14 @@ function get_residual_vector{P<:PlaneStressElasticPlasticProblem}(problem::Probl
F = I + gradu
E = 1/2*(F'*F - I)
#E = 1/2*(gradu + gradu') # finite strain (total)
# material
young = element("youngs modulus", ip, time)
poisson = element("poissons ratio", ip, time)
stress_y = element("yield stress", time).data
mu = young/(2*(1+poisson))
lambda = young*poisson/((1+poisson)*(1-2*poisson))
if P == PlaneStressElasticPlasticProblem
lambda = 2*lambda*mu/(lambda + 2*mu) # <- correction for 2d problems
end
dstrain = E - last_strain
de_v = [dstrain[1,1], dstrain[2,2], dstrain[1,2]]
material_model = element("material model", time)
s = last_stress
de = copy(ForwardDiff.get_value(dstrain))
@@ -90,14 +88,8 @@ function get_residual_vector{P<:PlaneStressElasticPlasticProblem}(problem::Probl
stress_y,
Val{:vonMises},
Val{problem_stress_type})
nd = [dep[1] dep[3];
dep[3] dep[2]]
# a = dstrain - nd
# b = C * a
info("%% ", dep)
dif = dstrain - nd
mm = [dif[1,1], dif[2,2], dif[1,2]]
s_v += C * mm
s_v += C * (de_v - dep)
info("--: ", ForwardDiff.get_value(s_v))
# stress
if P == PlaneStressElasticPlasticProblem
src/linear_elasticity.jl
+55
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@@ -45,6 +45,13 @@ function assemble!{E<:CG, P<:LinearElasticityProblem}(assembly::Assembly, proble
B[6, 3*(i-1)+1] = dN[3,i]
B[6, 3*(i-1)+3] = dN[1,i]
end
# L = b * B'
# D = 0.5 * (L' + L)
# F = ...
# E = 0.5 * (F'*F - I)
# de = E - E_last
# S = vonMisesStress(de, stress)
# K = B' * S * J * w
add!(assembly.stiffness_matrix, gdofs, gdofs, w*B'*C*B*det(J))
end
if haskey(element, "displacement load")
@@ -114,3 +121,51 @@ function assemble!{E<:CG, P<:PlaneStressLinearElasticityProblem}(assembly::Assem
end
end
###############################
# Plastic material #
###############################
include("vonmises.jl")
abstract PlaneStressLinearElasticPlasticProblem <: LinearElasticityProblem
function PlaneStressLinearElasticPlasticProblem(name="plane stress linear elasticity", dim::Int=2, elements=[])
return Problem{PlaneStressLinearElasticPlasticProblem}(name, dim, elements)
end
""" Elasticity equations, plane stress. """
function assemble!{E<:CG, P<:PlaneStressLinearElasticPlasticProblem}(assembly::Assembly, problem::Problem{P}, element::Element{E}, time::Real)
gdofs = get_gdofs(element, problem.dim)
ndim, nnodes = size(E)
B = zeros(3, 2*nnodes)
for ip in get_integration_points(element)
w = ip.weight
J = get_jacobian(element, ip, time)
N = element(ip, time)
if haskey(element, "youngs modulus") && haskey(element, "poissons ratio")
nu = element("poissons ratio", ip, time)
E_ = element("youngs modulus", ip, time)
C = E_/(1.0 - nu^2) .* [
1.0 nu 0.0
nu 1.0 0.0
0.0 0.0 (1.0-nu)/2.0]
dN = element(ip, time, Val{:grad})
fill!(B, 0.0)
for i=1:size(dN, 2)
B[1, 2*(i-1)+1] = dN[1,i]
B[2, 2*(i-1)+2] = dN[2,i]
B[3, 2*(i-1)+1] = dN[2,i]
B[3, 2*(i-1)+2] = dN[1,i]
end
add!(assembly.stiffness_matrix, gdofs, gdofs, w*B'*C*B*det(J))
end
if haskey(element, "displacement load")
b = element("displacement load", ip, time)
add!(assembly.force_vector, gdofs, w*N'*b*det(J))
end
if haskey(element, "displacement traction force")
T = element("displacement traction force", ip, time)
L = w*T*N*norm(J)
add!(assembly.force_vector, gdofs, vec(L))
end
end
end
src/vonmises.jl
+5 -3
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@@ -291,12 +291,14 @@ function calculate_stress(dstrain, stress, C, stress_y,
df = ForwardDiff.jacobian(f)
# Calculating root
results = find_root!(f, df, x)
stress_tot = stress + results[1:3]
dstress = results[1:3]
stress_tot = stress + dstress
plastic_multiplier = results[end]
vm_wrap(stress_) = vonMisesYieldPlaneStress(stress_, stress_y)
dfds = ForwardDiff.gradient(vm_wrap)
dep = plastic_multiplier * dfds(stress_tot)
dep = plastic_multiplier * dfds(vec(stress_tot))
info("II ", stress_tot)
return results[1:3], dep
info(vm_wrap(stress_tot))
return dstress, dep
end
end
test/test_linear_elasticity.jl
+48 -2
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@@ -10,7 +10,7 @@ using JuliaFEM.Core: Seg2, Quad4, Hex8, LinearElasticityProblem, get_connectivit
assemble, PlaneStressLinearElasticityProblem, DirichletProblem,
LinearSolver
using JuliaFEM.Preprocess: aster_parse_nodes
using JuliaFEM.Core: PlaneStressLinearElasticPlasticProblem
function test_plane_stress_linear_elasticity_with_surface_load()
nodes = Dict{Int64, Vector{Float64}}(
@@ -54,8 +54,54 @@ function test_plane_stress_linear_elasticity_with_surface_load()
# 2015-10-22-plane-stress/cplan_linear_traction_force.*
@test isapprox(u[:,3], [2.77777777777778E-03, -1.11111111111111E-02])
end
#test_plane_stress_linear_elasticity_with_surface_load()
function test_plane_stress_linear_elasticplastic_with_surface_load()
nodes = Dict{Int64, Vector{Float64}}(
1 => [0.0, 0.0],
2 => [1.0, 0.0],
3 => [1.0, 1.0],
4 => [0.0, 1.0])
function set_geometry!(element, nodes)
element["geometry"] = Vector{Float64}[nodes[i] for i in get_connectivity(element)]
end
element1 = Quad4([1, 2, 3, 4])
set_geometry!(element1, nodes)
element1["youngs modulus"] = 9000.0
element1["poissons ratio"] = 0.25
element2 = Seg2([3, 4])
set_geometry!(element2, nodes)
element2["displacement traction force"] = Vector{Float64}[[0.0, -100.0] for i=1:2]
# problem = PlaneStressLinearElasticityProblem()
problem = PlaneStressLinearElasticPlasticProblem()
push!(problem, element1)
push!(problem, element2)
free_dofs = Int64[3, 5, 6, 8]
ass = assemble(problem, 0.0)
f = full(ass.force_vector)
K = full(ass.stiffness_matrix)
# info("initial force vector")
# dump(reshape(f, 2, 4))
# info("initial stiffness matrix")
# dump(round(Int, K)[free_dofs, free_dofs])
u = zeros(2, 4)
u[free_dofs] = K[free_dofs, free_dofs] \ f[free_dofs]
info("result vector")
dump(u)
# verified using Code Aster.
# 2015-10-22-plane-stress/cplan_linear_traction_force.*
@test isapprox(u[:,3], [2.77777777777778E-03, -1.11111111111111E-02])
end
# test_plane_stress_linear_elasticplastic_with_surface_load()
function test_continuum_elasticity_with_surface_load()
nodes = JuliaFEM.Preprocess.aster_parse_nodes("""
@@ -141,7 +187,7 @@ function test_continuum_elasticity_with_surface_load()
# [1/36, 1/36, -1/9]
@test isapprox(u, [2.77777777777778E-02, 2.77777777777778E-02, -1.11111111111111E-01])
end
#test_continuum_elasticity_with_surface_load()
# test_continuum_elasticity_with_surface_load()
end