From 03f2794a85b5cf131782d2d2dc0a84dc7e919541 Mon Sep 17 00:00:00 2001 From: Jeremy Bleyer Date: Fri, 3 Apr 2020 23:10:15 +0200 Subject: [PATCH] Adds a few notebook demos --- README.md | 0 demos/finite_strain_elastoplasticity.ipynb | 228 + demos/logarithmic_strain_plasticity.py | 33 +- demos/non_linear_heat_equation.py | 61 +- demos/nonlinear_heat_transfer.ipynb | 191 +- demos/nonlinear_heat_transfer.py | 129 - demos/nonlinear_heat_transfer_3D.ipynb | 181 + demos/nonlinear_heat_transfer_3D.py | 113 + demos/small_strain_elastoplasticity.ipynb | 269 + demos/small_strain_vonMises_plasticity.py | 2 +- demos/supplementary_files/apa.csl | 1718 ++++ .../supplementary_files/fuel_rod_solution.png | Bin 0 -> 224411 bytes demos/supplementary_files/references.bib | 249 + .../references_template.tplx | 6 + materials/HeatTransfer.mfront | 0 .../IsotropicLinearHardeningPlasticity.mfront | 0 materials/LogarithmicStrainPlasticity.mfront | 0 materials/MultiphaseModel2D.mfront | 0 materials/MultiphaseModel3D.mfront | 0 materials/PhaseFieldDamage.mfront | 0 materials/PhaseFieldDisplacement.mfront | 6 +- materials/StationaryHeatTransfer.mfront | 6 +- materials/TensionCompressionSplit.mfront | 0 materials/src/Makefile.mfront | 6 +- materials/src/targets.lst | 76 +- materials/test.mfront | 0 meshes/rod3D.med | Bin 0 -> 168003 bytes meshes/rod3D.msh | 6984 +++++++++++++++++ meshes/thick_cylinder.xml | 0 meshes/thick_cylinder_facet_region.xml | 0 meshes/thick_cylinder_physical_region.xml | 0 mfront_wrapper/__init__.py | 0 mfront_wrapper/gradient_flux.py | 18 +- mfront_wrapper/nonlinear_material.py | 9 +- mfront_wrapper/nonlinear_problem.py | 8 +- mfront_wrapper/utils.py | 15 +- setup.py | 0 37 files changed, 10056 insertions(+), 252 deletions(-) mode change 100644 => 100755 README.md create mode 100644 demos/finite_strain_elastoplasticity.ipynb mode change 100644 => 100755 demos/logarithmic_strain_plasticity.py mode change 100644 => 100755 demos/nonlinear_heat_transfer.ipynb delete mode 100644 demos/nonlinear_heat_transfer.py create mode 100755 demos/nonlinear_heat_transfer_3D.ipynb create mode 100755 demos/nonlinear_heat_transfer_3D.py create mode 100644 demos/small_strain_elastoplasticity.ipynb mode change 100644 => 100755 demos/small_strain_vonMises_plasticity.py create mode 100644 demos/supplementary_files/apa.csl create mode 100755 demos/supplementary_files/fuel_rod_solution.png create mode 100755 demos/supplementary_files/references.bib create mode 100755 demos/supplementary_files/references_template.tplx mode change 100644 => 100755 materials/HeatTransfer.mfront mode change 100644 => 100755 materials/IsotropicLinearHardeningPlasticity.mfront mode change 100644 => 100755 materials/LogarithmicStrainPlasticity.mfront mode change 100644 => 100755 materials/MultiphaseModel2D.mfront mode change 100644 => 100755 materials/MultiphaseModel3D.mfront mode change 100644 => 100755 materials/PhaseFieldDamage.mfront mode change 100644 => 100755 materials/PhaseFieldDisplacement.mfront mode change 100644 => 100755 materials/StationaryHeatTransfer.mfront mode change 100644 => 100755 materials/TensionCompressionSplit.mfront mode change 100644 => 100755 materials/test.mfront create mode 100755 meshes/rod3D.med create mode 100755 meshes/rod3D.msh mode change 100644 => 100755 meshes/thick_cylinder.xml mode change 100644 => 100755 meshes/thick_cylinder_facet_region.xml mode change 100644 => 100755 meshes/thick_cylinder_physical_region.xml mode change 100644 => 100755 mfront_wrapper/__init__.py mode change 100644 => 100755 mfront_wrapper/gradient_flux.py mode change 100644 => 100755 mfront_wrapper/nonlinear_material.py mode change 100644 => 100755 mfront_wrapper/nonlinear_problem.py mode change 100644 => 100755 mfront_wrapper/utils.py mode change 100644 => 100755 setup.py diff --git a/README.md b/README.md old mode 100644 new mode 100755 diff --git a/demos/finite_strain_elastoplasticity.ipynb b/demos/finite_strain_elastoplasticity.ipynb new file mode 100644 index 0000000..4697290 --- /dev/null +++ b/demos/finite_strain_elastoplasticity.ipynb @@ -0,0 +1,228 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Finite-strain elastoplasticity within the logarithmic strain framework\n", + "\n", + "This demo is dedicated to the resolution of a finite-strain elastoplastic problem using the logarithmic strain framework proposed in (Miehe et al., 2002). \n", + "\n", + "## Logarithmic strains \n", + "\n", + "This framework expresses constitutive relations between the Hencky strain measure $\\boldsymbol{H} = \\dfrac{1}{2}\\log (\\boldsymbol{F}^T\\cdot\\boldsymbol{F})$ and its dual stress measure $\\boldsymbol{T}$. This approach makes it possible to extend classical small strain constitutive relations to a finite-strain setting. In particular, the total (Hencky) strain can be split **additively** into many contributions (elastic, plastic, thermal, swelling, etc.). Its trace is also linked with the volume change $J=\\exp(\\operatorname{tr}(\\boldsymbol{H}))$. As a result, the deformation gradient $\\boldsymbol{F}$ is used for expressing the Hencky strain $\\boldsymbol{H}$, a small-strain constitutive law is then written for the $(\\boldsymbol{H},\\boldsymbol{T})$-pair and the dual stress $\\boldsymbol{T}$ is then post-processed to an appropriate stress measure such as the Cauchy stress $\\boldsymbol{\\sigma}$ or Piola-Kirchhoff stresses.\n", + "\n", + "## MFront implementation\n", + "\n", + " TODO:\n", + "* Write the gallery example comments and refer to it?\n", + "\n", + "* or use standard brick with comments here ?\n", + " \n", + "\n", + "\n", + "## FEniCS implementation\n", + "\n", + "We define a box mesh representing half of a beam oriented along the $x$-direction. The beam will be fully clamped on its left side and symmetry conditions will be imposed on its right extremity. The loading consists of a uniform self-weight." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "from dolfin import *\n", + "import mfront_wrapper as mf\n", + "import numpy as np\n", + "import ufl\n", + "\n", + "length, width, height = 1., 0.04, 0.1\n", + "nx, ny, nz = 30, 5, 10\n", + "mesh = BoxMesh(Point(0, -width/2, -height/2.), Point(length, width/2, height/2.), nx, ny, nz)\n", + "\n", + "V = VectorFunctionSpace(mesh, \"CG\", 2)\n", + "u = Function(V, name=\"Displacement\")\n", + "\n", + "def left(x, on_boundary):\n", + " return near(x[0], 0) and on_boundary\n", + "def right(x, on_boundary):\n", + " return near(x[0], length) and on_boundary\n", + "\n", + "bc = [DirichletBC(V, Constant((0.,)*3), left),\n", + " DirichletBC(V.sub(0), Constant(0.), right)]\n", + "\n", + "selfweight = Expression((\"0\", \"0\", \"-t*qmax\"), t=0., qmax = 50e6, degree=0)\n", + "\n", + "file_results = XDMFFile(\"results/finite_strain_plasticity.xdmf\")\n", + "file_results.parameters[\"flush_output\"] = True\n", + "file_results.parameters[\"functions_share_mesh\"] = True" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `MFrontNonlinearMaterial` instance is loaded from the MFront `LogarithmicStrainPlasticity` behaviour. This behaviour is a finite-strain behaviour (`material.finite_strain=True`) which relies on a kinematic description using the total deformation gradient $\\boldsymbol{F}$. By default, a MFront behaviour always returns the Cauchy stress as the stress measure after integration. However, the stress variable dual to the deformation gradient is the first Piloa-Kirchhoff (PK1) stress. An internal option of the MGIS interface is therefore used in the finite-strain context to return the PK1 stress as the \"flux\" associated to the \"gradient\" $\\boldsymbol{F}$. Both quantities are non-symmetric tensors, aranged as a 9-dimensional vector in 3D following [MFront conventions on tensors](http://tfel.sourceforge.net/tensors.html)." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "StandardFiniteStrainBehaviour\n", + "F_CAUCHY\n", + "['DeformationGradient'] [9]\n", + "['FirstPiolaKirchhoffStress'] [9]\n" + ] + } + ], + "source": [ + "material = mf.MFrontNonlinearMaterial(\"../materials/src/libBehaviour.so\",\n", + " \"LogarithmicStrainPlasticity\")\n", + "print(material.behaviour.getBehaviourType())\n", + "print(material.behaviour.getKinematic())\n", + "print(material.get_gradient_names(), material.get_gradient_sizes())\n", + "print(material.get_flux_names(), material.get_flux_sizes())" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `MFrontNonlinearProblem` instance must therefore register the deformation gradient as `Identity(3)+grad(u)`. This again done automatically since `\"DeformationGradient\"` is a predefined gradient. The following message will be shown upon calling `solve`:\n", + "```\n", + "Automatic registration of 'DeformationGradient' as I + (grad(Displacement)).\n", + "```\n", + "The loading is then defined and, as for the [small-strain elastoplasticity example](small_strain_elastoplasticity.ipynb), state variables include the `ElasticStrain` and `EquivalentPlasticStrain` since the same behaviour is used as in the small-strain case with the only difference that the total strain is now given by the Hencky strain measure. In particular, the `ElasticStrain` is still a symmetric tensor (vector of dimension 6). Note that it has not been explicitly defined as a state variable in the MFront behaviour file since this is done automatically when using the `IsotropicPlasticMisesFlow` parser.\n", + "\n", + "Finally, we setup a few parameters of the Newton non-linear solver." + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "(6,)\n" + ] + } + ], + "source": [ + "problem = mf.MFrontNonlinearProblem(u, material, bcs=bc)\n", + "problem.set_loading(dot(selfweight, u)*dx)\n", + "\n", + "p = problem.get_state_variable(\"EquivalentPlasticStrain\")\n", + "epsel = problem.get_state_variable(\"ElasticStrain\")\n", + "print(ufl.shape(epsel))\n", + "\n", + "prm = problem.solver.parameters\n", + "prm[\"absolute_tolerance\"] = 1e-6\n", + "prm[\"relative_tolerance\"] = 1e-6\n", + "prm[\"linear_solver\"] = \"mumps\"" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "During the load incrementation, we monitor the evolution of the vertical downwards displacement at the middle of the right extremity.\n", + "\n", + "This simulation is a bit heavy to run so we suggest running it in parallel:\n", + "```bash\n", + "mpirun -np 16 python3\n", + "```" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Increment 1\n", + "Automatic registration of 'DeformationGradient' as I + (grad(Displacement)).\n", + "\n", + "Automatic registration of 'Temperature' as a Constant value = 293.15.\n", + "\n", + "Increment 2\n", + "Increment 3\n", + "Increment 4\n" + ] + } + ], + "source": [ + "P0 = FunctionSpace(mesh, \"DG\", 0)\n", + "p_avg = Function(P0, name=\"Plastic strain\")\n", + "\n", + "Nincr = 30\n", + "load_steps = np.linspace(0., 1., Nincr+1)\n", + "results = np.zeros((Nincr+1, 3))\n", + "for (i, t) in enumerate(load_steps[1:]):\n", + " selfweight.t = t\n", + " print(\"Increment \", i+1)\n", + " problem.solve(u.vector())\n", + "\n", + " results[i+1, 0] = -u(length, 0, 0)[2]\n", + " results[i+1, 1] = t\n", + "\n", + " file_results.write(u, t)\n", + " p_avg.assign(project(p, P0))\n", + " file_results.write(p_avg, t)\n", + "\n", + "plt.figure()\n", + "plt.plot(results[:, 0], results[:, 1], \"-o\")\n", + "plt.xlabel(r\"Displacement\")\n", + "plt.ylabel(\"Load\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The load-displacement curve exhibits a classical elastoplastic behaviour rapidly followed by a stiffening behaviour due to membrane catenary effects. " + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.9" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/demos/logarithmic_strain_plasticity.py b/demos/logarithmic_strain_plasticity.py old mode 100644 new mode 100755 index 988438b..c0be87c --- a/demos/logarithmic_strain_plasticity.py +++ b/demos/logarithmic_strain_plasticity.py @@ -18,29 +18,19 @@ def right(x, on_boundary): bc = [DirichletBC(V, Constant((0.,)*3), left), DirichletBC(V.sub(0), Constant(0.), right)] -facets = MeshFunction("size_t", mesh, 2) -AutoSubDomain(right).mark(facets, 1) -ds = Measure("ds", subdomain_data=facets) -# Building function with vx=1 on left boundary to compute reaction -v = Function(V) -bcv = DirichletBC(V.sub(0), Constant(1.), left) -bcv.apply(v.vector()) - -Vpost = FunctionSpace(mesh, "CG", 1) -file_results = XDMFFile("results/beam_GL_plasticity.xdmf") +file_results = XDMFFile("results/finie_strain_plasticity.xdmf") file_results.parameters["flush_output"] = True file_results.parameters["functions_share_mesh"] = True - selfweight = Expression(("0", "0", "-t*qmax"), t=0., qmax = 50e6, degree=0) + material = mf.MFrontNonlinearMaterial("../materials/src/libBehaviour.so", "LogarithmicStrainPlasticity") problem = mf.MFrontNonlinearProblem(u, material, bcs=bc) problem.set_loading(dot(selfweight, u)*dx) p = problem.get_state_variable("EquivalentPlasticStrain") -assert (ufl.shape(p) == ()) epsel = problem.get_state_variable("ElasticStrain") print(ufl.shape(epsel)) @@ -51,29 +41,24 @@ prm["linear_solver"] = "mumps" P0 = FunctionSpace(mesh, "DG", 0) p_avg = Function(P0, name="Plastic strain") -Nitermax, tol = 20, 1e-4 # parameters of the Newton-Raphson procedure + Nincr = 30 load_steps = np.linspace(0., 1., Nincr+1) -file_results.write(u, 0) -file_results.write(p_avg, 0) results = np.zeros((Nincr+1, 3)) for (i, t) in enumerate(load_steps[1:]): selfweight.t = t - problem.solve(u.vector()) - results[i+1, 0] = assemble(-u[2]*ds(1))/(width*height) + # problem.solve(u.vector()) + + results[i+1, 0] = u(length, 0, 0) results[i+1, 1] = t - results[i+1, 2] = assemble(action(-problem.L, v)) file_results.write(u, t) -# file_results.write(p_avg, t) + p_avg.assign(project(p, V0)) + file_results.write(p_avg, t) plt.figure() plt.plot(results[:, 0], results[:, 1], "-o") plt.xlabel(r"Displacement") plt.ylabel("Load") -plt.figure() -plt.plot(results[:, 1], results[:, 2], "-o") -plt.xlabel(r"Load") -plt.ylabel("Horizontal Reaction") -plt.show() + diff --git a/demos/non_linear_heat_equation.py b/demos/non_linear_heat_equation.py index 92ee471..72c9d71 100755 --- a/demos/non_linear_heat_equation.py +++ b/demos/non_linear_heat_equation.py @@ -8,25 +8,60 @@ Created on Fri Feb 1 08:49:11 2019 from dolfin import * import mfront_wrapper as mf import numpy as np +import meshio -length = 30e-3 -width = 5.4e-3 -mesh = RectangleMesh(Point(0., 0.), Point(length, width), 100, 10) +fname = "../meshes/rod3D.msh" +msh = meshio.read("../meshes/rod3D.msh") +for cell in msh.cells: + if cell.type == "triangle": + triangle_cells = cell.data + elif cell.type == "tetra": + tetra_cells = cell.data + +for key in msh.cell_data_dict["gmsh:physical"].keys(): + if key == "triangle": + triangle_data = msh.cell_data_dict["gmsh:physical"][key] + elif key == "tetra": + tetra_data = msh.cell_data_dict["gmsh:physical"][key] +tetra_mesh = meshio.Mesh(points=msh.points, cells={"tetra": tetra_cells}, + cell_data={"name_to_read":[tetra_data]}) +# triangle_mesh =meshio.Mesh(points=msh.points, +# cells=[("triangle", triangle_cells)], +# cell_data={"name_to_read":[triangle_data]}) +triangle_mesh =meshio.Mesh(points=msh.points, + cells=[("triangle", triangle_cells)], + cell_data={"name_to_read":[triangle_data]}) +meshio.write("mesh.xdmf", tetra_mesh) +meshio.write("mf.xdmf", triangle_mesh) + +# remove blank spaces in field_date keys +tags = dict([(key.strip(), value) for (key, value) in msh.field_data.items()]) -V = FunctionSpace(mesh, "CG", 1) -T = Function(V, name="Temperature") -def left(x, on_boundary): - return near(x[1], 0) and on_boundary -def right(x, on_boundary): - return near(x[0], length) and on_boundary +mesh = Mesh() +mvc = MeshValueCollection("size_t", mesh, 3) +with XDMFFile("mesh.xdmf") as infile: + infile.read(mesh) + infile.read(mvc, "name_to_read") +cf = cpp.mesh.MeshFunctionSizet(mesh, mvc) +mvc = MeshValueCollection("size_t", mesh, 2) +with XDMFFile("mf.xdmf") as infile: + infile.read(mvc, "name_to_read") +mf = MeshFunction("size_t", mesh, 2) -Tl = 300 -Tr = 800 +def get_tag(tag): + return tags[tag][0] -bc = [DirichletBC(V, Constant(Tl), left), - DirichletBC(V, Constant(Tr), right)] +dx = Measure("dx", domain=mesh, subdomain_data=cf) +ds = Measure("ds", domain=mesh, subdomain_data=mf) + +V = FunctionSpace(mesh, "CG", 2) +T = Function(V, name="Temperature") +Text = 1e3 +v = Function(V) +bc = DirichletBC(V, Constant(Tl), mf, get_tag("00SOO")) +bc[0].apply(v.vector()) facets = MeshFunction("size_t", mesh, 1) ds = Measure("ds", subdomain_data=facets) diff --git a/demos/nonlinear_heat_transfer.ipynb b/demos/nonlinear_heat_transfer.ipynb old mode 100644 new mode 100755 index bb19f73..96b45e8 --- a/demos/nonlinear_heat_transfer.ipynb +++ b/demos/nonlinear_heat_transfer.ipynb @@ -8,6 +8,189 @@ "\n", "## Description of the non-linear constitutive heat transfer law\n", "\n", + "The thermal material is described by the following non linear Fourier\n", + "Law:\n", + "\n", + "$$\n", + "\\mathbf{j}=-k\\left(T\\right)\\,\\mathbf{\\nabla} T\n", + "$$\n", + "\n", + "where $\\mathbf{j}$ is the heat flux and $\\mathbf{\\nabla} T$ is the\n", + "temperature gradient.\n", + "\n", + "Expression of the thermal conductivity\n", + "--------------------------------------\n", + "\n", + "The thermal conductivity is assumed to be given by:\n", + "\n", + "$$\n", + "k\\left(T\\right)={\\displaystyle \\frac{\\displaystyle 1}{\\displaystyle A+B\\,T}}\n", + "$$\n", + "\n", + "This expression accounts for the phononic contribution to the thermal\n", + "conductivity.\n", + "\n", + "Derivatives\n", + "-----------\n", + "\n", + "As discussed below, the consistent linearisation of the heat transfer\n", + "equilibrium requires to compute:\n", + "\n", + "- the derivative\n", + " ${\\displaystyle \\frac{\\displaystyle \\partial \\mathbf{j}}{\\displaystyle \\partial \\mathbf{\\nabla} T}}$\n", + " of the heat flux with respect to the temperature gradient.\n", + " ${\\displaystyle \\frac{\\displaystyle \\partial \\mathbf{j}}{\\displaystyle \\partial \\mathbf{\\nabla} T}}$\n", + " is given by: $$\n", + " {\\displaystyle \\frac{\\displaystyle \\partial \\mathbf{j}}{\\displaystyle \\partial \\mathbf{\\nabla} T}}=-k\\left(T\\right)\\,\\matrix{I}\n", + " $$\n", + "- the derivative\n", + " ${\\displaystyle \\frac{\\displaystyle \\partial \\mathbf{j}}{\\displaystyle \\partial T}}$\n", + " of the heat flux with respect to the temperature.\n", + " ${\\displaystyle \\frac{\\displaystyle \\partial \\mathbf{j}}{\\displaystyle \\partial T}}$\n", + " is given by: $$\n", + " {\\displaystyle \\frac{\\displaystyle \\partial \\mathbf{j}}{\\displaystyle \\partial T}}=-{\\displaystyle \\frac{\\displaystyle \\partial k\\left(T\\right)}{\\displaystyle \\partial T}}\\,\\mathbf{\\nabla} T=B\\,k^{2}\\,\\mathbf{\\nabla} T\n", + " $$\n", + "\n", + "`MFront`’ implementation\n", + "========================\n", + "\n", + "Choice of the the domain specific language\n", + "------------------------------------------\n", + "\n", + "Every `MFront` file is handled by a domain specific language (DSL), which\n", + "aims at providing the most suitable abstraction for a particular choice\n", + "of behaviour and integration algorithm. See `mfront mfront --list-dsl`\n", + "for a list of the available DSLs.\n", + "\n", + "The name of DSL’s handling generic behaviours ends with\n", + "`GenericBehaviour`. The first part of a DSL’s name is related to the\n", + "integration algorithm used.\n", + "\n", + "In the case of this non linear transfer behaviour, the heat flux is\n", + "explicitly computed from the temperature and the temperature gradient.\n", + "The `DefaultGenericBehaviour` is the most suitable choice:\n", + "\n", + "``` cxx\n", + "@DSL DefaultGenericBehaviour;\n", + "```\n", + "\n", + "Some metadata\n", + "-------------\n", + "\n", + "The following lines define the name of the behaviour, the name of the\n", + "author and the date of its writing:\n", + "\n", + "``` cxx\n", + "@Behaviour StationaryHeatTransfer;\n", + "@Author Thomas Helfer;\n", + "@Date 15/02/2019;\n", + "```\n", + "\n", + "Gradients and fluxes\n", + "--------------------\n", + "\n", + "Generic behaviours relate pairs of gradients and fluxes. Gradients and\n", + "fluxes are declared independently but the first declared gradient is\n", + "assumed to be conjugated with the first declared fluxes and so on…\n", + "\n", + "The temperature gradient is declared as follows (note that Unicode characters are supported):\n", + "\n", + "``` cxx\n", + "@Gradient TemperatureGradient ∇T;\n", + "∇T.setGlossaryName(\"TemperatureGradient\");\n", + "```\n", + "\n", + "Note that we associated to `∇T` the glossary name `TemperatureGradient`.\n", + "This is helpful for the calling code.\n", + "\n", + "After this declaration, the following variables will be defined:\n", + "\n", + "- The temperature gradient `∇T` at the beginning of the time step.\n", + "- The increment of the temperature gradient `Δ∇T` over the time step.\n", + "\n", + "The heat flux is then declared as follows:\n", + "\n", + "``` cxx\n", + "@Flux HeatFlux j;\n", + "j.setGlossaryName(\"HeatFlux\");\n", + "```\n", + "\n", + "In the following code blocks, `j` will be the heat flux at the end of\n", + "the time step.\n", + "\n", + "Tangent operator blocks\n", + "-----------------------\n", + "\n", + "By default, the derivatives of the gradients with respect to the fluxes\n", + "are declared. Thus the variable `∂j∕∂Δ∇T` is automatically declared.\n", + "\n", + "However, as discussed in the next section, the consistent linearisation\n", + "of the thermal equilibrium requires to return the derivate of the heat\n", + "flux with respect to the increment of the temperature (or equivalently\n", + "with respect to the temperature at the end of the time step).\n", + "\n", + "``` cxx\n", + "@AdditionalTangentOperatorBlock ∂j∕∂ΔT;\n", + "```\n", + "\n", + "Parameters\n", + "----------\n", + "\n", + "The `A` and `B` coefficients that appears in the definition of the\n", + "thermal conductivity are declared as parameters:\n", + "\n", + "``` cxx\n", + "@Parameter real A = 0.0375;\n", + "@Parameter real B = 2.165e-4;\n", + "```\n", + "\n", + "Parameters are stored globally and can be modified from the calling\n", + "solver or from `python` in the case of the coupling with `FEniCS`\n", + "discussed below.\n", + "\n", + "Local variable\n", + "--------------\n", + "\n", + "A local variable is accessible in each code blocks.\n", + "\n", + "Here, we declare the thermal conductivity `k` as a local variable in\n", + "order to be able to compute its value during the behaviour integration\n", + "and to reuse this value when computing the tangent operator.\n", + "\n", + "``` cxx\n", + "@LocalVariable thermalconductivity k;\n", + "```\n", + "\n", + "Integration of the behaviour\n", + "----------------------------\n", + "\n", + "The behaviour integration is straightforward: one starts to compute the\n", + "temperature at the end of the time step, then we compute the thermal\n", + "conductivity (at the end of the time step) and the heat flux using the\n", + "temperature gradient (at the end of the time step).\n", + "\n", + "``` cxx\n", + "@Integrator{\n", + " // temperature at the end of the time step\n", + " const auto T_ = T + ΔT;\n", + " // thermal conductivity\n", + " k = 1 / (A + B ⋅ T_);\n", + " // heat flux\n", + " j = -k ⋅ (∇T + Δ∇T);\n", + "} // end of @Integrator\n", + "```\n", + "\n", + "Tangent operator\n", + "----------------\n", + "\n", + "The computation of the tangent operator blocks is equally simple:\n", + "\n", + "``` cxx\n", + "@TangentOperator {\n", + " ∂j∕∂Δ∇T = -k ⋅ tmatrix::Id();\n", + " ∂j∕∂ΔT = B ⋅ k ⋅ k ⋅ (∇T + Δ∇T);\n", + "} // end of @TangentOperator \n", + "```\n", "## FEniCS implementation\n", "\n", "We consider a rectanglar domain with imposed temperatures `Tl` (resp. `Tr`) on the left (resp. right boundaries). We want to solve for the temperature field `T` inside the domain using a $P^1$-interpolation. We initialize the temperature at value `Tl` throughout the domain. We finally load the material library with a `plane_strain` hypothesis." @@ -211,10 +394,10 @@ "source": [ "j = problem.fluxes[\"HeatFlux\"].function\n", "g = problem.gradients[\"TemperatureGradient\"].function\n", - "k_gauss = j.vector().get_local()[::2]/g.vector().get_local()[::2]\n", + "k_gauss = -j.vector().get_local()[::2]/g.vector().get_local()[::2]\n", "T_gauss = problem.state_variables[\"external\"][\"Temperature\"].function.vector().get_local()\n", - "A = 0.0375;\n", - "B = 2.165e-4;\n", + "A = material.get_parameter(\"A\");\n", + "B = material.get_parameter(\"B\");\n", "k_ref = 1/(A + B*T_gauss)\n", "plt.plot(T_gauss, k_gauss, 'o', label=\"FE\")\n", "plt.plot(T_gauss, k_ref, '.', label=\"ref\")\n", @@ -248,7 +431,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.6.8" + "version": "3.6.9" } }, "nbformat": 4, diff --git a/demos/nonlinear_heat_transfer.py b/demos/nonlinear_heat_transfer.py deleted file mode 100644 index 42b8f41..0000000 --- a/demos/nonlinear_heat_transfer.py +++ /dev/null @@ -1,129 +0,0 @@ -#!/usr/bin/env python -# coding: utf-8 - -# # Stationnary non-linear heat transfer -# -# ## Description of the non-linear constitutive heat transfer law -# -# ## FEniCS implementation -# -# We consider a rectanglar domain with imposed temperatures `Tl` (resp. `Tr`) on the left (resp. right boundaries). We want to solve for the temperature field `T` inside the domain using a $P^1$-interpolation. We initialize the temperature at value `Tl` throughout the domain. We finally load the material library with a `plane_strain` hypothesis. - -# In[1]: - - -import matplotlib.pyplot as plt -from dolfin import * -import mfront_wrapper as mf - -length = 30e-3 -width = 5.4e-3 -mesh = RectangleMesh(Point(0., 0.), Point(length, width), 100, 10) - -V = FunctionSpace(mesh, "CG", 1) -T = Function(V, name="Temperature") - -def left(x, on_boundary): - return near(x[0], 0) and on_boundary -def right(x, on_boundary): - return near(x[0], length) and on_boundary - -Tl = 300 -Tr = 800 -T.interpolate(Constant(Tl)) - -bc = [DirichletBC(V, Constant(Tl), left), - DirichletBC(V, Constant(Tr), right)] - -material = mf.MFrontNonlinearMaterial("../materials/src/libBehaviour.so", - "StationaryHeatTransfer", - hypothesis="plane_strain") - - -# The MFront behaviour implicitly declares the temperature as an external state variable called `"Temperature"`. We must therefore associate this external state variable to a known mechanical field. This can be achieved explicitly using the `register_external_state_variable` method. In the present case, this can be donc automatically since the name of the unknown temperature field matches the [TFEL Glossary](http://tfel.sourceforge.net/glossary.html) name `"Temperature"`. In this case, the following message is printed: -# ``` -# Automatic registration of 'Temperature' as an external state variable. -# ``` -# For problems in which the temperature only acts as a parameter (no jacobian blocks with respect to the temperature), the temperature can be automatically registered as a constant value ($293.15 \text{ K}$ by default) or to any other (`dolfin.Constant` or `float`) value using the `register_external_state_variable` method. -# -# In the FEniCS interface, we instantiate the main mechanical unknown, here the temperature field `T` which has to be named `"Temperature"` in order to match MFront's predefined name. Using another name than this will later result in an error saying: -# ``` -# ValueError: 'Temperature' could not be associated with a registered gradient or a known state variable. -# ``` -# -# The MFront behaviour declares the field `"TemperatureGradient"` as a Gradient variable, with its associated Flux called `"HeatFlux"`. We can check that the `material` object retrieves MFront's gradient and flux names, as well as the different tangent operator blocks which have been defined, namely `dj_ddgT` and `dj_ddT` in the present case: - -# In[2]: - - -print(material.get_gradient_names()) -print(material.get_flux_names()) -print(["d{}_d{}".format(*t) for t in material.get_tangent_block_names()]) - - -# When defining the non-linear problem, we will specify the boundary conditions and the requested quadrature degree which will control the number of quadrature points used in each cell to compute the non-linear constitutive law. Here, we specify a quadrature of degree 2 (i.e. 3 Gauss points for a triangular element). Finally, we need to associate to MFront gradient object the corresponding UFL expression as a function of the unknown field `T`. To do so, we use the `register_gradient` method linking MFront `"TemperatureGradient"` object to the UFL expression `grad(T)`. Doing so, the corresponding non-linear variational problem will be automatically be built: -# -# \begin{equation} -# F(\widehat{T}) = \int_\Omega \boldsymbol{j}\cdot \nabla \widehat{T} \text{dx} = 0 \quad \forall \widehat{T} -# \end{equation} - -# In[3]: - - -problem = mf.MFrontNonlinearProblem(T, material, quadrature_degree=2, bcs=bc) -problem.register_gradient("TemperatureGradient", grad(T)) - - -# From the two tangent operator blocks `dj_ddgT` and `dj_ddT`, it will automatically be deduced that the heat flux $\boldsymbol{j}$ is a function of both the temperature gradient $\boldsymbol{g}=\nabla T$ and the temperature itself i.e. $\boldsymbol{j}=\boldsymbol{j}(\boldsymbol{g}, T)$. The following tangent bilinear form will therefore be used when solving the above non-linear problem: -# -# \begin{equation} -# J(\widehat{T},T^*) = \int_{\Omega} \nabla \widehat{T}\cdot\left(\dfrac{\partial \boldsymbol{j}}{\partial \boldsymbol{g}}\cdot \nabla T^*+\dfrac{\partial \boldsymbol{j}}{\partial T}\cdot T^*\right) \text{dx} -# \end{equation} -# -# Similarly to the case of external state variables, common gradient expressions for some [TFEL Glossary](http://tfel.sourceforge.net/glossary.html) names have been already predefined which avoid calling explicitly the `register_gradient` method. Predefined expressions can be obtained from: - -# In[4]: - - -mf.list_predefined_gradients() - - -# We can see that the name `"Temperature Gradient"` is in fact a predefined gradient. Omitting calling the `register_gradient` method will in this case print the following message upon calling `solve`: -# ``` -# Automatic registration of 'TemperatureGradient' as grad(Temperature). -# ``` -# meaning that a predefined gradient name has been found and registered as the UFL expression $\nabla T$. -# -# We finally solve the non-linear problem using a default Newton non-linear solver. The `solve` method returns the number of Newton iterations (4 in the present case) and converged status . - -# In[5]: - - -problem.solve(T.vector()) - - -# We finally check that the thermal conductivity coefficient $k$, computed from the ratio between the horizontal heat flux and temperature gradient matches the temperature-dependent expressions implemented in the MFront behaviour. - -# In[7]: - - -j = problem.fluxes["HeatFlux"].function -g = problem.gradients["TemperatureGradient"].function -k_gauss = j.vector().get_local()[::2]/g.vector().get_local()[::2] -T_gauss = problem.state_variables["external"]["Temperature"].function.vector().get_local() -A = 0.0375; -B = 2.165e-4; -k_ref = 1/(A + B*T_gauss) -plt.plot(T_gauss, k_gauss, 'o', label="FE") -plt.plot(T_gauss, k_ref, '.', label="ref") -plt.xlabel(r"Temperature $T\: (K)$") -plt.ylabel(r"Thermal conductivity $k\: (W.m^{-1}.K^{-1})$") -plt.legend() -plt.show() - - -# In[ ]: - - - - diff --git a/demos/nonlinear_heat_transfer_3D.ipynb b/demos/nonlinear_heat_transfer_3D.ipynb new file mode 100755 index 0000000..981d2be --- /dev/null +++ b/demos/nonlinear_heat_transfer_3D.ipynb @@ -0,0 +1,181 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Stationnary non-linear heat transfer: 3D problem and performance comparisons\n", + "\n", + "## Description of the non-linear constitutive heat transfer law\n", + "\n", + "This example is a direct continuation of the [previous 2D example on non-linear heat transfer](nonlinear_heat_transfer.ipynb). The present computations will use the same behaviour `StationaryHeatTransfer.mfront`.\n", + "\n", + "![3D fuel rod example](supplementary_files/fuel_rod_solution.png)\n", + "\n", + "## FEniCS implementation\n", + "\n", + "We now consider a portion of nuclear fuel rod (Uranium Dioxide $\\text{UO}_2$) subject to an external imposed temperature $T_{ext}=1000\\text{ K}$ and uniform volumetric heat source $r=300 \\text{ MW/m}^3$. From the steady state heat balance equation $\\operatorname{div}\\boldsymbol{j} = r$, the variational formulation is now:\n", + "\n", + "\\begin{equation}\n", + "F(\\widehat{T}) = \\int_\\Omega \\boldsymbol{j}(T,\\nabla T)\\cdot\\nabla \\widehat{T}\\,\\text{dx} + \\int_\\Omega r \\widehat{T} \\,\\text{dx}=0 \\quad \\forall \\widehat{T}\n", + "\\end{equation}\n", + "\n", + "which fits the general default format of a `MFrontNonlinearProblem`:\n", + "\\begin{equation}\n", + "F(\\widehat{u}) = \\sum_i \\int_\\Omega \\boldsymbol{\\sigma}_i(\\boldsymbol{u})\\cdot \\boldsymbol{g}_i(\\widehat{u})\\,\\text{dx} -L(\\widehat{u}) =0 \\quad \\forall \\widehat{u}\n", + "\\end{equation}\n", + "\n", + "where $(\\boldsymbol{\\sigma}_i,\\boldsymbol{g}_i)$ are pairs of dual flux/gradient and here the external loading form $L$ is given by $-\\int_\\Omega r \\widehat{T} \\,\\text{dx}$. Compared to the previous example, we just add this source term using the `set_loading` method. Here we use a quadratic interpolation for the temperature field and external temperature is imposed on the surface numbered 12. Finally, we also rely on automatic registration of the gradient and external state variables as explained in the first demo." + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": {}, + "outputs": [], + "source": [ + "from dolfin import *\n", + "import mfront_wrapper as mf\n", + "from time import time\n", + "\n", + "mesh = Mesh()\n", + "mvc = MeshValueCollection(\"size_t\", mesh, 3)\n", + "with XDMFFile(\"mesh.xdmf\") as infile:\n", + " infile.read(mesh)\n", + "mvc = MeshValueCollection(\"size_t\", mesh, 2)\n", + "with XDMFFile(\"mf.xdmf\") as infile:\n", + " infile.read(mvc, \"name_to_read\")\n", + "facets = cpp.mesh.MeshFunctionSizet(mesh, mvc)\n", + "\n", + "V = FunctionSpace(mesh, \"CG\", 2)\n", + "T = Function(V, name=\"Temperature\")\n", + "T_ = TestFunction(V)\n", + "dT = TrialFunction(V)\n", + "T0 = Constant(300.)\n", + "T.interpolate(T0)\n", + "\n", + "Text = Constant(1e3)\n", + "bc = DirichletBC(V, Text, facets, 12)\n", + "\n", + "r = Constant(3e8)\n", + "\n", + "quad_deg = 2\n", + "material = mf.MFrontNonlinearMaterial(\"../materials/src/libBehaviour.so\",\n", + " \"StationaryHeatTransfer\")\n", + "problem = mf.MFrontNonlinearProblem(T, material, quadrature_degree=quad_deg, bcs=bc)\n", + "problem.set_loading(-r*T*dx)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The `solve` method computing time is monitored:" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Automatic registration of 'TemperatureGradient' as grad(Temperature).\n", + "\n", + "Automatic registration of 'Temperature' as an external state variable.\n", + "\n", + "MFront/FEniCS solve time: 58.29069375991821\n" + ] + } + ], + "source": [ + "tic = time()\n", + "problem.solve(T.vector())\n", + "print(\"MFront/FEniCS solve time:\", time()-tic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "For the purpose of performance comparison, we also implement a direct non-linear variational problem with pure UFL expressions. This is possible in the present case since the non-linear heat constitutive law is very simple. Note that we enfore the use of the same quadrature rule degree. The temperature field is also reinterpolated to its previous initial value for a fair comparison between both solution strategies." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Calling FFC just-in-time (JIT) compiler, this may take some time.\n", + " Ignoring precision in integral metadata compiled using quadrature representation. Not implemented.\n" + ] + } + ], + "source": [ + "A = Constant(material.get_parameter(\"A\"))\n", + "B = Constant(material.get_parameter(\"B\"))\n", + "j = -1/(A + B*T)*grad(T)\n", + "F = (dot(grad(T_), j) + r*T_)*dx(metadata={'quadrature_degree': quad_deg})\n", + "J = derivative(F, T, dT)\n", + "\n", + "T.interpolate(T0)\n", + "tic = time()\n", + "solve(F == 0, T, bc, J=J)\n", + "print(\"Pure FEniCS solve time:\", time()-tic)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Performance comparison\n", + "\n", + "We can observe that both methods, relying on the same default Newton solver, yield the same total iteration counts and residual values. As regards computing time, the pure FEniCS implementation is slightly faster as expected. In the following table, comparison has been made for a coarse (approx 4 200 cells) and a refined (approx 34 000 cells) mesh with quadrature degrees equal either to 2 or 5.\n", + "\n", + "|Mesh type | Quadrature degree | FEniCS/MFront | Pure FEniCS |\n", + "|:--------:|:-----------------:|:-------------:|:-----------:|\n", + "|coarse | 2 | 1.2 s | 0.8 s |\n", + "| coarse | 5 | 2.2 s | 1.0 s |\n", + "| fine | 2 | 62.8 s | 58.4 s |\n", + "| fine | 5 | 77.0 s | 66.3 s | \n", + "\n", + "The difference is slightly larger for large quadrature degrees, however, the difference is moderate when compared to the total computing time for large scale problems. FE \n", + "\n", + "## On the use of the correct tangent operator\n", + "\n", + "Most FE software do not take into account the contribution of $\\dfrac{\\partial \\boldsymbol{j}}{\\partial T}$ to the tangent operator. One can easily test this variant by assigning `dj_ddT` in the MFront behaviour or change the expression of the jacobian in the pure FEniCS implementation by:\n", + "```\n", + "J = dot(grad(T_), -grad(dT)/(A+B*T))*dx(metadata={'quadrature_degree': quad_deg})\n", + "```\n", + "In the present case, using this partial tangent operator yields a convergence in 4 iterations instead of 3, giving a computational cost increase by roughly 25%." + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.9" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/demos/nonlinear_heat_transfer_3D.py b/demos/nonlinear_heat_transfer_3D.py new file mode 100755 index 0000000..85c8895 --- /dev/null +++ b/demos/nonlinear_heat_transfer_3D.py @@ -0,0 +1,113 @@ +#!/usr/bin/env python3 +# -*- coding: utf-8 -*- +""" +Created on Fri Feb 1 08:49:11 2019 + +@author: bleyerj +""" +from dolfin import * +import mfront_wrapper as mf +import numpy as np +import meshio + +fname = "../meshes/rod3D.msh" +msh = meshio.read(fname) +for cell in msh.cells: + if cell.type == "triangle": + triangle_cells = cell.data + elif cell.type == "tetra": + tetra_cells = cell.data + +for key in msh.cell_data_dict["gmsh:physical"].keys(): + if key == "triangle": + triangle_data = msh.cell_data_dict["gmsh:physical"][key] + elif key == "tetra": + tetra_data = msh.cell_data_dict["gmsh:physical"][key] +tetra_mesh = meshio.Mesh(points=msh.points, cells={"tetra": tetra_cells}, + cell_data={"name_to_read":[tetra_data]}) +triangle_mesh =meshio.Mesh(points=msh.points, + cells=[("triangle", triangle_cells)], + cell_data={"name_to_read":[triangle_data]}) +meshio.write("mesh.xdmf", tetra_mesh) +meshio.write("mf.xdmf", triangle_mesh) + +# remove blank spaces in field_date keys +tags = dict([(key.strip(), value) for (key, value) in msh.field_data.items()]) +def get_tag(tag): + return tags[tag][0] +# get points on top line for postprocess +top_cells = msh.get_cell_data("gmsh:physical","line")==get_tag("00LRM01") +line = np.unique(msh.points[msh.get_cells_type("line")[top_cells, :].flatten(), :], axis=0) + +mesh = Mesh() +mvc = MeshValueCollection("size_t", mesh, 3) +with XDMFFile("mesh.xdmf") as infile: + infile.read(mesh) + infile.read(mvc, "name_to_read") +domains = cpp.mesh.MeshFunctionSizet(mesh, mvc) +mvc = MeshValueCollection("size_t", mesh, 2) +with XDMFFile("mf.xdmf") as infile: + infile.read(mvc, "name_to_read") +facets = cpp.mesh.MeshFunctionSizet(mesh, mvc) + + +dx = Measure("dx", domain=mesh, subdomain_data=domains) +ds = Measure("ds", domain=mesh, subdomain_data=facets) + +V = FunctionSpace(mesh, "CG", 2) +T = Function(V, name="Temperature") +T_ = TestFunction(V) +dT = TrialFunction(V) +T0 = Constant(300.) +T.interpolate(T0) + +Text = Constant(1e3) +v = Function(V) +bc = DirichletBC(V, Text, facets, get_tag("00SOO")) +bc.apply(v.vector()) + +r = Constant(3e8) + +quad_deg=2 +material = mf.MFrontNonlinearMaterial("../materials/src/libBehaviour.so", + "StationaryHeatTransfer") +problem = mf.MFrontNonlinearProblem(T, material, quadrature_degree=quad_deg, bcs=bc) +problem.set_loading(-r*T*dx) + +from time import time +tic = time() +problem.solve(T.vector()) +print("MFront/FEniCS solve time:", time()-tic) + +ffile = XDMFFile("results/3D_heat_transfer.xdmf") +ffile.parameters["functions_share_mesh"] = True +ffile.write(T, 0) + +Tline = np.zeros((line.shape[0],1)) +for (i, x) in enumerate(line): + Tline[i] = T(*x) +np.savetxt("fuel_rod_3d_results.csv", np.hstack((line, Tline)), delimiter=",") +# T.interpolate(T0) +# t = problem.fluxes["HeatFlux"].tangent_blocks["TemperatureGradient"] +# problem.a = inner(grad(T_), t*grad(dT))*problem.dx +# tic = time() +# problem.solve(T.vector()) +# print("MFront/FEniCS solve time (wrong jacobian):", time()-tic) + +T.interpolate(T0) +A = Constant(material.get_parameter("A")) +B = Constant(material.get_parameter("B")) +j = -1/(A + B*T)*grad(T) +F = (dot(grad(T_), j) + r*T_)*dx(metadata={'quadrature_degree': quad_deg}) +J = derivative(F, T) + +tic = time() +solve(F == 0, T, bc, J=J) +print("Pure FEniCS solve time:", time()-tic) + +T2 = Function(V, name="Temperature (fenics)") +T2.assign(T) + +ffile.write(T2, 0) + +ffile.close() \ No newline at end of file diff --git a/demos/small_strain_elastoplasticity.ipynb b/demos/small_strain_elastoplasticity.ipynb new file mode 100644 index 0000000..5a73c5d --- /dev/null +++ b/demos/small_strain_elastoplasticity.ipynb @@ -0,0 +1,269 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Small-strain von Mises elastoplasticity\n", + "\n", + "This demo is the third installment in a series of two previous demos considering the implementation of von Mises elastoplasticity in FEniCS published on [Numerical tours of continuum mechanics using FEniCS](https://comet-fenics.readthedocs.io):\n", + "\n", + "1. [Elasto-plastic analysis of a 2D von Mises material](https://comet-fenics.readthedocs.io/en/latest/demo/2D_plasticity/vonMises_plasticity.py.html): this first installment presents a pure FEniCS implementation of von Mises plasticity which uses UFL operators for implementing the return mapping procedure. It is therefore not general since it relies heavily on the fact that the return mapping can be expressed in closed-form analytic expression in the case of von Mises plasticity with linear isotropic hardening. It nevertheless shows how to integrate the constitutive relation using `Quadrature` elements, including the use of consistent tangent operators, inside a global Newton-Raphson method.\n", + "\n", + "\n", + "2. [Elasto-plastic analysis implemented using the MFront code generator](https://comet-fenics.readthedocs.io/en/latest/demo/plasticity_mfront/plasticity_mfront.py.html): this second installment is in fact the original demo which led to the development of the proposed FEniCS/MFront interface. It shows how to rely on MFront for the constitutive relation update using the MGIS interface. The way how information is exchanged between FEniCS and MFront in this demo is extremely similar to how the `MFrontNonlinearProblem` class is implemented.\n", + "\n", + "The present demo therefore directly follows up on this second installment by offering to the use a much more compact syntax, especially avoiding the cumbersome definition of `Quadrature` spaces and the implementation of a Newton method by hand. The mechanical problem is exactly the same as in these two demos, namely the expansion of a hollow cylinder under internal pressure. The main difference in the present demo is that the same problem will also be solved in axisymmetric conditions, referring therefore to the expansion of a hollow sphere under internal pressure.\n", + "\n", + "## MFront implementation\n", + "\n", + " TODO:\n", + "* Write the gallery example comments and refer to it?\n", + "\n", + "* or use standard brick with comments here ?\n", + " \n", + "\n", + "\n", + "## FEniCS implementation\n", + "\n", + "We first load the mesh and define values for the material properties. We will see later how to pass them to MFront. We will use a standard $P_2$ Lagrange interpolation for the displacement field and roller conditions are defined on the horizontal (tagged `1`) and vertical boundaries (tagged `3`) of the domain. The inner surface is tagged as `4` in the `facets` MeshFunction." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "from dolfin import *\n", + "import mfront_wrapper as mf\n", + "import numpy as np\n", + "import ufl\n", + "\n", + "Re, Ri = 1.3, 1. # external/internal radius\n", + "# elastic parameters\n", + "E = 70e3\n", + "nu = 0.3\n", + "# yield strength\n", + "sig0 = 250.\n", + "Et = E/100.\n", + "# hardening slope\n", + "H = E*Et/(E-Et)\n", + "\n", + "mesh = Mesh(\"../meshes/thick_cylinder.xml\")\n", + "plt.figure()\n", + "plot(mesh, linewidth=0.5)\n", + "plt.show()\n", + "\n", + "facets = MeshFunction(\"size_t\", mesh, \"../meshes/thick_cylinder_facet_region.xml\")\n", + "ds = Measure('ds', subdomain_data=facets)\n", + "\n", + "\n", + "V = VectorFunctionSpace(mesh, \"CG\", 2)\n", + "bc = [DirichletBC(V.sub(1), 0, facets, 1), DirichletBC(V.sub(0), 0, facets, 3)]\n", + "n = FacetNormal(mesh)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We now define the loading expression which consists of a uniform internal pressure $q$ which will be progressively increased from 0 to a value slightly larger than $q_{lim}$, the analytical limit load in the case of perfect plasticity, which is known to be $q_{lim} = \\dfrac{2}{\\sqrt{3}}\\ln\\left(\\dfrac{R_e}{R_i}\\right)\\sigma_0$ for the hollow cylinder (plane strain conditions) and $q_{lim} = 2\\ln\\left(\\dfrac{R_e}{R_i}\\right)\\sigma_0$ for the hollow sphere (axisymmetric conditions) and in which $R_i$ (resp. $R_e$) denotes the internal (resp. external) radius. \n", + "\n", + "The `MFrontNonlinearMaterial` instance is loaded from the MFront `IsotropicLinearHardeningPlasticity` behaviour. Material properties can be defined by passing a dictionary to the `material_properties` keyword argument. Note that the keys must match the entry names defined in the MFront behaviour. Temperature is not involved in this behaviour so we will let it be automatically registered as a constant default value.\n", + "\n", + "The `MFrontNonlinearProblem` instance is then defined by specifying the quadrature degree used for the computation of the constitutive relation. The present computation is a standard quasi-static mechanical problem involving only the stress and strains as the pair of dual flux/gradient variables. As in the heat equation example, we should therefore register the gradient variable named `Strain` as `sym(grad(u))` in plane strain conditions. However, `Strain` is again a predefined gradient variable so that we can rely on automatic registration. This is especially efficient in the present case where the registration is different depending on the hypothesis. For the `\"plane_strain\"` hypothesis, we get the following message:\n", + "```\n", + "Automatic registration of 'Strain' as sym(grad(Displacement)).\n", + "```\n", + "whereas for the `\"axisymmetric\"` hypothesis (see [the FEniCS tour on axisymmetric computations](https://comet-fenics.readthedocs.io/en/latest/demo/elasticity/axisymmetric_elasticity.html)), we get:\n", + "```\n", + "Automatic registration of 'Strain' as sym([\n", + " [(grad(Displacement[0]))[0], (grad(Displacement[0]))[1], 0],\n", + " [(grad(Displacement[1]))[0], (grad(Displacement[1]))[1], 0],\n", + " [0, 0, Displacement[0] / x[0]]\n", + "]).\n", + "```\n", + "in which the first two components refer to the $r$ and $z$ directions whereas the third component refers to the out-of-plane $\\theta$ direction.\n", + "\n", + "The linear form corresponding to the work of external forces can be specified through the `set_loading` method, namely in the present case:\n", + "\n", + "$$\n", + "W_{ext}(u) = \\int_{r=R_i} -q(t)\\boldsymbol{n}\\cdot\\boldsymbol{u} \\text{ dS}\n", + "$$\n", + "\n", + "Note that we pass directly the action of the form on the solution `u` rather than the linear form itself, in order to avoid the need of defining a `TestFunction`. Note also the use of the additional integration measure $2\\pi r$ in the axisymmetric case.\n", + "\n", + "Finally, load-stepping is done very easily by just updating the necessary expressions involved in the linear form definition (in the present case) or in the boundary conditions. At each step, the `solve` method is called on the displacement field, no updates are necessary from the user side.\n", + "\n", + "State variables can also be retrieved using the `get_state_variable` method, again with names matching the entry names defined in the MFront behaviour. In the present case, state variables include the elastic strain (represented by a 4-dimensional vector) and the equivalent plastic strain $p$ (a scalar). The `get_state_variable` method returns a `dolfin.Function` defined on the `Quadrature` space corresponding to the problem `quadrature_degree`. Such functions must therefore be projected on function spaces suitable for visualization or other post-processing purposes, such as (DG, 0) in the present case for the equivalent plastic strain.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Expansion of a thick cylinder in plane strain conditions\n", + "--------------------------------------------------------\n", + "Automatic registration of 'Strain' as sym(grad(Displacement)).\n", + "\n", + "Automatic registration of 'Temperature' as a Constant value = 293.15.\n", + "\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Expansion of a thick sphere in axisymmetric conditions\n", + "--------------------------------------------------------\n", + "Automatic registration of 'Strain' as sym([\n", + " [(grad(Displacement[0]))[0], (grad(Displacement[0]))[1], 0],\n", + " [(grad(Displacement[1]))[0], (grad(Displacement[1]))[1], 0],\n", + " [0, 0, Displacement[0] / x[0]]\n", + "]).\n", + "\n", + "Automatic registration of 'Temperature' as a Constant value = 293.15.\n", + "\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "for hypothesis in [\"plane_strain\", \"axisymmetric\"]:\n", + " u = Function(V, name=\"Displacement\")\n", + " if hypothesis == \"plane_strain\":\n", + " title = \"Expansion of a thick cylinder in plane strain conditions\"\n", + " q_lim = float(2/sqrt(3)*ln(Re/Ri)*sig0)\n", + " measure = 1\n", + " elif hypothesis == \"axisymmetric\":\n", + " title = \"Expansion of a thick sphere in axisymmetric conditions\"\n", + " x = SpatialCoordinate(mesh)\n", + " q_lim = float(2*ln(Re/Ri)*sig0)\n", + " measure = 2*pi*abs(x[0])\n", + " print(title + \"\\n\"+\"-\"*56)\n", + " loading = Expression(\"-q*t\", q=q_lim, t=0, degree=2)\n", + "\n", + " mat_prop = {\"YoungModulus\": E,\n", + " \"PoissonRatio\": nu,\n", + " \"HardeningSlope\": H,\n", + " \"YieldStrength\": sig0}\n", + " material = mf.MFrontNonlinearMaterial(\"../materials/src/libBehaviour.so\",\n", + " \"IsotropicLinearHardeningPlasticity\",\n", + " hypothesis=hypothesis,\n", + " material_properties=mat_prop)\n", + " problem = mf.MFrontNonlinearProblem(u, material, quadrature_degree=2, bcs=bc)\n", + " problem.set_loading(loading*dot(n, u)*measure*ds(4))\n", + "\n", + " p = problem.get_state_variable(\"EquivalentPlasticStrain\")\n", + " assert (ufl.shape(p) == ())\n", + " epsel = problem.get_state_variable(\"ElasticStrain\")\n", + " assert (ufl.shape(epsel)==(4, ))\n", + "\n", + " file_results = XDMFFile(\"results/plasticity_{}_results.xdmf\".format(hypothesis))\n", + " file_results.parameters[\"flush_output\"] = True\n", + " file_results.parameters[\"functions_share_mesh\"] = True\n", + " P0 = FunctionSpace(mesh, \"DG\", 0)\n", + " p_avg = Function(P0, name=\"Plastic_strain\")\n", + "\n", + " Nincr = 20\n", + " load_steps = np.linspace(0, 1.1, Nincr+1)[1:]**0.5\n", + " results = np.zeros((Nincr+1, 2))\n", + " for (i, t) in enumerate(load_steps):\n", + " loading.t = t\n", + " problem.solve(u.vector())\n", + "\n", + " file_results.write(u, t)\n", + "\n", + " p_avg.assign(project(p, P0))\n", + " file_results.write(p_avg, t)\n", + " results[i+1, :] = (u(Ri, 0)[0], t)\n", + " \n", + " plt.figure()\n", + " plt.title(title)\n", + " plt.plot(results[:, 0], results[:, 1], \"-o\")\n", + " plt.xlabel(\"Displacement of inner boundary\")\n", + " plt.ylabel(r\"Applied pressure $q/q_{lim}$\")\n", + " plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can check that the obtained results match those of the first two installments, both in terms of load-displacement curves, number of iterations and residual values for the plane strain case. In the axisymmetric case, we obtain similar results with plastic flow occuring at a critical pressure very close to the analytical limit load $q_{lim}$ in the perfectly plastic case." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.6.9" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/demos/small_strain_vonMises_plasticity.py b/demos/small_strain_vonMises_plasticity.py old mode 100644 new mode 100755 index 051e4c6..43ed776 --- a/demos/small_strain_vonMises_plasticity.py +++ b/demos/small_strain_vonMises_plasticity.py @@ -59,7 +59,7 @@ for hypothesis in ["plane_strain", "axisymmetric"]: P0 = FunctionSpace(mesh, "DG", 0) p_avg = Function(P0, name="Plastic_strain") - Nincr = 10 + Nincr = 20 load_steps = np.linspace(0, 1.1, Nincr+1)[1:]**0.5 results = np.zeros((Nincr+1, 2)) for (i, t) in enumerate(load_steps): diff --git a/demos/supplementary_files/apa.csl b/demos/supplementary_files/apa.csl new file mode 100644 index 0000000..284e56c --- /dev/null +++ b/demos/supplementary_files/apa.csl @@ -0,0 +1,1718 @@ + + diff --git a/demos/supplementary_files/fuel_rod_solution.png b/demos/supplementary_files/fuel_rod_solution.png new file mode 100755 index 0000000000000000000000000000000000000000..02d057d386ee943f824b82132178e5c89e700845 GIT binary patch literal 224411 zcmeEt^-~;e(Cy%s;6a1CyE_C4?(PyCg1ZE_#ob|Xch}$$+&#ga0Kx6<``!Bfh5OU3 z*{#~$nVOn9-OoAQz2}KkR+RpTOn?jkz{jsLUsM4Angsx0ND!eRza(_#Lr#zaU%!Z{ zdm5f~uO?BBg=efoc)Lid_{+4<$$%MJD)mH_~t#IMSLeRGw?=4 zk?~8D#XCXXJ1ygvyM+Kp2^4~02^2akQoN|g@}e7wj@R&hDKR+%1H&c#_tKf7fU4>a 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ziPFM1Z&E?hez6|goGl=#*dafgn`vlhjPoBW>%!D@85H)OmKGDe)_GW{Al8Z}2Y(Ck z>R1HO_59&D@X32N@w%KxhbPXzK4%@uU7A9CPu2|flN}YPMZNSa@z&M-*kiZlCEwF7 z{lAzWQdcYj+4E7Twn%%~-(O(*?DTG{SP+a?zzggQFkDAWuX`1RQvgTDsu9^MQOtfx z9fQGaWezWU$g)Fn&HSr^Ot`6A)TI;mjlP|pnzL|prg`jEZlfawqpq&zr<3_77G7S=tv&<}9 ztAVAZxL73%4EA!Q!$bQHz{qWH1D%CXRi5(!q#0MW_LzoX2CBMm=9S3wM}~%d0OQMd znttT7fVXg&Zsx!&Z36b5X&eg6sc2zlR`skI8$iRLiH%b8+P#SckwfqR7(Gx?`LoVP tUSJ?YK@;m6q>!L0Yi9%N|MP0~l;S26iNiiDBoP8G4K*FrZ^)::Id(); - dj_ddT = -B * k * k * (gT + dgT); + dj_ddgT = -k * tmatrix::Id(); + dj_ddT = B * k * k * (gT + dgT); } // end of @TangentOperator diff --git a/materials/TensionCompressionSplit.mfront b/materials/TensionCompressionSplit.mfront old mode 100644 new mode 100755 diff --git a/materials/src/Makefile.mfront b/materials/src/Makefile.mfront index 67d0418..ed0863e 100644 --- a/materials/src/Makefile.mfront +++ b/materials/src/Makefile.mfront @@ -1,6 +1,6 @@ # Makefile generated by mfront. # tfel -# Version : 3.3.0 +# Version : 3.4.0-dev # Compiled with on - # Please submit bug at tfel-contact@cea.fr @@ -12,7 +12,7 @@ INCLUDES := -I../include \ CXXFLAGS := -Wall -Wfatal-errors -ansi $(shell tfel-config --oflags) -fPIC $(INCLUDES) -SRCCXX = IsotropicLinearHardeningPlasticity-generic.cxx IsotropicLinearHardeningPlasticity.cxx LogarithmicStrainPlasticity-generic.cxx LogarithmicStrainPlasticity.cxx MultiphaseModel-generic.cxx MultiphaseModel.cxx MultiphaseModel3D-generic.cxx MultiphaseModel3D.cxx PhaseField-generic.cxx PhaseField.cxx PhaseFieldCoupled-generic.cxx PhaseFieldCoupled.cxx PhaseFieldDamage-generic.cxx PhaseFieldDamage.cxx PhaseFieldDisplacement-generic.cxx PhaseFieldDisplacement.cxx StationaryHeatTransfer-generic.cxx StationaryHeatTransfer.cxx TensionCompressionSplit-generic.cxx TensionCompressionSplit.cxx +SRCCXX = IsotropicLinearHardeningPlasticity-generic.cxx IsotropicLinearHardeningPlasticity.cxx LogarithmicStrainPlasticity-generic.cxx LogarithmicStrainPlasticity.cxx PhaseFieldDamage-generic.cxx PhaseFieldDamage.cxx PhaseFieldDisplacement-generic.cxx PhaseFieldDisplacement.cxx StationaryHeatTransfer-generic.cxx StationaryHeatTransfer.cxx makefiles1 = $(SRCCXX:.cxx=.d) makefiles2 = $(makefiles1:.cpp=.d) @@ -22,7 +22,7 @@ makefiles = $(makefiles2) all : libBehaviour.so -libBehaviour.so : MultiphaseModel-generic.o MultiphaseModel.o PhaseField-generic.o PhaseField.o PhaseFieldCoupled-generic.o PhaseFieldCoupled.o IsotropicLinearHardeningPlasticity-generic.o IsotropicLinearHardeningPlasticity.o LogarithmicStrainPlasticity-generic.o LogarithmicStrainPlasticity.o StationaryHeatTransfer-generic.o StationaryHeatTransfer.o TensionCompressionSplit-generic.o TensionCompressionSplit.o MultiphaseModel3D-generic.o MultiphaseModel3D.o PhaseFieldDisplacement-generic.o PhaseFieldDisplacement.o PhaseFieldDamage-generic.o PhaseFieldDamage.o +libBehaviour.so : LogarithmicStrainPlasticity-generic.o LogarithmicStrainPlasticity.o StationaryHeatTransfer-generic.o StationaryHeatTransfer.o PhaseFieldDisplacement-generic.o PhaseFieldDisplacement.o PhaseFieldDamage-generic.o PhaseFieldDamage.o IsotropicLinearHardeningPlasticity-generic.o IsotropicLinearHardeningPlasticity.o @$(CXX) -shared $^ -o $@ -L"$(strip $(shell tfel-config --library-path))" $(patsubst %,-l%,$(shell tfel-config --library-dependency --material --mfront-profiling --physical-constants)) install : diff --git a/materials/src/targets.lst b/materials/src/targets.lst index ea317bb..56222f7 100644 --- a/materials/src/targets.lst +++ b/materials/src/targets.lst @@ -6,26 +6,16 @@ prefix : "lib"; suffix : "so"; install_path : ""; sources : { -"MultiphaseModel-generic.cxx", -"MultiphaseModel.cxx", -"PhaseField-generic.cxx", -"PhaseField.cxx", -"PhaseFieldCoupled-generic.cxx", -"PhaseFieldCoupled.cxx", -"IsotropicLinearHardeningPlasticity-generic.cxx", -"IsotropicLinearHardeningPlasticity.cxx", "LogarithmicStrainPlasticity-generic.cxx", "LogarithmicStrainPlasticity.cxx", "StationaryHeatTransfer-generic.cxx", "StationaryHeatTransfer.cxx", -"TensionCompressionSplit-generic.cxx", -"TensionCompressionSplit.cxx", -"MultiphaseModel3D-generic.cxx", -"MultiphaseModel3D.cxx", "PhaseFieldDisplacement-generic.cxx", "PhaseFieldDisplacement.cxx", "PhaseFieldDamage-generic.cxx", -"PhaseFieldDamage.cxx" +"PhaseFieldDamage.cxx", +"IsotropicLinearHardeningPlasticity-generic.cxx", +"IsotropicLinearHardeningPlasticity.cxx" }; cppflags : { "$(shell tfel-config --cppflags --compiler-flags)" @@ -40,23 +30,6 @@ link_libraries : { "$(shell tfel-config --library-dependency --material --mfront-profiling --physical-constants)" }; epts : { -"MultiphaseModel_PlaneStrain", -"MultiphaseModel_Tridimensional", -"PhaseField_AxisymmetricalGeneralisedPlaneStrain", -"PhaseField_Axisymmetrical", -"PhaseField_PlaneStrain", -"PhaseField_GeneralisedPlaneStrain", -"PhaseField_Tridimensional", -"PhaseFieldCoupled_AxisymmetricalGeneralisedPlaneStrain", -"PhaseFieldCoupled_Axisymmetrical", -"PhaseFieldCoupled_PlaneStrain", -"PhaseFieldCoupled_GeneralisedPlaneStrain", -"PhaseFieldCoupled_Tridimensional", -"IsotropicLinearHardeningPlasticity_AxisymmetricalGeneralisedPlaneStrain", -"IsotropicLinearHardeningPlasticity_Axisymmetrical", -"IsotropicLinearHardeningPlasticity_PlaneStrain", -"IsotropicLinearHardeningPlasticity_GeneralisedPlaneStrain", -"IsotropicLinearHardeningPlasticity_Tridimensional", "LogarithmicStrainPlasticity_AxisymmetricalGeneralisedPlaneStrain", "LogarithmicStrainPlasticity_Axisymmetrical", "LogarithmicStrainPlasticity_PlaneStrain", @@ -67,12 +40,6 @@ epts : { "StationaryHeatTransfer_PlaneStrain", "StationaryHeatTransfer_GeneralisedPlaneStrain", "StationaryHeatTransfer_Tridimensional", -"TensionCompressionSplit_AxisymmetricalGeneralisedPlaneStrain", -"TensionCompressionSplit_Axisymmetrical", -"TensionCompressionSplit_PlaneStrain", -"TensionCompressionSplit_GeneralisedPlaneStrain", -"TensionCompressionSplit_Tridimensional", -"MultiphaseModel3D_Tridimensional", "PhaseFieldDisplacement_AxisymmetricalGeneralisedPlaneStrain", "PhaseFieldDisplacement_Axisymmetrical", "PhaseFieldDisplacement_PlaneStrain", @@ -82,26 +49,15 @@ epts : { "PhaseFieldDamage_Axisymmetrical", "PhaseFieldDamage_PlaneStrain", "PhaseFieldDamage_GeneralisedPlaneStrain", -"PhaseFieldDamage_Tridimensional" +"PhaseFieldDamage_Tridimensional", +"IsotropicLinearHardeningPlasticity_AxisymmetricalGeneralisedPlaneStrain", +"IsotropicLinearHardeningPlasticity_Axisymmetrical", +"IsotropicLinearHardeningPlasticity_PlaneStrain", +"IsotropicLinearHardeningPlasticity_GeneralisedPlaneStrain", +"IsotropicLinearHardeningPlasticity_Tridimensional" }; }; headers : { -"MFront/GenericBehaviour/MultiphaseModel-generic.hxx", -"TFEL/Material/MultiphaseModel.hxx", -"TFEL/Material/MultiphaseModelBehaviourData.hxx", -"TFEL/Material/MultiphaseModelIntegrationData.hxx", -"MFront/GenericBehaviour/PhaseField-generic.hxx", -"TFEL/Material/PhaseField.hxx", -"TFEL/Material/PhaseFieldBehaviourData.hxx", -"TFEL/Material/PhaseFieldIntegrationData.hxx", -"MFront/GenericBehaviour/PhaseFieldCoupled-generic.hxx", -"TFEL/Material/PhaseFieldCoupled.hxx", -"TFEL/Material/PhaseFieldCoupledBehaviourData.hxx", -"TFEL/Material/PhaseFieldCoupledIntegrationData.hxx", -"MFront/GenericBehaviour/IsotropicLinearHardeningPlasticity-generic.hxx", -"TFEL/Material/IsotropicLinearHardeningPlasticity.hxx", -"TFEL/Material/IsotropicLinearHardeningPlasticityBehaviourData.hxx", -"TFEL/Material/IsotropicLinearHardeningPlasticityIntegrationData.hxx", "MFront/GenericBehaviour/LogarithmicStrainPlasticity-generic.hxx", "TFEL/Material/LogarithmicStrainPlasticity.hxx", "TFEL/Material/LogarithmicStrainPlasticityBehaviourData.hxx", @@ -110,14 +66,6 @@ headers : { "TFEL/Material/StationaryHeatTransfer.hxx", "TFEL/Material/StationaryHeatTransferBehaviourData.hxx", "TFEL/Material/StationaryHeatTransferIntegrationData.hxx", -"MFront/GenericBehaviour/TensionCompressionSplit-generic.hxx", -"TFEL/Material/TensionCompressionSplit.hxx", -"TFEL/Material/TensionCompressionSplitBehaviourData.hxx", -"TFEL/Material/TensionCompressionSplitIntegrationData.hxx", -"MFront/GenericBehaviour/MultiphaseModel3D-generic.hxx", -"TFEL/Material/MultiphaseModel3D.hxx", -"TFEL/Material/MultiphaseModel3DBehaviourData.hxx", -"TFEL/Material/MultiphaseModel3DIntegrationData.hxx", "MFront/GenericBehaviour/PhaseFieldDisplacement-generic.hxx", "TFEL/Material/PhaseFieldDisplacement.hxx", "TFEL/Material/PhaseFieldDisplacementBehaviourData.hxx", @@ -125,6 +73,10 @@ headers : { "MFront/GenericBehaviour/PhaseFieldDamage-generic.hxx", "TFEL/Material/PhaseFieldDamage.hxx", "TFEL/Material/PhaseFieldDamageBehaviourData.hxx", -"TFEL/Material/PhaseFieldDamageIntegrationData.hxx" +"TFEL/Material/PhaseFieldDamageIntegrationData.hxx", +"MFront/GenericBehaviour/IsotropicLinearHardeningPlasticity-generic.hxx", +"TFEL/Material/IsotropicLinearHardeningPlasticity.hxx", +"TFEL/Material/IsotropicLinearHardeningPlasticityBehaviourData.hxx", +"TFEL/Material/IsotropicLinearHardeningPlasticityIntegrationData.hxx" }; }; diff --git a/materials/test.mfront b/materials/test.mfront old mode 100644 new mode 100755 diff --git a/meshes/rod3D.med b/meshes/rod3D.med new file mode 100755 index 0000000000000000000000000000000000000000..f2fd3348bff862237f9c020def63176c33da999d GIT binary patch literal 168003 zcmeFa2UJzdvM5T9N)*9>Bt<}woP{FioHL7@VUdG^3JNHoC?Jv)L6VXsgCK~Bq#z(> z1SF}5fuJD1i89yPM~`>!bKf0*jQ`$SW4Mc|uCA)CuBz@CdhQb%Dr%dlwo?&NP!OQM z?;AhmWTGD=p^b*7my_oD8Y)Ia?1Hbt?Ed;MjEG^K2knSLDk1_x0s^w_1PGwj)Kk+p zwpUlxQ#Df5Q8m7~A(Ra1Nk~Ahs%LDktEhMw;a~re(X3O6)f9~dIe!{K@I%ATR{Vd@ z$tBACdy_8xS0*tr5Rm+C?j{Zb0%D|L(|V(>q80%i;uGXgm=GRcm3~R!oT-t{N@tXLs|s znvsS9!FqNQ5zyg%f#%qk4QE+zIDI2v(ZI!Z*o6D*zy1RegGxdsZ~e!EK;=X<$aKhp zI+RQ_R1k|05%3Y&2|0#Vqy)FtIXHe2OjOG^ z5tOZSY!H+JeRdH@{)Hgv)@DSIvQ9uM)w)oHm)Kx}@V^iOh1%i?`u@`8t&egNf%LkT 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1092 1117 1093 +5837 4 2 14 27 1098 1117 1092 1005 +5838 4 2 14 27 1092 1005 1117 1093 +5839 4 2 14 27 1098 1117 1005 1101 +5840 4 2 14 27 1005 1101 1117 1095 +5841 4 2 14 27 1005 1095 1117 1093 +$EndElements diff --git a/meshes/thick_cylinder.xml b/meshes/thick_cylinder.xml old mode 100644 new mode 100755 diff --git a/meshes/thick_cylinder_facet_region.xml b/meshes/thick_cylinder_facet_region.xml old mode 100644 new mode 100755 diff --git a/meshes/thick_cylinder_physical_region.xml b/meshes/thick_cylinder_physical_region.xml old mode 100644 new mode 100755 diff --git a/mfront_wrapper/__init__.py b/mfront_wrapper/__init__.py old mode 100644 new mode 100755 diff --git a/mfront_wrapper/gradient_flux.py b/mfront_wrapper/gradient_flux.py old mode 100644 new mode 100755 index 6479378..44a4313 --- a/mfront_wrapper/gradient_flux.py +++ b/mfront_wrapper/gradient_flux.py @@ -42,12 +42,24 @@ class Gradient: return ufl.derivative(self.expression, self.variable, v) def initialize_function(self, mesh, quadrature_degree): - We = get_quadrature_element(mesh.ufl_cell(), quadrature_degree, self.shape) + self.quadrature_degree = quadrature_degree + self.dx = Measure("dx", metadata={"quadrature_degree": quadrature_degree}) + We = get_quadrature_element(mesh.ufl_cell(), self.quadrature_degree, self.shape) self.function_space = FunctionSpace(mesh, We) self.function = Function(self.function_space, name=self.name) - def update(self, x): - self.function.vector().set_local(x) + def update(self, x=None): + if x is None: + self._evaluate_at_quadrature_points(self.expression) + else: + if isinstance(x, np.ndarray): + self.function.vector().set_local(x) + else: + self._evaluate_at_quadrature_points(x) + + def _evaluate_at_quadrature_points(self, x): + local_project(x, self.function_space, self.dx, self.function) + # class Grad(Gradient): # """ Gradient operator : grad(u) """ diff --git a/mfront_wrapper/nonlinear_material.py b/mfront_wrapper/nonlinear_material.py old mode 100644 new mode 100755 index 7cb17f7..a7d57a0 --- a/mfront_wrapper/nonlinear_material.py +++ b/mfront_wrapper/nonlinear_material.py @@ -1,6 +1,7 @@ import mgis.behaviour as mgis_bv from .gradient_flux import Var import dolfin +from .utils import local_project mgis_hypothesis = {"plane_strain": mgis_bv.Hypothesis.PlaneStrain, "plane_stress": mgis_bv.Hypothesis.PlaneStress, @@ -58,10 +59,12 @@ class MFrontNonlinearMaterial: if isinstance(value, dolfin.Function): value = value.vector().get_local() elif isinstance(value, Var): - value.function.interpolate(value.expression) - value = value.function.vector().get_local() - mgis_bv.setExternalStateVariable(s, key, value, mgis_bv.MaterialStateManagerStorageMode.LocalStorage) + value.update() + values = value.function.vector().get_local() + mgis_bv.setExternalStateVariable(s, key, values, mgis_bv.MaterialStateManagerStorageMode.LocalStorage) + def get_parameter(self, name): + return self.behaviour.getParameterDefaultValue(name) def get_external_state_variable_names(self): return [svar.name for svar in self.behaviour.external_state_variables] diff --git a/mfront_wrapper/nonlinear_problem.py b/mfront_wrapper/nonlinear_problem.py old mode 100644 new mode 100755 index cd99712..0b1c70c --- a/mfront_wrapper/nonlinear_problem.py +++ b/mfront_wrapper/nonlinear_problem.py @@ -233,7 +233,8 @@ class MFrontNonlinearProblem(NonlinearProblem): buff = 0 for (i, g) in enumerate(self.material.get_gradient_names()): gradient = self.gradients[g] - local_project(gradient(self.u), gradient.function_space, self.dx, gradient.function) + gradient.update() + # local_project(gradient(self.u), gradient.function_space, self.dx, gradient.function) block_shape = self.material.get_gradient_sizes()[i] grad_vals = gradient.function.vector().get_local() if gradient.shape > 0: @@ -247,7 +248,8 @@ class MFrontNonlinearProblem(NonlinearProblem): buff = 0 for (i, g) in enumerate(self.material.get_gradient_names()): gradient = self.gradients[g] - local_project(gradient(self.u), gradient.function_space, self.dx, gradient.function) + gradient.update() + # local_project(gradient(self.u), gradient.function_space, self.dx, gradient.function) block_shape = self.material.get_gradient_sizes()[i] grad_vals = gradient.function.vector().get_local() if gradient.shape > 0: @@ -261,6 +263,8 @@ class MFrontNonlinearProblem(NonlinearProblem): buff = 0 for (i, s) in enumerate(self.material.get_internal_state_variable_names()): state_var = self.state_variables["internal"][s] + if state_var is None: + raise ValueError("The state variable '{}' has not been initialized.".format(s)) block_shape = self.material.get_internal_state_variable_sizes()[i] self.material.data_manager.s0.internal_state_variables[:,buff:buff+block_shape] = state_var.vector().get_local().reshape(self.material.data_manager.n, block_shape) buff += block_shape diff --git a/mfront_wrapper/utils.py b/mfront_wrapper/utils.py old mode 100644 new mode 100755 index 8942e11..a380137 --- a/mfront_wrapper/utils.py +++ b/mfront_wrapper/utils.py @@ -19,14 +19,21 @@ def local_project(v, V, dx, u=None): v_ = TestFunction(V) a_proj = inner(dv, v_)*dx b_proj = inner(v, v_)*dx - solver = LocalSolver(a_proj, b_proj) - solver.factorize() + v0 = Function(V) + v0.vector().set_local(1.+0*v0.vector().get_local()) + a_proj = assemble(inner(v0, v_)*dx) + b_proj = assemble(inner(v, v_)*dx) + r_proj = b_proj.get_local()/a_proj.get_local() + # solver = LocalSolver(a_proj, b_proj, LocalSolver.SolverType.Cholesky) + # solver.factorize() if u is None: u = Function(V) - solver.solve_local_rhs(u) + # solver.solve_local_rhs(u) + u.vector().set_local(r_proj) return u else: - solver.solve_local_rhs(u) + # solver.solve_local_rhs(u) + u.vector().set_local(r_proj) return def symmetric_tensor_to_vector(T, T22=0): diff --git a/setup.py b/setup.py old mode 100644 new mode 100755 -- GitLab