mirror of
https://github.com/JuliaFEM/JuliaFEM.jl.git
synced 2026-08-06 04:21:33 +00:00
Jukka Aho
295 lines
8.0 KiB
Julia
295 lines
8.0 KiB
Julia
# This file is a part of JuliaFEM.
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# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md
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#using PyPlot
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#using JuliaFEM
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#using JuliaFEM.Testing
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#using JuliaFEM.MaterialModels: stiffnessTensor, calculate_stress, State
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#using JuliaFEM.MaterialModels: stiffnessTensorPlaneStress
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#=
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function test_von_mises_3D_basic()
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steps = 1000
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strain_max = 0.003
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num_cycles = 3
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E = 200.0e3
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nu = 0.3
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ν = 0.3
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nu = 0.3
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C = E/((1.0+nu)*(1.0-2.0*nu)) * [
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1.0-nu nu nu 0.0 0.0 0.0
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nu 1.0-nu nu 0.0 0.0 0.0
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nu nu 1.0-nu 0.0 0.0 0.0
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0.0 0.0 0.0 0.5-nu 0.0 0.0
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0.0 0.0 0.0 0.0 0.5-nu 0.0
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0.0 0.0 0.0 0.0 0.0 0.5-nu]
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strain_tot = zeros(Float64, (steps, 6))
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strain_tot2 = zeros(Float64, (steps, 6))
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strain_tot3 = zeros(Float64, (steps, 6))
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# Adding only strain in x-axis and counting for the poisson effect
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strain_tot[:, 1] = strain_max * sin(2 * pi * linspace(0, num_cycles, steps))
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strain_tot[:, 2] = strain_max * sin(2 * pi * linspace(0, num_cycles, steps)).*-ν
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strain_tot[:, 3] = strain_max * sin(2 * pi * linspace(0, num_cycles, steps)).*-ν
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strain_tot[:, 4] = strain_max / 10 * sin(2 * pi * linspace(0, num_cycles, steps))
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strain_last = zeros(Float64, (6))
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strain_p = zeros(Float64, (6))
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stress = zeros(Float64, (6, 1))
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stress_y = 200.0
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ss = Float64[]
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ee = Float64[]
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eig_stress = zeros(Float64, (3, 3))
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eig_vals = zeros(Float64, (steps, 3))
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function fill_tensor(a, b)
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a[1, 1] = b[1]
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a[2, 2] = b[2]
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a[3, 3] = b[3]
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a[1, 2] = b[6]
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a[1, 3] = b[5]
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a[2, 3] = b[4]
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a[2, 1] = b[6]
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a[3, 1] = b[5]
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a[3, 2] = b[4]
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end
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info("Starting calculation")
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tic()
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params = Dict("yield_stress" => stress_y)
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stress_new = zeros(Float64, 6)
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stress_last = zeros(Float64, 6)
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strain = zeros(Float64, 6)
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Dtan = zeros(6,6)
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#for i=1:steps
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# strain_new = reshape(strain_tot[i, :, :], (6, 1))
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# dstrain = strain_new - strain
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# JuliaFEM.plastic_von_mises!(stress_new, stress_last, dstrain, C, params, Dtan, Val{:type_3d})
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# strain[:] = vec(strain_new)[:]
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# push!(ss, stress[1])
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# push!(ee, strain[1])
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# fill_tensor(eig_stress, stress_new)
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# eig_vals[i, :] = sort(eigvals(eig_stress))
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# stress_last[:] = stress_new[:]
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#end
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toc()
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# ================ Plotting =================== #
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n(θ, ϕ) = [sin(θ)*cos(ϕ)
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sin(θ)*sin(ϕ)
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cos(θ)]
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m(θ, ϕ, χ) = [-sin(ϕ)*cos(χ)-cos(θ)*cos(ϕ)*sin(χ)
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cos(ϕ)*cos(χ)-cos(θ)*sin(ϕ)*sin(χ)
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sin(θ)*sin(χ)]
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w = [sqrt(2/3) * 200 * m(54.735 * pi / 180, 45 * pi/180, x) for x=0:0.15:(2*pi+0.1)]
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base_vec = [1 1 1] / sqrt(3)
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for i=-5:5
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tt = [w[x] + vec(base_vec) + 50 * i for x=1:length(w)]
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x = map(x->tt[x][1], collect(1:length(w)))
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y = map(x->tt[x][2], collect(1:length(w)))
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z = map(x->tt[x][3], collect(1:length(w)))
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plot3D(x, y, z, color="blue")
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end
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tt = [w[x] + vec(base_vec) + 50 * -5 for x=1:length(w)]
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x_start = map(x->tt[x][1], collect(1:length(w)))[1:5:end]
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y_start = map(x->tt[x][2], collect(1:length(w)))[1:5:end]
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z_start = map(x->tt[x][3], collect(1:length(w)))[1:5:end]
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tt = [w[x] + vec(base_vec) + 50 * 5 for x=1:length(w)]
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x_end = map(x->tt[x][1], collect(1:length(w)))[1:5:end]
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y_end = map(x->tt[x][2], collect(1:length(w)))[1:5:end]
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z_end = map(x->tt[x][3], collect(1:length(w)))[1:5:end]
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for i=1:length(x_start)
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x = [x_start[i], x_end[i]]
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y = [y_start[i], y_end[i]]
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z = [z_start[i], z_end[i]]
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plot3D(x, y, z, color="blue")
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end
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info("Calculation finished")
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# plot3D(ee, ss)
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# plot the surface
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xx = zeros(10, 10)
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yy = zeros(10, 10)
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for i=1:10
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for j=1:10
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xx[i, j] = (i - 5) * 100
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yy[i, j] = (j - 5) * 100
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end
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end
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# calculate corresponding z
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z = zeros(10, 10)
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for i=1:10
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for j=1:10
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z[i, j] = 1
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end
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end
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# ==================================================================
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# plot the surface
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plot_surface(xx, yy, z, color="blue")
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stress_y = 200.0
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function vm_upper(a, c)
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vals = f(a[1], a[2], c)
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vm(vals[1], vals[2], 200)
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end
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vm(a,b) = sqrt(a^2 - a*b + b^2) - stress_y
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f(m,c) = [600*cos(c) 600*sin(c)].*m
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x_vals = []
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max_iter = 100
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y_vals = []
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for i=0:0.1:(2*pi+0.3)
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wf(x) = f(x, i)
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t = 0.01
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step = 2
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merkki = -1
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s11, s22 = wf(t)
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ii = 0
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while (abs(vm(s11, s22)) > 1e-7) && ii < max_iter
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val = vm(s11, s22)
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if sign(val) != merkki
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merkki *= -1
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step *= -0.5
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end
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t += step
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s11, s22 = wf(t)
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ii += 1
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end
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push!(x_vals, s11)
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push!(y_vals, s22)
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end
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plot(x_vals, y_vals, zeros(length(y_vals)), color="yellow")
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axis("equal")
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# ==================================================================
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plot3D(eig_vals[:, 1], eig_vals[:, 2], eig_vals[:, 3], color="red")
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PyPlot.title("Stress path and von Mises yield surface")
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PyPlot.xlabel("Eig Stress 1")
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PyPlot.ylabel("Eig Stress 2")
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PyPlot.zlabel("Eig Stress 3")
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PyPlot.grid()
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PyPlot.show()
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end
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function test_von_mises_planestress_basic()
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steps = 1000
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strain_max = 0.004
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num_cycles = 1.
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E = 200000.
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nu = 0.3
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ν = 0.3
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C = E/((1+nu)*(1-2*nu)) .* [
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1-nu nu 0
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nu 1-nu 0
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0 0 (1-2*nu)/2]
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strain_tot = zeros(Float64, (steps, 3))
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# Adding only strain in x-axis and counting for the poisson effect
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strain_tot[:, 1] = strain_max * sin(2 * pi * linspace(0, num_cycles, steps))
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strain_tot[:, 2] = strain_max * sin(2 * pi * linspace(0, num_cycles, steps)).*-ν
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strain_tot[:, 3] = strain_max * sin(2 * pi * linspace(0, num_cycles, steps)).*-ν
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strain_last = zeros(Float64, (3))
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strain_p = zeros(Float64, (3))
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stress = zeros(Float64, (3, 1))
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stress_y = 400
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ss = Float64[]
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ee = Float64[]
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ss2 = Float64[]
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ee2 = Float64[]
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eig_stress = zeros(Float64, (3, 3))
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eig_vals = zeros(Float64, (steps, 3))
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info("Starting calculation")
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tic()
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stress_new = zeros(Float64, 3)
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stress_last = zeros(Float64, 3)
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strain = zeros(Float64, 3)
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strain_last = zeros(Float64, 3)
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params = Dict("yield_stress" => stress_y)
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#Dtan = C
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Dtan = zeros(3,3)
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for i=1:steps
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println("last stress: ", round(stress_last, 2))
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strain_new = vec(strain_tot[i, :, :])
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dstrain = strain_new - strain
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println("analytical stress: ", round((C * strain_new)', 2))
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JuliaFEM.plastic_von_mises!(stress_new, stress_last, dstrain, C, params, Dtan, Val{:type_2d})
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strain[:] = vec(strain_new)[:]
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s1, s2, t12 = stress_new
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se1 = (s1 + s2)/2 + sqrt(((s1 - s2)/2)^2 + t12^2)
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se2 = (s1 + s2)/2 - sqrt(((s1 - s2)/2)^2 + t12^2)
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push!(ss, se1)
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push!(ee, se2)
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stress_last[:] = stress_new[:]
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end
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toc()
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function vm_upper(a, c)
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vals = f(a[1], a[2], c)
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vm(vals[1], vals[2], 200)
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end
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vm(a,b) = sqrt(a^2 - a*b + b^2) - stress_y
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f(m,c) = [600*cos(c) 600*sin(c)].*m
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x_vals = []
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max_iter = 100
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y_vals = []
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for i=0:0.1:(2*pi+0.3)
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wf(x) = f(x, i)
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t = 0.01
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step = 2
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merkki = -1
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s11, s22 = wf(t)
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ii = 0
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while (abs(vm(s11, s22)) > 1e-7) && ii < max_iter
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val = vm(s11, s22)
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if sign(val) != merkki
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merkki *= -1
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step *= -0.5
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end
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t += step
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s11, s22 = wf(t)
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ii += 1
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end
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push!(x_vals, s11)
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push!(y_vals, s22)
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end
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plot(x_vals, y_vals)
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plot(ee, ss)
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show()
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end
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test_von_mises_3D_basic()
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# test_von_mises_planestress_basic()
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=#
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