From fbb1eb5afde83bb1ad1c6350ccee178094582d57 Mon Sep 17 00:00:00 2001 From: olli vainola Date: Mon, 2 May 2016 21:20:11 +0300 Subject: [PATCH] Notebook - viscoplastic material --- ...2_viscoplastic_material_small_strain.ipynb | 286 ++++++++++++++++++ 1 file changed, 286 insertions(+) create mode 100644 notebooks/2016_5_2_viscoplastic_material_small_strain.ipynb diff --git a/notebooks/2016_5_2_viscoplastic_material_small_strain.ipynb b/notebooks/2016_5_2_viscoplastic_material_small_strain.ipynb new file mode 100644 index 0000000..1ff88f2 --- /dev/null +++ b/notebooks/2016_5_2_viscoplastic_material_small_strain.ipynb @@ -0,0 +1,286 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Viscoplastic material\n", + "\n", + "Small example, how to create a material model with viscoplastic properties. Formulation is done in context of small strains" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "using ForwardDiff\n", + "using PyPlot" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "6x6 Array{Float64,2}:\n", + " 2.04615e5 87692.3 87692.3 0.0 0.0 0.0 \n", + " 87692.3 2.04615e5 87692.3 0.0 0.0 0.0 \n", + " 87692.3 87692.3 2.04615e5 0.0 0.0 0.0 \n", + " 0.0 0.0 0.0 1.16923e5 0.0 0.0 \n", + " 0.0 0.0 0.0 0.0 1.16923e5 0.0 \n", + " 0.0 0.0 0.0 0.0 0.0 1.16923e5" + ] + }, + "execution_count": 2, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "\n", + "\"\"\"\n", + "Hooke isotropic stiffness tensor\n", + "\"\"\"\n", + "function hookeStiffnessTensor(E, ν)\n", + " a = 1 - ν\n", + " b = 1 - 2*ν\n", + " c = 1 + ν\n", + " multiplier = E / (b * c)\n", + " return Float64[a ν ν 0 0 0;\n", + " ν a ν 0 0 0;\n", + " ν ν a 0 0 0;\n", + " 0 0 0 b 0 0;\n", + " 0 0 0 0 b 0;\n", + " 0 0 0 0 0 b].*multiplier\n", + "end\n", + "\n", + "# Pick material values\n", + "E = 152.0e3\n", + "ν = 0.3\n", + "C = hookeStiffnessTensor(E, ν)" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "text/plain": [ + "calculate_stress (generic function with 1 method)" + ] + }, + "execution_count": 39, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "# Equations can be found from: http://mms2.ensmp.fr/msi_paris/transparents/Georges_Cailletaud/2013-GC-plas3D.pdf\n", + "\n", + "\"\"\"\n", + "J2 plasticity\n", + "\"\"\"\n", + "function J(σ)\n", + " e1 = (σ[1] - σ[2])^2\n", + " e2 = (σ[2] - σ[3])^2\n", + " e3 = (σ[3] - σ[1])^2\n", + " e4 = σ[4]^2 \n", + " e5 = σ[5]^2\n", + " e6 = σ[6]^2\n", + " return sqrt((e1 + e2 + e3 + 6 * (e4 + e5 + e6)) / 2.)\n", + "end\n", + "\n", + "\"\"\"\n", + "Yield function\n", + "\"\"\"\n", + "function f(σ, σ_y)\n", + " return J(σ) - σ_y\n", + "end\n", + "\n", + "\"\"\"\n", + "Viscoplastic potential\n", + "\n", + "Parameters\n", + "----------\n", + " f_val: float\n", + " Yield function value\n", + " n: float\n", + " Material constant\n", + " K: float\n", + " Material constant\n", + "\"\"\"\n", + "function viscoplastic_potential(f_val, n, K)\n", + " n_1 = n+1\n", + " return K / n_1 * ( f_val./ K) ^ n_1\n", + "end\n", + "\n", + "\"\"\"\n", + "Function for calculating stress\n", + "\"\"\"\n", + "function calculate_stress(σ_old, dϵ, C, dt, σ_y, n, K)\n", + " σ_new = σ_old + C * dϵ * dt\n", + " if f(σ_new, σ_y) > 0\n", + " \n", + " # Viscoplastic potential derivated via ForwardDiff\n", + " visco_wrap(x) = viscoplastic_potential(f(x, σ_y), n, K)\n", + " dϵ_vp = ForwardDiff.gradient(visco_wrap)\n", + " σ_new = σ_old + C * (dϵ - dϵ_vp(σ_new)) * dt\n", + " end\n", + " return σ_new\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 75, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "steps = 30\n", + "\n", + "ϵ_hist = zeros(6)\n", + "max_strain = 0.0001\n", + "ϵ_hist[1] = max_strain\n", + "ϵ_hist[2] = max_strain*-0.3\n", + "ϵ_hist[3] = max_strain*-0.3;" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Plotting with three different $dt$" + ] + }, + { + "cell_type": "code", + "execution_count": 78, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "ϵ_tot_1 = zeros(6)\n", + "ϵ_tot_2 = zeros(6)\n", + "ϵ_tot_3 = zeros(6)\n", + "\n", + "nσ_1 = zeros(6)\n", + "nσ_2 = zeros(6)\n", + "nσ_3 = zeros(6)\n", + "\n", + "dt_1 = 0.01\n", + "dt_2 = 0.1\n", + "dt_3 = 0.4\n", + "\n", + "σ_1 = []\n", + "σ_2 = []\n", + "σ_3 = []\n", + "\n", + "ϵ_1 = []\n", + "ϵ_2 = []\n", + "ϵ_3 = []\n", + "\n", + "σ_y = 150.0\n", + "nn = 0.92\n", + "K = 180.0e3\n", + "\n", + "for n=1:steps\n", + " dϵ_1 = ϵ_hist / dt_1\n", + " dϵ_2 = ϵ_hist / dt_2\n", + " dϵ_3 = ϵ_hist / dt_3\n", + " \n", + " nσ_1 = calculate_stress(nσ_1, dϵ_1, C, dt_1, σ_y, nn, K)\n", + " nσ_2 = calculate_stress(nσ_2, dϵ_2, C, dt_2, σ_y, nn, K)\n", + " nσ_3 = calculate_stress(nσ_3, dϵ_3, C, dt_3, σ_y, nn, K)\n", + " \n", + " ϵ_tot_1 += dϵ_1 * dt_1\n", + " ϵ_tot_2 += dϵ_2 * dt_2\n", + " ϵ_tot_3 += dϵ_3 * dt_3\n", + " \n", + " push!(σ_1, nσ_1[1])\n", + " push!(σ_2, nσ_2[1])\n", + " push!(σ_3, nσ_3[1])\n", + " \n", + " push!(ϵ_1, ϵ_tot_1[1])\n", + " push!(ϵ_2, ϵ_tot_2[1])\n", + " push!(ϵ_3, ϵ_tot_3[1])\n", + "end" + ] + }, + { + "cell_type": "code", + "execution_count": 82, + "metadata": { + "collapsed": false + }, + "outputs": [ + { + "data": { + "image/png": "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", + "text/plain": [ + "PyPlot.Figure(PyObject )" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/plain": [ + "PyObject " + ] + }, + "execution_count": 82, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "PyPlot.plot(ϵ_1, σ_1)\n", + "PyPlot.plot(ϵ_2, σ_2)\n", + "PyPlot.plot(ϵ_1, σ_3)\n", + "PyPlot.xlabel(\"Total strain\")\n", + "PyPlot.ylabel(\"Stress\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": true + }, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Julia 0.4.6-pre", + "language": "julia", + "name": "julia-0.4" + }, + "language_info": { + "file_extension": ".jl", + "mimetype": "application/julia", + "name": "julia", + "version": "0.4.6" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +}