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Von mises ideal plastic material, still couple of bugs

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This commit is contained in:
Olli Väinölä
2015-12-17 17:13:23 +02:00
parent 695a9134a9
commit 80f021e16b
5 changed files with 690 additions and 24 deletions
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test/test_directsolver_with_vonmises.jl
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# This file is a part of JuliaFEM.
# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
module DirectSolverVonMisesTests
using JuliaFEM.Test
using JuliaFEM.Core: Seg2, Quad4
using JuliaFEM.Core: PlaneStressElasticityProblem, DirichletProblem
using JuliaFEM.Core: PlaneStressElasticPlasticProblem
using JuliaFEM.Core: DirectSolver
function test_solver_multiple_dirichlet_bc()
N = Vector[[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [1.0, 1.0]]
e1 = Quad4([1, 2, 4, 3])
e1["geometry"] = Vector[N[1], N[2], N[4], N[3]]
e1["youngs modulus"] = 900.0
e1["poissons ratio"] = 0.25
e1["yield stress"] = 100.0
e1["material model"] = :vonMises
b1 = Seg2([3, 4])
b1["geometry"] = Vector[N[3], N[4]]
b1["displacement traction force"] = (
0.0 => Vector[[0.0, 0.0], [0.0, 0.0]],
1.0 => Vector[[0.0, -100.0], [0.0, -100.0]])
#problem = PlaneStressElasticityProblem()
problem = PlaneStressElasticPlasticProblem()
push!(problem, e1)
push!(problem, b1)
# boundary elements for dirichlet dx=0
dx = Seg2([1, 3])
dx["geometry"] = Vector[N[1], N[3]]
dx["displacement 1"] = 0.0
# boundary elements for dirichlet dy=0
dy = Seg2([1, 2])
dy["geometry"] = Vector[N[1], N[2]]
dy["displacement 2"] = 0.0
problem2 = DirichletProblem("displacement", 2)
push!(problem2, dx)
problem3 = DirichletProblem("displacement", 2)
push!(problem3, dy)
solver = DirectSolver()
#solver.dump_matrices = true
solver.name = "test_solver_multiple_dirichlet_bc"
push!(solver, problem)
push!(solver, problem2)
push!(solver, problem3)
# launch solver
#norm = solver(0.0)
norm = solver(1.0)
disp = e1("displacement", [1.0, 1.0], 1.0)
info("displacement at tip: $disp")
#@test isapprox(disp, [3.17431158889468E-02, -1.38591518927826E-01])
end
test_solver_multiple_dirichlet_bc()
#=
function test_direct_cholesky_with_non_homogeneous_dirichlet_conditions()
N = Vector[[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [1.0, 1.0]]
e1 = Quad4([1, 2, 4, 3])
e1["geometry"] = Vector[N[1], N[2], N[4], N[3]]
e1["youngs modulus"] = 900.0
e1["poissons ratio"] = 0.25
problem = PlaneStressElasticityProblem()
push!(problem, e1)
# left boundary: dx=-0.1, dy=0.1
bc1 = Seg2([1, 3])
bc1["geometry"] = Vector[N[1], N[3]]
bc1["displacement 1"] = -0.1
bc1["displacement 2"] = 0.1
# right boundary: dx=0.2, dy=-0.2
bc2 = Seg2([2, 4])
bc2["geometry"] = Vector[N[2], N[4]]
bc2["displacement 1"] = 0.2
bc2["displacement 2"] = -0.2
boundary = DirichletProblem("displacement", 2)
push!(boundary, bc1)
push!(boundary, bc2)
solver = DirectSolver("test_direct_cholesky_with_non_homogeneous_dirichlet_boundary_conditions")
push!(solver, problem)
push!(solver, boundary)
# launch solver
solver.method = :UMFPACK
solver.dump_matrices = true
solver.max_iterations = 1
iters, status = solver(0.0)
# FIXME: solver gives no convergence warning when all dofs are fixed.
n1disp = e1("displacement", [-1.0, -1.0], 0.0)
n2disp = e1("displacement", [ 1.0, -1.0], 0.0)
n3disp = e1("displacement", [-1.0, 1.0], 0.0)
n4disp = e1("displacement", [ 1.0, 1.0], 0.0)
udisp = [n1disp n2disp n3disp n4disp]
info("nodal disp = ", udisp)
@test isapprox(n1disp, [-0.1, 0.1])
@test isapprox(n3disp, [-0.1, 0.1])
@test isapprox(n2disp, [ 0.2, -0.2])
@test isapprox(n4disp, [ 0.2, -0.2])
@test status == true
end
#test_direct_cholesky_with_non_homogeneous_dirichlet_conditions()
function test_solver_no_convergence()
N = Vector[[0.0, 0.0], [1.0, 0.0], [0.0, 1.0], [1.0, 1.0]]
e1 = Quad4([1, 2, 4, 3])
e1["geometry"] = Vector[N[1], N[2], N[4], N[3]]
e1["youngs modulus"] = 900.0
e1["poissons ratio"] = 0.25
b1 = Seg2([3, 4])
b1["geometry"] = Vector[N[3], N[4]]
b1["displacement traction force"] = Vector[[100.0, 100.0], [100.0, 100.0]]
problem = PlaneStressElasticityProblem()
push!(problem, e1)
push!(problem, b1)
# boundary elements for dirichlet dx=0
dx = Seg2([1, 3])
dx["geometry"] = Vector[N[1], N[3]]
dx["displacement 1"] = 0.0
# boundary elements for dirichlet dy=0
dy = Seg2([1, 2])
dy["geometry"] = Vector[N[1], N[2]]
dy["displacement 2"] = 0.0
problem2 = DirichletProblem("displacement", 2)
push!(problem2, dx)
problem3 = DirichletProblem("displacement", 2)
push!(problem3, dy)
solver = DirectSolver()
solver.max_iterations = 1
push!(solver, problem)
push!(solver, problem2)
push!(solver, problem3)
# launch solver
iterations, status = solver(0.0)
@test status == false
end
function test_solver_multiple_bodies_multiple_dirichlet_bc()
N = Vector[
[0.0, 0.0], [1.0, 0.0],
[0.0, 1.0], [1.0, 1.0],
[0.0, 2.0], [1.0, 2.0]]
e1 = Quad4([1, 2, 4, 3])
e1["geometry"] = Vector[N[1], N[2], N[4], N[3]]
e2 = Quad4([3, 4, 6, 5])
e2["geometry"] = Vector[N[3], N[4], N[6], N[5]]
for el in [e1, e2]
el["youngs modulus"] = 900.0
el["poissons ratio"] = 0.25
end
b1 = Seg2([5, 6])
b1["geometry"] = Vector[N[5], N[6]]
b1["displacement traction force"] = Vector[[0.0, -100.0], [0.0, -100.0]]
body1 = PlaneStressElasticityProblem()
push!(body1, e1)
body2 = PlaneStressElasticityProblem()
push!(body2, e2)
push!(body2, b1)
# boundary elements for dirichlet dx=0
dx1 = Seg2([1, 3])
dx1["geometry"] = Vector[N[1], N[3]]
dx2 = Seg2([3, 5])
dx2["geometry"] = Vector[N[3], N[5]]
for dx in [dx1, dx2]
dx["displacement 1"] = 0.0
end
boundary1 = DirichletProblem("displacement", 2)
push!(boundary1, dx1)
push!(boundary1, dx2)
# boundary elements for dirichlet dy=0
dy1 = Seg2([1, 2])
dy1["geometry"] = Vector[N[1], N[2]]
dy1["displacement 2"] = 0.0
boundary2 = DirichletProblem("displacement", 2)
push!(boundary2, dy1)
solver = DirectSolver()
push!(solver, body1)
push!(solver, body2)
push!(solver, boundary1)
push!(solver, boundary2)
# launch solver
norm = solver(0.0)
disp = e2("displacement", [1.0, 1.0], 0.0)
info("displacement at tip: $disp")
# code aster verification, two_elements.comm
@test isapprox(disp, [3.17431158889468E-02, -2.77183037855653E-01])
end
#test_solver_multiple_bodies_multiple_dirichlet_bc()
=#
end
test/test_von_mises_material.jl
+114 -5
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@@ -1,9 +1,12 @@
module VonMisesTests
using PyPlot
using JuliaFEM.MaterialModels: stiffnessTensor, calculate_stress!, State
using JuliaFEM.Test
using JuliaFEM.MaterialModels: stiffnessTensor, calculate_stress, State
using JuliaFEM.MaterialModels: stiffnessTensorPlaneStress
function test_von_mises_basic()
function test_von_mises_3D_basic()
steps = 1000
strain_max = 0.003
@@ -51,7 +54,7 @@ function test_von_mises_basic()
info("Starting calculation")
tic()
#=
#=
for i=1:steps
strain_new = reshape(strain_tot[i, :, :], (6, 1))
dstrain = strain_new - mat.strain
@@ -76,7 +79,7 @@ function test_von_mises_basic()
fill_tensor(eig_stress, stress)
eig_vals[i, :] = sort(eigvals(eig_stress))
end
toc()
# ================ Plotting =================== #
n(θ, ϕ) = [sin(θ)*cos(ϕ)
@@ -127,6 +130,112 @@ function test_von_mises_basic()
PyPlot.show()
end
test_von_mises_basic()
function test_von_mises_planestress_basic()
steps = 1000
strain_max = 0.003
num_cycles = 5
E = 200.0e3
nu = 0.3
ν = 0.3
C = stiffnessTensorPlaneStress(E, ν)
strain_tot = zeros(Float64, (steps, 3))
# Adding only strain in x-axis and counting for the poisson effect
strain_tot[:, 1] = strain_max * sin(2 * pi * linspace(0, num_cycles, steps))
strain_tot[:, 2] = strain_max * sin(2 * pi * linspace(0, num_cycles, steps)).*-ν
strain_tot[:, 3] = strain_max * sin(2 * pi * linspace(0, num_cycles, steps)).*-ν
strain_last = zeros(Float64, (3))
strain_p = zeros(Float64, (3))
stress = zeros(Float64, (3, 1))
stress_y = 200.0
ss = Float64[]
ee = Float64[]
ss2 = Float64[]
ee2 = Float64[]
eig_stress = zeros(Float64, (3, 3))
eig_vals = zeros(Float64, (steps, 3))
#mat = State(C, stress_y, zeros(Float64, 6), zeros(Float64, 6))
info("Starting calculation")
tic()
#=
for i=1:steps
strain_new = reshape(strain_tot[i, :, :], (6, 1))
dstrain = strain_new - mat.strain
calculate_stress!(dstrain, mat, Val{:vonMises})
mat.strain += vec(dstrain)
push!(ss, mat.stress[1])
push!(ee, mat.strain[1])
fill_tensor(eig_stress, mat.stress)
eig_vals[i, :] = sort(eigvals(eig_stress))
end
=#
stress = zeros(Float64, 3)
strain = zeros(Float64, 3)
for i=1:steps
strain_new = reshape(strain_tot[i, :, :], (3, 1))
dstrain = strain_new - strain
stress_inc, lambda = calculate_stress(dstrain,
stress,
C,
stress_y,
Val{:vonMises},
Val{:PlaneStressElasticPlasticProblem})
stress += stress_inc
strain = vec(strain_new)
s1, s2, t12 = stress
se1 = (s1 + s2)/2 + sqrt(((s1 - s2)/2)^2 + t12^2)
se2 = (s1 + s2)/2 - sqrt(((s1 - s2)/2)^2 + t12^2)
push!(ss, se1)
push!(ee, se2)
end
toc()
function vm_upper(a, c)
vals = f(a[1], a[2], c)
vm(vals[1], vals[2], 200)
end
vm(a,b) = sqrt(a^2 - a*b + b^2) - 200
f(m,c) = [600*cos(c) 600*sin(c)].*m
x_vals = []
max_iter = 100
y_vals = []
for i=0:0.1:(2*pi+0.3)
wf(x) = f(x, i)
t = 0.01
step = 2
merkki = -1
s11, s22 = wf(t)
ii = 0
while (abs(vm(s11, s22)) > 1e-7) && ii < max_iter
val = vm(s11, s22)
if sign(val) != merkki
merkki *= -1
step *= -0.5
end
t += step
s11, s22 = wf(t)
ii += 1
end
push!(x_vals, s11)
push!(y_vals, s22)
end
PyPlot.plot(x_vals, y_vals)
PyPlot.plot(ee, ss)
PyPlot.grid()
PyPlot.show()
end
# test_von_mises_3D_basic()
test_von_mises_planestress_basic()
end