JuliaFEM.jl/test/test_von_mises_material.jl

# This file is a part of JuliaFEM.
# License is MIT: see https://github.com/JuliaFEM/JuliaFEM.jl/blob/master/LICENSE.md

#using PyPlot
#using JuliaFEM
#using JuliaFEM.MaterialModels: stiffnessTensor, calculate_stress, State
#using JuliaFEM.MaterialModels: stiffnessTensorPlaneStress
using Test

#=
function test_von_mises_3D_basic()

    steps = 1000
    strain_max = 0.003
    num_cycles = 3
    E = 200.0e3
    nu =  0.3
    ν = 0.3
    nu = 0.3
    C = E/((1.0+nu)*(1.0-2.0*nu)) * [
        1.0-nu nu nu 0.0 0.0 0.0
        nu 1.0-nu nu 0.0 0.0 0.0
        nu nu 1.0-nu 0.0 0.0 0.0
        0.0 0.0 0.0 0.5-nu 0.0 0.0
        0.0 0.0 0.0 0.0 0.5-nu 0.0
        0.0 0.0 0.0 0.0 0.0 0.5-nu]

    strain_tot = zeros(Float64, (steps, 6))
    strain_tot2 = zeros(Float64, (steps, 6))
    strain_tot3 = zeros(Float64, (steps, 6))

    # 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_tot[:, 4] = strain_max / 10 * sin(2 * pi * linspace(0, num_cycles, steps))

    strain_last = zeros(Float64, (6))
    strain_p = zeros(Float64, (6))
    stress = zeros(Float64, (6, 1))
    stress_y =  200.0
    ss = Float64[]
    ee = Float64[]

    eig_stress = zeros(Float64, (3, 3))
    eig_vals = zeros(Float64, (steps, 3))

    function fill_tensor(a, b)
        a[1, 1] = b[1]
        a[2, 2] = b[2]
        a[3, 3] = b[3]

        a[1, 2] = b[6]
        a[1, 3] = b[5]
        a[2, 3] = b[4]

        a[2, 1] = b[6]
        a[3, 1] = b[5]
        a[3, 2] = b[4]
    end

    @info("Starting calculation")
    tic()
    params = Dict("yield_stress" => stress_y)
    stress_new = zeros(Float64, 6)
    stress_last = zeros(Float64, 6)
    strain = zeros(Float64, 6)
    Dtan = zeros(6,6)
    #for i=1:steps
    #    strain_new = reshape(strain_tot[i, :, :], (6, 1))
    #    dstrain = strain_new - strain
    #    JuliaFEM.plastic_von_mises!(stress_new, stress_last, dstrain, C, params, Dtan, Val{:type_3d})
    #    strain[:] = vec(strain_new)[:]
    #    push!(ss, stress[1])
    #    push!(ee, strain[1])
    #    fill_tensor(eig_stress, stress_new)
    #    eig_vals[i, :] = sort(eigvals(eig_stress))
    #    stress_last[:] = stress_new[:]
    #end

    toc()
    # ================ Plotting =================== #
    n(θ, ϕ) = [sin(θ)*cos(ϕ)
               sin(θ)*sin(ϕ)
               cos(θ)]
    m(θ, ϕ, χ) = [-sin(ϕ)*cos(χ)-cos(θ)*cos(ϕ)*sin(χ)
                   cos(ϕ)*cos(χ)-cos(θ)*sin(ϕ)*sin(χ)
                   sin(θ)*sin(χ)]

    w = [sqrt(2/3) * 200 * m(54.735 * pi / 180, 45 * pi/180, x) for x=0:0.15:(2*pi+0.1)]
    base_vec =  [1 1 1] / sqrt(3)

    for i=-5:5
        tt = [w[x] + vec(base_vec) + 50 * i for x=1:length(w)]
        x = map(x->tt[x][1], collect(1:length(w)))
        y = map(x->tt[x][2], collect(1:length(w)))
        z = map(x->tt[x][3], collect(1:length(w)))
        plot3D(x, y, z, color="blue")
    end

    tt = [w[x] + vec(base_vec) + 50 * -5 for x=1:length(w)]
    x_start = map(x->tt[x][1], collect(1:length(w)))[1:5:end]
    y_start = map(x->tt[x][2], collect(1:length(w)))[1:5:end]
    z_start = map(x->tt[x][3], collect(1:length(w)))[1:5:end]


    tt = [w[x] + vec(base_vec) + 50 * 5 for x=1:length(w)]
    x_end = map(x->tt[x][1], collect(1:length(w)))[1:5:end]
    y_end = map(x->tt[x][2], collect(1:length(w)))[1:5:end]
    z_end = map(x->tt[x][3], collect(1:length(w)))[1:5:end]

    for i=1:length(x_start)
        x = [x_start[i], x_end[i]]
        y = [y_start[i], y_end[i]]
        z = [z_start[i], z_end[i]]
        plot3D(x, y, z, color="blue")
    end


    @info("Calculation finished")
    # plot3D(ee, ss)


    # plot the surface
    xx = zeros(10, 10)
    yy = zeros(10, 10)

    for i=1:10
        for j=1:10
            xx[i, j] = (i - 5) * 100
            yy[i, j] = (j - 5) * 100
        end
    end

    # calculate corresponding z
    z = zeros(10, 10)
    for i=1:10
        for j=1:10
            z[i, j] = 1
        end
    end

    # ==================================================================
    # plot the surface
    plot_surface(xx, yy, z, color="blue")

    stress_y =  200.0

    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) - stress_y
    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
    plot(x_vals, y_vals, zeros(length(y_vals)), color="yellow")
    axis("equal")
    # ==================================================================


    plot3D(eig_vals[:, 1], eig_vals[:, 2], eig_vals[:, 3], color="red")
    PyPlot.title("Stress path and von Mises yield surface")
    PyPlot.xlabel("Eig Stress 1")
    PyPlot.ylabel("Eig Stress 2")
    PyPlot.zlabel("Eig Stress 3")
    PyPlot.grid()
    PyPlot.show()

end

function test_von_mises_planestress_basic()

    steps = 1000
    strain_max = 0.004
    num_cycles = 1.
    E = 200000.
    nu = 0.3
    ν = 0.3
    C = E/((1+nu)*(1-2*nu)) .* [
        1-nu   nu 0
        nu   1-nu 0
        0    0    (1-2*nu)/2]

    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 =  400
    ss = Float64[]
    ee = Float64[]


    ss2 = Float64[]
    ee2 = Float64[]

    eig_stress = zeros(Float64, (3, 3))
    eig_vals = zeros(Float64, (steps, 3))

    @info("Starting calculation")
    tic()

    stress_new = zeros(Float64, 3)
    stress_last = zeros(Float64, 3)
    strain = zeros(Float64, 3)
    strain_last = zeros(Float64, 3)
    params = Dict("yield_stress" => stress_y)
    #Dtan = C
    Dtan = zeros(3,3)
    for i=1:steps
        println("last stress: ", round(stress_last, 2))
        strain_new = vec(strain_tot[i, :, :])
        dstrain = strain_new - strain
        println("analytical stress: ", round((C * strain_new)', 2))

        JuliaFEM.plastic_von_mises!(stress_new, stress_last, dstrain, C, params, Dtan, Val{:type_2d})
        strain[:] = vec(strain_new)[:]
        s1, s2, t12  = stress_new
        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)
        stress_last[:] = stress_new[:]
    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) - stress_y
    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

    plot(x_vals, y_vals)
    plot(ee, ss)
    show()
end

test_von_mises_3D_basic()

# test_von_mises_planestress_basic()

=#