{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Linear Elasticity in 2D\n", "\n", "## Introduction\n", "\n", "This example provides a demonstration of using PyMKS to compute the linear strain field for a two-phase composite material. The example introduces the governing equations of linear elasticity, along with the unique boundary conditions required for the MKS. It subsequently demonstrates how to generate data for delta microstructures and then use this data to calibrate the first order MKS influence coefficients for all strain fields. The calibrated influence coefficients are used to predict the strain response for a random microstructure and the results are compared with those from finite element. Finally, the influence coefficients are scaled up and the MKS results are again compared\n", "with the finite element data for a large problem.\n", "\n", "PyMKS uses the finite element tool [SfePy](http://sfepy.org) to generate both the strain fields to fit the MKS model and the verification data to evaluate the MKS model's accuracy." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Elastostatics Equations\n", "\n", "For the sake of completeness, a description of the equations of linear elasticity is included. The constitutive equation that describes the linear elastic phenomena is Hook's law.\n", "\n", "$$ \\sigma_{ij} = C_{ijkl}\\varepsilon_{kl} $$\n", "\n", "$\\sigma$ is the stress, $\\varepsilon$ is the strain, and $C$ is the stiffness tensor that relates the stress to the strain fields. For an isotropic material the stiffness tensor can be represented by lower dimension terms which can relate the stress and the strain as follows.\n", "\n", "$$ \\sigma_{ij} = \\lambda \\delta_{ij} \\varepsilon_{kk} + 2\\mu \\varepsilon_{ij} $$\n", "\n", "$\\lambda$ and $\\mu$ are the first and second Lame parameters and can be defined in terms of the Young's modulus $E$ and Poisson's ratio $\\nu$ in 2D.\n", "\n", "$$ \\lambda = \\frac{E\\nu}{(1-\\nu)(1-2\\nu)} $$\n", "\n", "$$ \\mu = \\frac{E}{3(1+\\nu)} $$\n", "\n", "\n", "Linear strain is related to displacement using the following equation.\n", "\n", "$$ \\varepsilon_{ij} = \\frac{u_{i,j}+u_{j,i}}{2} $$\n", "\n", "We can get an equation that relates displacement and stress by plugging the equation above back into our expression for stress.\n", "\n", "$$ \\sigma_{ij} = \\lambda u_{k,k} + \\mu( u_{i,j}+u_{j,i}) $$\n", "\n", "The equilibrium equation for elastostatics is defined as\n", "\n", "$$ \\sigma_{ij,j} = 0 $$\n", "\n", "and can be cast in terms of displacement.\n", "\n", "$$ \\mu u_{i,jj}+(\\mu + \\lambda)u_{j,ij}=0 $$\n", "\n", "In this example, a displacement controlled simulation is used to calculate the strain. The domain is a square box of side $L$ which has an macroscopic strain $\\bar{\\varepsilon}_{xx}$ imposed.\n", "\n", "In general, generating the calibration data for the MKS requires boundary conditions that are both periodic and displaced, which are quite unusual boundary conditions and are given by:\n", "\n", "$$ u(L, y) = u(0, y) + L\\bar{\\varepsilon}_{xx}$$\n", "$$ u(0, L) = u(0, 0) = 0 $$\n", "$$ u(x, 0) = u(x, L) $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Modeling with MKS\n", "\n", "### Calibration Data and Delta Microstructures\n", "\n", "The first order MKS influence coefficients are all that is needed to compute a strain field of a random microstructure, as long as the ratio between the elastic moduli (also known as the contrast) is less than 1.5. If this condition is met, we can expect a mean absolute error of 2% or less, when comparing the MKS results with those computed using finite element methods [1]. \n", "\n", "Because we are using distinct phases and the contrast is low enough to only need the first order coefficients, delta microstructures and their strain fields are all that we need to calibrate the first order influence coefficients [2]. \n", "\n", "Here we use the `make_delta_microstructure` function from `pymks.datasets` to create the two delta microstructures needed to calibrate the first order influence coefficients for a two-phase microstructure. The `make_delta_microstructure` function uses SfePy to generate the data" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "The autoreload extension is already loaded. To reload it, use:\n", " %reload_ext autoreload\n" ] } ], "source": [ "#PYTEST_VALIDATE_IGNORE_OUTPUT\n", "\n", "import pymks\n", "\n", "%matplotlib inline\n", "%load_ext autoreload\n", "%autoreload 2\n", "\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 21\n", "\n", "from pymks.tools import draw_microstructures\n", "from pymks.datasets import make_delta_microstructures\n", "\n", "X_delta = make_delta_microstructures(n_phases=2, size=(n, n))\n", "draw_microstructures(X_delta)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using delta microstructures for the calibration of the first order influence coefficients is essentially the same as using a unit [impulse response](http://en.wikipedia.org/wiki/Impulse_response) to find the kernel of a system in signal processing. Any given delta microstructure is composed of only two phases with the center cell having an alternative phase from the remainder of the domain. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Generating Calibration Data\n", "\n", "The `make_elasticFEstrain_delta` function from `pymks.datasets` provides an easy interface to generate delta microstructures and their strain fields, which can then be used for calibration of the influence coefficients. The function calls the `ElasticFESimulation` class to compute the strain fields with the boundary conditions given above.\n", "\n", "In this example, lets look at a two-phase microstructure with elastic moduli values of 100 and 120 and Poisson's ratio values of 0.3 and 0.3 respectively. Let's also set the macroscopic imposed strain equal to 0.02. All of these parameters used in the simulation must be passed into the `make_elasticFEstrain_delta` function. Note that `make_elasticFEstrain_delta` does not take a number of samples argument as the number of samples to calibrate the MKS is fixed by the number of phases." ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [], "source": [ "from pymks.datasets import make_elastic_FE_strain_delta\n", "from pymks.tools import draw_microstructure_strain\n", "\n", "elastic_modulus = (100, 120)\n", "poissons_ratio = (0.3, 0.3)\n", "macro_strain = 0.02\n", "size = (n, n)\n", "\n", "X_delta, y_delta = make_elastic_FE_strain_delta(elastic_modulus=elastic_modulus,\n", " poissons_ratio=poissons_ratio,\n", " size=size, macro_strain=macro_strain) \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's take a look at one of the delta microstructures and the $\\varepsilon_{xx}$ strain field." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_microstructure_strain(X_delta[0], y_delta[0])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Calibrating First Order Influence Coefficients\n", "\n", "Now that we have the delta microstructures and their strain fields, we can calibrate the influence coefficients by creating an instance of the `MKSLocalizationModel` class. Because we have 2 phases we will create an instance of MKSLocalizationModel with the number of states `n_states` equal to 2. Then, pass the delta microstructures and their strain fields to the `fit` method. " ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [], "source": [ "from pymks import MKSLocalizationModel\n", "from pymks import PrimitiveBasis\n", "\n", "p_basis = PrimitiveBasis(n_states=2, domain=[0, 1])\n", "model = MKSLocalizationModel(basis=p_basis)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now, pass the delta microstructures and their strain fields into the `fit` method to calibrate the first-order influence coefficients." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "model.fit(X_delta, y_delta)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That's it, the influence coefficient have be calibrated. Let's take a look at them." ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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8Zn4rIt4Y6p2JiBdjfDmMuVDr9zZ/hOuRKAIAAG3yaLz1ZsuYquqFFWXXYipJ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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pymks.tools import draw_coeff\n", "\n", "draw_coeff(model.coef_)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The influence coefficients for $l=0$ have a Gaussian-like shape, while the influence coefficients for $l=1$ are constant-valued. The constant-valued influence coefficients may seem superfluous, but are equally as important. They are equivalent to the constant term in multiple linear regression with [categorical variables](http://en.wikipedia.org/wiki/Dummy_variable_%28statistics%29)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Predict the Strain Field for a Random Microstructure\n", "\n", "Let's now use our instance of the `MKSLocalizationModel` class with calibrated influence coefficients to compute the strain field for a random two phase microstructure and compare it with the results from a finite element simulation. \n", "\n", "The `make_elasticFEstrain_random` function from `pymks.datasets` is an easy way to generate a random microstructure and its strain field results from finite element analysis. " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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N75fxX70cjuEvxd/7993+mXAMSTqnb1Y4xv/4xJZwjPEXj4VjSNLUrnPDMZbf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\nFjRwLZIo+gAAAABEeYFvTcg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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pymks.datasets import make_elastic_FE_strain_random\n", "\n", "np.random.seed(99)\n", "X, strain = make_elastic_FE_strain_random(n_samples=1, elastic_modulus=elastic_modulus,\n", " poissons_ratio=poissons_ratio, size=size, \n", " macro_strain=macro_strain)\n", "draw_microstructure_strain(X[0] , strain[0])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Note that the calibrated influence coefficients can only be used to reproduce the simulation with the same boundary conditions that they were calibrated with.**\n", "\n", "Now to get the strain field from the `MKSLocalizationModel` just pass the same microstructure to the `predict` method." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "strain_pred = model.predict(X)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Finally let's compare the results from finite element simulation and the MKS model." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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8KfH+4LXv+6NwjBMnxn5/SdLX/7/Y79GXdu8P5zDp3FeEY3x95Y3hGOMboD/4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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pymks.tools import draw_strains_compare\n", "\n", "draw_strains_compare(strain[0], strain_pred[0])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lastly, let's look at the difference between the two strain fields." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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flSb5dWb2XMsH3yISOQBgPtop6fnKE3d/QdK2yDpR5e7+3bSFfaB2w2bWJ2mTmfVWLf6G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\nXesAAJQYLXIAQJDndPczTj8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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pymks.tools import draw_differences\n", "\n", "draw_differences([strain[0] - strain_pred[0]], ['Finite Element - MKS'])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The MKS model is able to capture the strain field for the random microstructure after being calibrated with delta microstructures." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Resizing the Coefficients to use on Larger Microstructures \n", "\n", "The influence coefficients that were calibrated on a smaller microstructure can be used to predict the strain field on a larger microstructure though spectral interpolation [3], but accuracy of the MKS model drops slightly. To demonstrate how this is done, let's generate a new larger random microstructure and its strain field." ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(63, 63)\n" ] }, { "data": { "image/png": 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96q9e7dSyMnmIzdMP/oPWfcfhcSfx8JyBvfo7tW6deIjNC1NfovWrL/0qrW/d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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "m = 3 * n\n", "size = (m, m)\n", "print(size)\n", "\n", "X, strain = make_elastic_FE_strain_random(n_samples=1, elastic_modulus=elastic_modulus,\n", " poissons_ratio=poissons_ratio, size=size, \n", " macro_strain=macro_strain)\n", "\n", "draw_microstructure_strain(X[0] , strain[0])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The influence coefficients that have already been calibrated need to be resized to match the shape of the new larger microstructure that we want to compute the strain field for. This can be done by passing the shape of the new larger microstructure into the `resize_coeff` method." ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "model.resize_coeff(X[0].shape)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's now take a look that ther resized influence coefficients." ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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2gz+aeVkBAE5ZawMdozjAmHaERBEAAOjnoA2zm+cQk9cdMcBnEwAAgNOkRREA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\nRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_coeff(model.coef_)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Because the coefficients have been resized, they will no longer work for our original $n$ by $n$ sized microstructures they were calibrated on, but they can now be used on the $m$ by $m$ microstructures. Just like before, just pass the microstructure as the argument of the `predict` method to get the strain field." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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LGw0KhRBCCCGEEKXiI/+LNWKxTpciGhQKIYQQQgghSkVPCi9vXDl3ZAaAzBt+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\nCvP/ASETyKRO+iq9AAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "strain_pred = model.predict(X)\n", "\n", "draw_strains_compare(strain[0], strain_pred[0])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Again, let's look at the difference between the two strain fields." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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CdTHLRYS5DL9mL/7DL2h8D7neLGFlxri+LYtRJlTrNu4/azrUOj/W/VN7ybZN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\nL60E+bKGSndPkqtjD6a4evc2UeomDJW3pRi2/MN7iBr5kFG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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "draw_differences([strain[0] - strain_pred[0]], ['Finite Element - MKS'])\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As you can see, the results from the strain field computed with the resized influence coefficients is not as close to the finite element results as they were before they were resized. This decrease in accuracy is expected when using spectral interpolation [4]." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "## References\n", "\n", "[1] Binci M., Fullwood D., Kalidindi S.R., A new spectral framework for establishing localization relationships for elastic behavior of composites and their calibration to finite-element models. Acta Materialia, 2008. 56 (10) p. 2272-2282 [doi:10.1016/j.actamat.2008.01.017](http://dx.doi.org/10.1016/j.actamat.2008.01.017).\n", "\n", "\n", "[2] Landi, G., S.R. Niezgoda, S.R. Kalidindi, Multi-scale modeling of elastic response of three-dimensional voxel-based microstructure datasets using novel DFT-based knowledge systems. Acta Materialia, 2009. 58 (7): p. 2716-2725 [doi:10.1016/j.actamat.2010.01.007](http://dx.doi.org/10.1016/j.actamat.2010.01.007).\n", "\n", "\n", "[3] Marko, K., Kalidindi S.R., Fullwood D., Computationally efficient database and spectral interpolation for fully plastic Taylor-type crystal plasticity calculations of face-centered cubic polycrystals. International Journal of Plasticity 24 (2008) 1264–1276 [doi:10.1016/j.ijplas.2007.12.002](http://dx.doi.org/10.1016/j.ijplas.2007.12.002).\n", "\n", "\n", "[4] Marko, K. Al-Harbi H. F. , Kalidindi S.R., Crystal plasticity simulations using discrete Fourier transforms. Acta Materialia 57 (2009) 1777–1784 [doi:10.1016/j.actamat.2008.12.017](http://dx.doi.org/10.1016/j.actamat.2008.12.017)." ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": true }, "outputs": [], "source": [] } ], "metadata": { "anaconda-cloud": {}, "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": "3.6.1" } }, "nbformat": 4, "nbformat_minor": 1 }