{ "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": 1, "metadata": { "collapsed": false }, "outputs": [], "source": [ "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": 2, "metadata": { "collapsed": false }, "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": 3, "metadata": { "collapsed": false }, "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": 4, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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lypXKzc1VTU2NJCkcDmvp0qXq6OjQxIkTNXPmTO3Zs0crV66Uw+FQUVGRvv/9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\nADAD08S2mCYGAAAwGJ1BAAB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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": 5, "metadata": { "collapsed": false }, "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": 6, "metadata": { "collapsed": false }, "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": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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N++Jq/9e/xXd7gigd5YPYRvBs1ZQ4TzYpca4j3voAgARIsqu2rc7yQRIAAFxC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\n1CsZjhWu2k62K5KT8Zco2Y6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"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": 8, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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VCAsLAwBMmjQJ8+bNQ0FBgcMYurq68PLLL+Ohhx6CVquF2WzG6dOnBx23zHMv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\nc3MHHDeXoYmIiEhyvO+W3EBwcDCWLl3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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": 9, "metadata": { "collapsed": false }, "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": 10, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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MV4X7+GrFBqH8ujX/K9xHVOzTQvnMf30j3MfR4nyhvL5B/ALy/xo3Rii/beO3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\nkg2dTofy8nKUl5ejt7cXWq0WBQUF0Gq1o+Jqa2tx/Phx6+u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"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": 11, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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xhPWqVatG3BYdHY3e3l40NjbKUxh1dXUwm83Das1mM2pra2G1WuW6sLAwhIaGQqPReO0z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\n8EnHJaH6WQax/rUusX9s2j1iA4NTrf5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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": 12, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "(63, 63)\n" ] }, { "data": { "image/png": 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lq3HdIvaxqmsoVwllL6yagbj8h0WaMoa8+CTpOcqa13HD40m3frg9\n6d9mcLZmjXCt1/3Yes7WVOuVeegM6cpd2M/pUcabtJtF69nfto77SdfXOynn4DILs/ieFxeyJ/yf\nb79CespczhwFAA//Eh/rtfIRmu2OIINF5yFPFgVBEARBcDmKNf+zERxFBouCIAiCILgcxcXaldME\nx5DBoiAIgiAILofMhnYehoPF0r4tPf+TWQ+ViiOeLLO+SKMy7cknNCrTEW+fWU+cUQafPd5Lo/Y1\n8nfeadvrncORtjM6p3oOs3mFgHEWo5FXVsWez496D83mear3w56+bXYNcr11zu+UMoGBtp+t/pzR\ndm4+r/NbY3Ar0qnntNeYb+XMQo9AzvW7cvQc6cbtu5P+7ewK0r5N2KNYPoj9bwBQxo9zFE+msQf5\nwkkuE+5ut9V+TUI1ZWxJ2k66xSPseZv3FXvkmvbmjL29C9mLFtNYm+P3/tgPSau5l1Xa1iN9NYf9\noJkreF3hKn14HW4AOPUjewwbDOF67j7KvrzQ1jVIL9ywnHREJf5slg0oqynz5Fm+H8GNuJ+fXcO5\niSdO8/rV1vPcDnW7NtOUsecY91VLVc5AXLaZfZKVlTzQh/7BntRVc9grC2hzLT0CvDT7lGbcZ5+T\nbtGF29rP21dzzOqv2Y+5/Df2Uka04uzNY4vY56rmMKZfzCCtWd8dQNF1q+1n1cPqKPeiZzE7OxsT\nJ07E/v37ERgYiEGDBiEmJkZ332XLlmHJkiXIy8tDdHQ0Ro4cCU9PT1itVkyePBlJSUnIzs5GxYoV\nER8fj6ZNmwIArFYrvvjiC5w8eRKZmZl4++230aBBAzr3yZMnMWPGDCQnJ8Pb2xuPPPIIunfvrlcN\nAPJkURAEQRAEF+ReHCxOmTIFFosFU6ZMQXJyMj766CNERERoHhTs3bsXixcvxttvv41y5cphzJgx\nSExMRHx8PAoLCxEcHIyEhAQEBwdj9+7dGDt2LMaMGYOQkBv/sa1fvz569OiBsWPHauqQlZWFDz/8\nEMOGDUN0dDSsVisuXLig2a802mlQgiAIgiAIf3OKi4v/0n9G5ObmYvv27Rg4cCC8vb0RGRmJli1b\nYuPGjZp9N2zYgE6dOqFKlSrw9/dHv379sH79egCAt7c34uLiEBx8I6mgefPmCA0NRXLyjdV9PD09\n0b17d0RGRuquULds2TI0adIEMTEx8PT0hI+PDypXrqzZrzTyZFEQBEEQBJfjXnuyePbsWXh4eCAs\nrCQeLCIiAgcPHtTse/r0abRu3dqmq1evjitXriA7OxsBAWx5uXz5MtLS0nStaHqcOHEC1apVw5tv\nvolz586hdu3aGD58uG3wqYepwaKed+xO8+0c8ZKZzVE0u7/eMUbZjkbeMUfWhjZqG3vW1TY6h9k6\n2INRhuGdZljqHaNilMPoiE/VKBPRGZmhRp8fo7WkVexZz/3PWGPcLKP6DLP9/N+336Nt3jV5jeXz\nB7mNXhn8T835XnnjNdJq1l/9mKakj/6hZByW5Sy6nD3nSbcbzr4vAKhWkb+op34xiXTNmCjS6r1J\nvnCdtPVSrqaM9GMXSUd05/4Rdn9t0rvmbCDdYTivTTx3zUJNGbUbsSfxyFpew/rsgRTSasZeiyce\n4DrMXK8po+xD7EHMusZZmqoH0eLJ92/XbL6uB15vR7pCWa2n9Le1m0i7eXC//+f7r5L+evwE0h7l\n2IdXrgz3S0CbnZuXzGsqFyvrOKde4XWeH1a8s+u82SsIAEW5VtJ1GrF/8Ep2Fuk/ViWR3r15B+lR\nI0ZpytgQyr7hvYfZYwrlq8wjkD8v9Trz5+t0Bq+RnXswU1Nm6fYttORptv9dSEwsWe87KioKUVEl\nn/vc3Fz4+rJH1MfHB7m52s96bm4u/Pz8bPrmcbm5uTRYtFqtGDduHGJjYxEeHq45jx4XLlxAcnIy\n3nzzTVStWhWzZs3CF198gffee++Wx8iTRUEQBEEQXI67MRv60UcfveU2Hx8fXL/O/ynMycmBj482\ngF/dNycnx/b7mxQVFWH8+PGwWCwYPny43XX08vJC69atUbNmTQBAXFwchg8fjuvXr2sGszcRz6Ig\nCIIgCC7HveZZrFSpEgoLC3HuXEkyQmpq6i1XEEtJSaH9ypYta3uqWFxcjEmTJiErKwsvv/yyrjfx\nVui96TRCBouCIAiCILgc99pg0cfHB61bt8bcuXORl5eHI0eOYNeuXWjfvr1m3/bt22Pt2rU4ffo0\nsrOzsWDBAsTGxtq2T548GWfOnMFrr70Gi0UbRVRQUID8/BtLilqtVtvPABAbG4vt27cjJSUFVqsV\n8+fPR2Rk5C2fKgLyGloQBEEQBBfkXlzBZcSIEZg4cSJGjBiBwMBAjBw5ElWqVEFmZiZGjx6NsWPH\nokKFCmjatCl69+6NhIQE5OfnIzo62vaKOyMjA2vWrIHFYsGoUSWe01GjRtkyG1988UVkZt7whn7w\nwQcAgK+++grBwcFo2LAhBg0ahI8++gh5eXmoX78+XnjhhdvW263YYDhc+tGmkZkeMDb5O2LIVzEK\nPzYKGVYf1+pN3DE7ucFokoY9GAUqq+dUHyU7MmnDaJKG2Uk2ehjN0DK6n3ptqd7DO21/eyY5qZOB\njPqEPWHiKmYDyR2ZrHKnbfNnhHI/uf4d28+Lv55L29z9+X/NnmXYTP+/CRwiDQAvjx7Nx4T4kQ6o\nyJMTruexjyj/FE+4KL7OkwrcvTkYGQDinxxKOi+fTfrzps3mcxbxfegW/zDXKTdHU8baWRwW7lOr\nHGl18oM1k6/rtXfeIP35lHGaMqxX2GzfseeDpH+ZsYS0pRLPzIQycaQ4XxuwbAnzV/bhPvXC0H+Q\n/uSDj0gXXua27fhET9I5uXzdgHYSzdkLPGkpPDiMdKUKFUmvW8STTTz8tU9ziq18TwvOcmB5ZM+W\npH0Vr9qBNRxu3WtIX00Z+QUcOL9q/jKulzI5Ky/lCum2AzqT3rpkvaYMNwv3775D2Yfn7cVB4HO/\n/4G0uy8/hypSQrbVdgGAVv062H6u7l8J3/R4R7OPWYatefOOz2GGGZ1uPUHk7448WRQEQRAEweW4\n16Jz/s7IYFEQBEEQBJejCDJYdBYyWBQEQRAEweWQJ4vOw3CwaDb8WM/7dSf72xNkrGLkZzPymulh\n1Omc4e0zG2iu7q9XR7Oh6GY9cPa0nepTNdtW9gRLG/k9jXAk0NzsF5E94eJmPYpGHlO9z5cz2sbZ\n/LR6le1nSxUOLi68wv60pvez72v5Zm1wsXpMRDQHF19Wgotb1OMQ4U17VpH2rMCzBFW/IQAkLppH\n+vM3PyG9YE4i6SLFB+npwT4xq443tPAC+wkbPNKQ9O6FHDztVTWQ9BczviL9r3+8oinjvx//l/S6\nlatJq32sQxcO4V6TuJL31/Es9hsQR9rPm9t3zCfcdm6e/J2u+iS37uegaRRq78+Y0R+QfuldDuE+\ncYYDtNsPu490RofmpPcmclsDgEd5vg6vGmVJJx85wdVU+mmTzm1IX72m9fbVrBxBuiCDva194vuT\nnj9hFultyzjQ3Hpe642t1rsx6QtZHAYfFMDX1aNvL9JLZy4grX5e1M8TABw8cdj2c2EFbUi1I8hg\n0XnIk0VBEARBEFwOGSw6DxksCoIgCILgcshg0XnIYFEQBEEQBJfjbiz356qYGizq5eWZzRs060/T\n83kZ7WPk/VOPt+e6jPIhjTL27PHdqRj5z+zxkqnZgOo57KlnaRzxdzrbx6pXDyOvnyOe0jvt20Z1\n0MOofdXrNGorvUxEs3mef0XOYvaWM7afW43sQtsKrOzt27V+G2l3T+1CVCP/8xzpb7/9lnco5GsI\natyatJqr2Koj+9c2jluqKTNyRBPS363k7LnaLRuQLleGsx6Xfb+QtCVcyS8E4NcslPSBzbtJu3vz\nV3pozXDSFy+z92ztzo2aMu7vzKtJbJjD/k0PJedy7byfSPce1o/04kmcmwkAPt6cL5h+OZN00dV8\n0lA+Fm5efP86tu5A+lDyEU2Z4+dPJu0byt5YD3duu5Sz/LlIWs9treYZAlp/5pOPPU76m88m8DkC\nOK/wSOoxPqGON/aRDj1Ie5bjtvT34wxLdx8l81DJ4vSsxPsDQNrW46Rb1mdP79E/2HtZPpDzPlt1\nb0d66/y1pNVcTQCo2bbEJ1m5TLhmuyPIk0XnIU8WBUEQBEFwOe7FFVz+rshgURAEQRAEl0OeLDoP\nGSwKgiAIguByyGDRedzxYNHIE6diNtdPz4tmj6ftdmWa3a6H2Xrbk7Fn1iumei31/G5qPYzWzTa6\nDiPPo94+Kn9Gbp89XsrS2HPP79R7ac86z0btaXQOs/cLMN+P/oqcxdI+uBqVeM3zRVPZ8xbckrdf\nvcyZiQCw4zD7y8Ib8DFXsnm93IUfziRdscftcxk9yrDXDADCyit+wt8PkVb7h5oHm3+a1y6u0Fjr\npa4ayr/bMXsN6fse43Wcd63bqjlHaQojtRmIBxW/n09d9qMFBZcnferHfaTVbMCKMbU0ZRxJYW/e\n9sXsnazbkT1yB6ZzNmD7F3kd7eqV+HOyei1nQwKAeyDfM4sn//m7lsl9Yu0abluPIPYoFhforA2d\nx37A4KAKpN3c+bNlvcR5gs1jOWcx+/o1TRlz1ywiHdO7I+nvxrI38/44Xgt63ZfK8f9gDyQAbP6G\nszIvXeW2OTDvN9KtBnMd1LYNi6mtKUPl4E8lWZlFlesAD99mZzuRwaLzkCeLgiAIgiC4HDIb2nnI\nYFEQBEEQBJdDniw6DxksCoIgCILgcshg0XkYDhZL+5f0PFfVq7MXyKwPT8XIk+VIGY54sMz6z9Qy\n1f1Vb6c99TTKdjSb86dXhlFbqvfXKM9Q7xwqZtcDt2fdZr2szNvhyPFmv3hUb6A998eoTLNrdeu1\nnVH7G/mQ/4ycRTdLiX9v2YLFtO3xF0aRnjFxKh/rxWsqA0D4fZVIh5YLIb16znLSvvXYh3ctgz1a\nJ5IzSHf7J69tDGjb5eKxs7yD0n0ys/mz9MAzvUlvmv+Lpoy6/dj/1yqevWJbZnAmYrUevMZv3ao1\nSW9cyr48QLu+cWEWr1/8SP+hpMf/fJh0vep1SG9YoS3j4olzpPsMH0B6yQ+8trBnsB/pvALOYfxl\nG+f4RdTh6wS0HlH1s3Jw23bShYqfsExH/vy6eWjzPb292Nc452e+Du867P8sVPIkz2Rwn8lXrhMA\nCgvZZ3ru4nnSXhG8bvPvaSmkVb9t4zq8vjgAbK/yK+lfFyv+TeUce1ewh/HhJx8l3bBmfdJTx3De\nJAB0f6Ikn7OyT4hmuyMUqx86wWHkyaIgCIIgCC6HPFl0HjJYFARBEATB5SiSUG6nIYNFQRAEQRBc\nDnmy6DwMB4ulG9sRz5XqeTPy4amY9aLpYZRdZ8+6wKqPy8irqZah+mXsqZeKPbl9d4p6Xep129N2\n6j026ym1J7tTLdfsmsn2YDbz0J62UTFqmztdH1yv3xn1VfV+/BVfuMWFJWWEN6pB205npJEuSOMc\nvwGvD9ecb8lS9j26ed/+q65Sowguw1pA+oqSs3hZyZ0DgG1K5mHbIZx5uHUpZwW6+3FO328rePvj\nL7JXEwBmTf6WdP+hA0nv8t9E+vxRvtddWseSLjivzfHrP2wQ6cRvZpG+rGRUqrby5DT+/Kr5kQAw\n9I2nuIxZvI724OHDSM/8nLMDk3ZwtmPRZfZVDnnmCU2ZBYr/b/a4b0nfN4D9n5smsK81ezN/rzV8\n9H5NGQG+vM5yTt510tUq8ef36AHOA+016HHS33yh9fZ1Gs7rYCdOn03aEsL+zoxDXO/6j3CW44rf\ntN7Yyq04FzF1xQHSnkrmJCz8PbPsxyWk33szgbS6hjkA1Agv+dsT7BGo2e4IMlh0HvJkURAEQRAE\nl0MGi85DBouCIAiCILgcMlh0HjJYFARBEATB5ZAVXJyHDBYFQRAEQXA55Mmi8zAcLJY2v+tNqDCa\nlKEG1ZoNZLanTCOTv9EECr1JNEb1UK/LbDi5PceoGIU82zNR507LUNG7LrMTcRwJF1dRJ3Ko12k0\nqcaefmYUWG7Utnp935HA+DvFaAKLMyYHmaXNwAdsP2+bs462tXqpGWm1vheyLmrO51GWDfhFuRxk\nXK4Zf+bP/HaM9KhX/kl62nfTSO/J3KUp01KNTflbF/F1VI2J5P3d+ev3yJwtpM9f5CBwAGjYoQXp\nxG/nkPbw50kzAwbxBJjvps0g7akEcAPaSRqPjhpCet7suXyOirz/mp94woS7r/bPTH4BTyBq8UA0\n6avXeFJM0TXev1bDuqQPLuC2O5x8VFPmH+d5oodPXQ7IvpB1ibRnBW4bNYj62Bae9AEAXfv3Iu3v\nw5NN5o7n9q/YlkPWV2zhtnvgEZ4kBQDzZyeSLi7g7+x6UdzPKlUII/3LghWk3X2098dNmbCithWK\n+DOo/hUoVO7Xii2rSQc1rqwpc8ehksk+1f3DgHqaXUwjg0XnIU8WBUEQBEFwOe7FwWJ2djYmTpyI\n/fv3IzAwEIMGDUJMTIzuvsuWLcOSJUuQl5eH6OhojBw5Ep6enrBarZg8eTKSkpKQnZ2NihUrIj4+\nHk2bNrUde+DAAUydOhUXLlxA7dq18eyzzyI4OBgAUFBQgOnTp2PHjh0oLCxEvXr1MHLkSJQvX163\nHgCgzdUQBEEQBEH4m1NcXPyX/rOHKVOmwGKxYMqUKXjuuecwZcoU3UjBvXv3YvHixXjrrbcwYcIE\npKenIzHxxlPlwsJCBAcHIyEhATNmzMDAgQMxduxYZGTceBuRlZWFTz/9FAMHDsT06dNRq1YtjB07\n1nbuFStW4Pjx4/j000/x9ddfw9/fH9OmTdPUoTQyWBQEQRAEweUoLi76S/8ZkZubi+3bt2PgwIHw\n9vZGZGQkWrZsiY0bN2r23bBhAzp16oQqVarA398f/fr1w/r16wEA3t7eiIuLsz0pbN68OUJDQ5Gc\nnAwA2L59O6pWrYro6Gh4enoiLi4OqampSEu7kVmbkZGBJk2aIDAwEBaLBW3btjXMwDYVyq16nezB\nrCfLyBcGmA9LNgoydsSL6UiQtMqdesXs8ReabSsVo/8t6ZVpFORtNphdrw5GYe1G/U5ta71+ZuQ7\nVc/hDF+k0WdMrYMjofVqGWZD1P8MPDxLvoqKrrPfydubvWLu3h6kG9eO0pzv19UccF2seKyystgP\n2CWevWZffzSO9JAXOfh75phvNGW2j3+I6zCffVqntrIvsnv8w6SPum8jna+ESAPAvpVbSUd2bk76\n5O8nSS/4mcPJPQLZy1m2XiVNGcdO/U5a7Q/B9cJJn17E3r3qfZuS/uOY1tunhlXnKdd67mI66Vrd\n+XHUuTEAACAASURBVJyHF28n/eirHMK9cAb7+gDAI1DpR4q/88SmJNKVOtQhfeUKh5HXr8neQABY\n/vU80u2GdCXdoGsr0kfWcCi3mxf/SW43kr2cAOBfg/2DFQL51eHBdXzO1s+OJF2Uw58vPQpSOKw9\nuGOtW+x5A4sH11v1vW5epQTSW7TPqUIalbRNOZ8gwzraQ5HGTXl3OXv2LDw8PBAWVuIjjYiIwMGD\nBzX7nj59Gq1bt7bp6tWr48qVK8jOzkZAQADte/nyZaSlpdn+Hpw6dYr+pnl7eyMsLAynT59GeHg4\nOnbsiOnTp+PSpUvw8/PDpk2b0KwZe8NVxLMoCIIgCILLca95FnNzc+HryxOnfHx8kJubq7uvn1/J\nBKmbx+Xm5tJg0Wq1Yty4cYiNjUV4+I3/yOXl5SEwkCfc+fr64vr1G/9JCwsLQ4UKFfD000/D3d0d\n1apVw/Dh2pWwSiODRUEQBEEQXI67MVi86SsEgKioKERFlbz58PHxsQ3YbpKTkwMfHx/NedR9c3Jy\nbL+/SVFREcaPHw+LxUKDPR8fH9v+pY+/OeCcMmUKrFYrpk2bBm9vbyxevBgffvghPvjgg1telwwW\nBUEQBEFwOe7GYPHRRx+95bZKlSqhsLAQ586ds72KTk1N1bX6VK1aFSkpKYiOjrbtV7ZsWdtTxeLi\nYkyaNAlZWVl4/fXXKT6uSpUq2LCh5NV/bm4uzp8/b3tNnZqaikGDBsHf/4ZdoGvXrkhMTNR9xX0T\nw8Hinea+GWXoqT4u1Ttm5KkDjL17Rn5CvWtUf2fkPzPyONrTjma9Yka+Sb16GbWF2eu05/6o12WU\n82dPfqSRn1A9h5rDaI9v0sg/aOSLtMd/a/Y6jPy2RvcTMN8HzHpMHWHnhhIvnpeSV6iuwuDmxZ7F\n3Uf3a87XrC17w36bvJJ0vzceJ71s/hI+gWKpOnkmmXTrfh00ZW6cwWU88vxg0kt/WEj6l7XsafSq\nzte9Zjbn4QFAs15tSYeVDyV9dMM+0m4+3FZQ7m3LjlqfkocHH+PlwV6/jTP5Ojs+/wjptRMXka7c\nXespvXCFszH3reCcxI/GjiH95qcJpC2V+Q+anw+/2rNe0r7WK7zCvxv8ygjSc77iDMQLJ8+RVvMi\nO7Zspyljz0+/kd62hT2mqm/SI4ifKKne2tDyIZoycs5mkb72O7flyOefIT1lymTS7srn54E+2izH\nVePmk774K/f/Pv+MJ33pKvs5N/7wE+l2A9jPW8ZPOyBZtbSkX9WvWAu4/wXNPma5115D+/j4oHXr\n1pg7dy6efvppJCcnY9euXXj//fc1+7Zv3x4TJkxATEwMgoKCsGDBAsTGxtq2T548GWfOnMGbb74J\ni4X9t61bt8asWbOwbds2NGvWDPPnz0dERITtNXWtWrWwYcMGNGjQAF5eXli1ahXKly9/y4EiIE8W\nBUEQBEFwQe7F5f5GjBiBiRMnYsSIEQgMDMTIkSNRpUoVZGZmYvTo0Rg7diwqVKiApk2bonfv3khI\nSEB+fj6io6NtTy0zMjKwZs0aWCwWjBo1ynbuUaNGISYmBoGBgXj55Zcxbdo0jBs3DnXq1MGLL75o\n22/o0KGYNm0aXnjhBVitVlSrVg2vvPLKbestg0VBEARBEFyOe+3JIgAEBATg1Vdf1fw+ODgYM2fO\npN/17NkTPXv21OwbEhKCuXPnan5fmkaNGlG2olqH559/3kStZbAoCIIgCIILci8OFv+umBosOpLj\np3qsnLGWtJFXzCi7Ti3DnrWh1TKM1iI2Oh9gfq1hsx5GvTLM1tvofH/GeseOfMDNrtOs4oyMSqPt\nar8D7jzDUG1rZ6x5bXSP9a7jTrl+oCT3sOsrA2jbnLG8ssDAFzlTb/6MHzTn6zWIfXSqF+zYH5wl\n6KV44PzrVCT964xVpHs8q2Nid+e2z83P4zJqlCXt7cWZhxePsPfMq2oZTRGHDh0ifbIse8ks4Xwd\n1gs88/LBPt1I/zx/uaaMvo/xtakexuJ8Xmc7NCiYtHcEZ+RduXBZU8auVM5RdFMyD5PT2Ffbuk0b\nroNyP+d89z3XWfEGAkBRjpV0odKPiwtZq3mELz37IunPxmmf2qjrSRek8RrXfXsPJT37f9lP2GUU\n99txn32hKePRYYNIz0yYSHrTPvZ/lqnB9+f6VZ4lm6Wsww0AUD/iyvdK5RDO2lwynfMl1TzJk2dS\nSIcH83rVAFCneX3bz1XLaNeOdgR7grIF+5Ani4IgCIIguBzyZNF5yGBREARBEASXQwaLzkMGi4Ig\nCIIguBz34mzovyumBot6o3QjP6CRl8wZmW5GPi2jHDlHMhDNrketh1FOolHb2bOusFov1Z9ptu3s\nwWhtaKM+YJQ96Ei91P3V67Snbxtdl9Hxev3MrA/SyE9o1E/1MPLG/hX/Oy+dN5d9ndelLVB8dwVW\n9p71ju+nOd/i7zknzq8J5xH+fojXafYoy/7B7Kxs0p5hfqR/XsJZgwDQ7jFeB1hd2zlX8STmK7l9\nqt/t4X7sXwOAuf+dQjqkD+ckVgllr5enO/sNV83mPMnY/px/BwDzJ7H/76W3XyOtttWiHxaQ7taf\n19nOyuZcQABY9/VS0pW68jrLa3duJN2qPl/n9+Onk+43inP/fpyhnSmq+lIXLubcy6Jc9mJGPtSQ\n9B/n+W9TwSmt1y+qN3sr98/5lXRFJTfREsZ1WjefvbEPDeK2BIBzF9jv6eHP/syjW3gt7gFD2eM4\nawz3Ie/GvL44ABRb+e+4el0L1nE/8qlbgbQ6Dji1itfdrvGENnO2asWSv02VvCtotjuCPFl0HvJk\nURAEQRAEl0MGi85DBouCIAiCILgcxZDBorOQwaIgCIIgCC6HPFl0HoaDxdKeJ0fWiTa6WUZeMnty\n/IzWl3ZGBqLZjEN71o428ijas+5yafTa2mymnpG/0B5PnCO5lrc7Xu/+GfUTs2tY2+OLNDqHM9aG\nvtOMSmd4fs3mezqDFo+WrLW85XteM9kjkD1yvt6s1XVpAaBQWRu4x8CHSS8eN4d05S71SVsVX+TZ\nzdyuwxL+oSkzMTGRtGd5XvfXXVmn2ZrOeXdtBnYk7eWlzQr0COBrP7s/hXSPp0eSnjZ5KulnXuVV\nGyZ9MV5ThppheDo9jXThBW7bqu3Yb3hN8ZxmKutAA0CN3k1Jn9p8hPSlEH/SbaJakrZe5gzL6/lc\np+rR9TRlpp3i67CU4bbMS+Z+dGT1HtLBQeyji+zBdQKAQz/v5DIqstf1cAp7ZRvHch7hnsXscawW\npv2unDqZPYfw5M9vv8Gckzln6izS6trr25X1qwFtxmf8g/1Jv/v5fzXHlCYlWcn/rKKUuYmzIAFg\n5JMlfTfYI1Cz3RFkgovzkCeLgiAIgiC4HPJk0XnIYFEQBEEQBJdDVnBxHjJYFARBEATB5ZAni85D\nBouCIAiCILgcMlh0HoaDxdKmfnsmgpgNeTY7wcIejDqIPWWYnbBiNJlBb3KE2VBnFaPJEXrl3mn7\nmp08ZA9GE0P0Jliox5id2KG2g97xZoPYjbbb88VlNjTdbB3t2ceeIG9ns2/tdtvPljCe3FB0lcOt\nS4f3AsDsb2Zqzle9CwcqHz91knR4Z56UcX5XCmn3AAtpj0CebOJj4ckrAJCXfJl0XBxPNpn7HU+q\nUSca7Nm4g/SDrz6gKcPN4k66UTsOVJ701ljSbYZ0Ju3pwZNs3Hy0fwK8ynM4+MJFHF7tXbcc6YzT\n50g/3oNDoD8a+7GmDM3knzLcvt17dSc9e8Z3pD2U/csHBpFuGckh3gDw497fSecr9+u+ATzBaNtS\nDgbfun4z18GP+wig/byOGs0ToaZ/P4P3d+f9X3jnVdLjP/lCU0bjzq1J75y9jnRaJt+P/FSeuBPc\ntS7psPIcWA8Ah45sI71q21rS97W9j/T6mStIdxvJQfnLPue+HzOC7y8ApJ4r+U4v8A4GtHOUTCOD\nRechTxYFQRAEQXA5ZDa085DBoiAIgiAILoc8WXQeMlgUBEEQBMHlkMGi8zA1WNTzjhl5qIy8e6o/\nSg2qdiSU2wh7QqKd7RWzx0+oXquRf83I6weY9xiqdVDLVO+Pnr/N6NrN+ijVMvXqadY/qPYBe4Kn\njfq2Uds44h80Chs3CtB2RqC2I0HfZim8XBKqPOCFx2nbvEkcKpxyltuofgetPy1pEQcN9/rHANJL\nlFDu4Adqkc7LV0Kf96WTPnDykKbMopwC0leuXSXdrAN7zXy92be38ftVpDfvZ98YADTt3Zb03uUc\nbuymeC13/czbm9drTDq6Y4ymjMvZ7HFLWsleSje2PeL5f3LQ9/9+9Snpomz2nAJA3ZaNSAc1Lkt6\nyfT5pKO6cAD2vjmbSIeUCyY9btw4TZnxw4aQnjnmG9I7Vv9GullX9uVtnfQT6cghvB0AThziIO/0\nS5mkK9Xmz6Ma/r41iUO9VX8iAOyat4F07V7c/9d+/iOX2TuK9Pmfj5KOflEbLp7Xg/v/+inLSN//\n+EOk63Zn7+wf55XvDOVPU7O63A8BYNJnJQHx9cNrA/c/r9nHLDJYdB7yZFEQBEEQBJdDBovOQwaL\ngiAIgiC4HMXqI03BYWSwKAiCIAiC6yFjRadharCo+rwAY4+bkX/NKCvQnhw/R44pjd6jaiNPopGP\nyygj0d59SmPk59TzxBl588zmYtqTH6li1JZG+6tl6pVr5K008u458rpCbVujtrHHt6pyp58nvbY2\n+/kw208dwc29JD9Qbdc2j8Te9tgjm/ZpfudVnTMMf/mZ/YC+kRVIXzvLmXtFuewl865TnvSe39hb\nBgCeSj5hGb8A0ldzskn7+/iRbhfPPrBf17MvDwA8g7xJewRw3mBhNvsmrVdzSRcoHjm9jL3Nizm3\nr/vjj5BePmke6d/PJJOuUov7XFYYezcBYO9cvraHX4gnXe+BpqQPLGHvpbs//+lKy+BswWqN2YMK\nAEdTj5Mu7ZMFgJiBXUhvXf0raa8qZUj//st+TRlt4juR3nv8AOkKgdyP1Cdfah6o3pOxRn3YK5m0\nlL2tnqHcry7u579VaoZo5ZBKmjLWrllD2jeS6713N3szE176H9Kv/+vfXKdy/Nlwd+O8UAAovFzi\nkywqU6DZ7hDyGtppaO+YIAiCIAiCIPx/5DW0IAiCIAguhzxYdB4yWBQEQRAEwfW4B0eL2dnZmDhx\nIvbv34/AwEAMGjQIMTHaCCsAWLZsGZYsWYK8vDxER0dj5MiR8PT0hNVqxeTJk5GUlITs7GxUrFgR\n8fHxaNq0xL5x4MABTJ06FRcuXEDt2rXx7LPPIji4JGJq1qxZWLfuhuWkY8eOGDx48G3rbThYNOv1\nMvI3Gfns1O32+KvuNPPQnvw7Iw/cnfom7amX0XrUjmTqOdszp1cvs21j5D8EjPMGza6rbU+ep1Gu\npVonZ/hWjT4fjqCWeS/ESwS1KbmuDXt4Dd7KoeypUrPp8k9lac7XZHB70vt/YI/coDd43ebEccr6\n0p5KG+UWkm7aqY2mzF0/sNevTtWapH9csID0+2+8S/qNt/9DukM3XqsY0K77e+TIbtLuvvyVXpjF\n9VZ9lN9OmKIpo4WSL/jbge2k/Zqxz/HClUuk2zbmbMBZX07TlAFljevaVbitlicuJu1ZgT1vxTnc\nB5rW4bXAF61aoiny9B/s3fOuwetJb9/E2Zzxjz9GesaHk0h7BGjXho6qyWuOz/yS27fba5wdeCmL\n227fz0q2pof2+6HnSPa2Ji3lert7cR9wV9ewVtajnj5+sqaMB/pxGbuOsi/Y4sFlJJ08TLrYyr7j\n4gLuh9fzrmvKRGGR/s8uxpQpU2CxWDBlyhQkJyfjo48+QkREhCZXee/evVi8eDHefvttlCtXDmPG\njEFiYiLi4+NRWFiI4OBgJCQkIDg4GLt378bYsWMxZswYhISEICsrC59++imefvpptGzZEj/88APG\njh2LDz74AADwyy+/YOfOnfjkk08AAO+//z5CQ0PRpUsXTX1vIp5FQRAEQRBcj+K/+J8Bubm52L59\nOwYOHAhvb29ERkaiZcuW2Lhxo2bfDRs2oFOnTqhSpQr8/f3Rr18/rF+/HgDg7e2NuLg425PC5s2b\nIzQ0FMnJNyabbd++HVWrVkV0dDQ8PT0RFxeH1NRUpKWl2c7dq1cvlC9fHuXLl0evXr1s574VMlgU\nBEEQBMH1KC7+a/8ZcPbsWXh4eCAsLMz2u4iICN23badPn6aEjerVq+PKlSvIzs7W7Hv58mWkpaXZ\nnk6eOnWKjvX29kZYWJgtxUXv3EYJLzJYFARBEARB+JPJzc2Fry9bKnx8fJCbm6u7r59fSQzSzePU\nfa1WK8aNG4fY2FiEh4cDAPLy8ujYm8dfv379lufWq0NpDD2LRv4ys74tI4+cI/6pOy1DL4vObDag\n6qszWtdZr55my1T/J6DXdkYetzv1rzmyXrjZrEejdtArw8jTqKJ3f4x8kGa9mHpt62zvpT0+ViPf\nsHoOtS/r5a3eKVmHz9t+tlTyp22XkzNIt3+K10f2rsXeMwA4ujOJtFdVzl20ePJXX1E+e6rc3Xm7\nV1XO2Dt4+KCmTE+l3lsO8JrKDVtxduDCDbzebplavL6xtxdnKgLA4Z93kY7swmvypqbxvby6nvvH\n7mOcDehbj/MmASC3gNcFvryLv2fUHL92TdnjeE3Jk1T9ngA0jyny8nn96PwU9qE2HHg/6YOL2du3\nXVmTuWp17XeG6ve8ti2NdIthD5BWfXgo4s9F/1HaCQHffTOdtJq92boB369R/36WtJviOXWzaJ/n\nzF+9iMsI4fthzWQ/YEyXdqQ3zlxJ2r0MZ3UCQLUw/syvX/wzH6Pke/rG8nXWi1VyMr9jz/Cuo3s1\nZTYdUFLPiIBwzXaHuAt27MTERNvPUVFRiIoqWZvbx8fHNmC7SU5ODnx8eJ14vX1zcnJsv79JUVER\nxo8fD4vFguHDh9OxN/cvffzNAafeufXqUBqZDS0IgiAIgstxNybvPfroo7fcVqlSJRQWFuLcuXO2\nV9Gpqam3/E99SkoKoqOjbfuVLVsWAQE3JqkVFxdj0qRJ/6+9N4+rqtzb/y/mUVDAGWfNATNLJUwj\nTHMky1DTBm1AszqdOnbqPPWcBk89pzpWlnokjTSnSgU7IKU5gphTkkOamAM44zwhbjaw+f7RL+C6\n18J7L9yWZ/8+7169XlystddnDffa3K513deNixcv4pVXXoFnlYkNIiMjkZWVVaFtNhtOnDhR8Q//\n37bdqlWrq+5DVeQ1tCAIgiAIwnXG398f0dHRWLBgAYqLi5Gbm4ucnBzExsYa1o2NjcXq1atx5MgR\nFBYWIjU1FXFxcRXLP/30Uxw9ehQvv/wyfHx4xHt0dDQOHz6MTZs2wW63IyUlBc2bN694TR0bG4uM\njAycPXsWZ8+eRUZGBm3bDHmyKAiCIAiC+/HHp4IZSExMRFJSEhITExESEoIxY8YgMjISp0+fxvjx\n4zFp0iSEh4ejc+fOGDx4MCZMmAC73Y6YmJiKp5anTp3CqlWr4OPjg7Fjx1Zse+zYsejZsydCQkLw\n4osvYubMmZgyZQratGmDF154oWK9e+65BydOnMBf//pXAEDv3r3Rp0+fq+63R7nmOe3Ro0crfnZm\nnlmr8+VazUQErOcL1mTeYKtzJlvNywP0XjyrWY1mx6HLPNT5HtVtquub+dd0eZCu8Cha/YwzuYoq\nutFh1+qTNNuGiu7+UHHmuHS+SN0+NW7cWFvDKvWfq/RyJVb58gOAT96bQtpLyY27/5Ghhu0tTv6S\n9H1P8Kuh9DkppNW5oMvOsW+vcXwU6eAA9icCxjl2sxevJH3X0L6kS8vYy7cudQXpex8zHtf2feyV\nDPRjr9iurzlzr0lf3u9blDzCpV9wniEAeNdm71LJSfY+dejXhfRNTXkeZnW+6RkfJxlqqH/EH3pq\nFOn5U9n7V17GH7h1MHsYjyt+xHp12P8JANtTOb+z3l2tSYeH8vzHu1LZF3nXkwNJ20vYZwkA62ew\nH3Dwy4+QVs/VlMncttW/IiUnLxtq9HlsMOnMdG43nkFXz1V0XOL97pswyFBj2Vz2RZYpn+kyIo50\nj06cOzpjtpLdqHzHePp5GWo6rlTeg+3qtcSaF780rGOVxm+ah11fL46+uU6/0n8p8mRREARBEAQ3\n5AZ8tPhfinQWBUEQBEFwP6Sv6DKksygIgiAIgvshnUWXcc1zQ6tUHb4NGP2BNfEoqlj1E6oeLNVH\naeZNs5p5qKLuk1rTbB1dDav5hGaf0WXoWT23Og8doPdFquemJvNqq9Qk81BFd27UGq7I2rzW+8OZ\nuaStenxdcT10tOrSvuLngwVcT/U3OUrZ67ck3TgP8MsTeJ7lSZ98zNtUfF3lSoaebzPOZTyxJY90\npxHxhpq+Ppw91+N+nts5e3kmaccVPo5ewweQ3nNwn6FGeAj76nIWZpEe+dKTpFPmfkW6S9tbSNv3\nnzfUCLq3Dem2t7HvcftCzszze5jzIE+c5VzMNj1vNtSIUPyBX0ybTfrex9mv+fXEuaSb1OMcvq1L\n1pM+6ZNvqDnujRdIz5zNvsizxex79GnA+YW9urD/7Z2J7xpq+NRnL+tlG/s91+/gebZ9G/Fc3V7K\nvM4lBUbP4qq5nM/Zrj97SEMCORN0w+eckZj4D56fet4X8ww1VI+hl5LFqM5hrfpUo27tRPrgcSUP\n1qQXdzKrMtfySvMQw/KaIb1FVyFPFgVBEARBcDv+gJhFt0VyFgVBEARBEIRqkSeLgiAIgiC4H/Jk\n0WVIZ1EQBEEQBDdEeouuQttZrGpuNxsUoBvwoAtorsmgDV34sarV9XWDbqqrWxVdYLOKWXi1bmCH\n1fBqdXCR2TZ1A16sDuwxG3ChOw4V9dw4E0StOw5du9K1EbN1dDXU9WsSNq47F7rBJmobMFu/JuHh\n15u8Pfsrfs7fzQM7Bjx0H+klU3jQRkRn44CdmUvYtO8ZzAb9ei14gMTB9O2k4566l3TWbA5bXrNs\nlaHmvya8Q/pvE14l/fgTT5BO/mAa6VaRLUhnpnHYMgB4+PJgH69wDtCuUyuU9AMPcxj54vkLSfs2\nNQ4kuJJ3jvRtcXwudob8QPrHrzmIuPtwHtgTqQxGAYCSMg5BbxnLg2i8PPk4vZWBI98s4kFNXkH8\np6z0rM1Q88Ax/t7v2etO0iuTOIi60YAOpL9cnsr7FMbnHgCad+LBQWsX8OCSsS89Q/qHDB4spA7m\nGjRumKHGksnc/vdt/pn0X8aPJ70pdQ3pXw7z/dW8I4eTA8DelXw/qANeVDPgqhUcQP/XZ/9CeuLU\nD0l7hfCgKAAI6FS34mf/+nUMy2uE9BVdhngWBUEQBEEQhGqR19CCIAiCILgf8mTRZUhnURAEQRAE\n90Oyc1yGR7kmnfjo0aMVP5t5rlT/n+rD03n/rHrNzLDqy1O3aXYKVO+XLhxZdxzOhEDrauq8l2bB\n3+q5UT1xVkPXVcx8krr9trpPZjWshr1fj3Zldf2atDOrAebOeE5196TuejVqZPSgXSsRoys9a0+8\nMI6WzZo0nXT/UfeTXp7OfkIAKC/lNlV2yU767hEcgL1hG4cMBwSxR64g5SfSt47rY6hZp1Zt0mcv\nsvcvonY46UC/ANIrv2V/W7mdQ7sBoOToJdJtBnMgc6O6DUkfPXmM9JmLZ3kfMzlsHADuf+Fh0kum\ns8/x9mG9SG+Yz341nwgOsx73lz8ZauzO20NavR8PHMsnrQZ9n89g313vFxNIqx5TAPBtwNf04SdH\nk953iLeZPXsZ6bgn2bu55tMlhhodh3YnnX+Ev6fq1eXw6n0L2P/ZY9xA0mbfU+smc936Q9jvWT+s\nLukWjfg7Y9lC/rynv/GZUc++d5FelZTGKyhfyf2f5RD1zBWrSZddLCb957+ypxEApkyeXPFz+wat\nkPVaimEdqzR8Jeaat2GF4+9s/F3r/Z7Ik0VBEARBENwPebDoMqSzKAiCIAiC+yGvoV2GjIYWBEEQ\nBEEQqsXSk0VnPFc6L5ku002Xh+cMOn+gM/5BnY9Ot5/OZOxZzfFT0fndzFD322qWoyuuh9UsR2fa\nnS7b0WoupjPoauquL6A/dqseYHUf1PvRrKa6TbXtR0ZGXnW5Syiv3O/GSi6fR7AP6eWp35Ae+cSj\nhs3NfucT/oVi/aofzt4x+9FC0qWB7LHyaRRMum1TztMDgJPn2Fd35gL7A0+dO026bp0IrlGfvX5t\nmrYy1Pjpu82k8zfmkr77T7Gkv8/gjD3VB9n1Yc5EBIDLV4r4F958r/24KYe0f9sw0o5LJaTbNzOe\nqxnJM0hPemsi6RdefZG0ut++kbVId2zFmYiZV4x+wgadmpPe9ssO0o0i2O/pGcjZnBvWcJ5k4M3s\nDQSAA3vY91hewvt95Oh+0r4NuF09EBdP+o1JbxtqBMXw/XHpCLezy8fZK9unG/sPy4t5nx556nFD\njTnTZ5H2DjdmSlZl1SL2iHaP53a49tNvSf+0n7MhAeCe+yp9xI39jee2RsiDRZchr6EFQRAEQXA/\n5DW0y5DX0IIgCIIgCEK1yJNFQRAEQRDcD3mw6DK0ncWqvrmazA2t8wfWxKPozNzBVmo44yXT5fbp\n5gk2Oy6df9AVc/bqro9un6wuB67PNbeK7no4g85raXVec7McTF27UnHm/FfFmRxM3fW41ixOZ4i+\nr9LjlLKaM93u6Kf4n774jvSlIs4eBIxT2XrVYc/V4m95HmCHjecq7nXvPaRXzmefpBmNIhqQXv9N\nJu+Tcin6PcF+wZ+XbyEd1Yv9awDgPZD9m9tWcz7knMXzSXsG8Fe8V132Re7+hT2PAODhyzvqHcF5\nkA4ls3Lsn54mPWNKEunCK5cNNRzFfL73HeW8R8dl9j16BvFxe/jxcant3E/xUQLA6RMnSZeUco1f\n8tlv6KPkMpae4/mmhyU8ZKix6FM+/+pc3mr+Z3kZ6+ztnNN3a5fbDDVsxbwfW7/+nvTdozirQxm+\n3AAAIABJREFUccob75PuPpIzQh0m39dl57mGZyCff6/aiodROY4t234k7aN4TDMXc6YoAIx5vjJf\nta5XqGF5TXBmfILgHPIaWhAEQRAEQagWeQ0tCIIgCIL7IQ8WXYZ0FgVBEARBcD+ks+gytHNDV/WC\nmPnddPP4Wp1T2ZlcPzXn7Vqz6MzQeR10XkD1OMxq6j5jdbmZt8zqvNhWsxudyY+0er2uR7ajVa+f\nGepx6K6HM+1S3S9dDTUvUnf/mNXUnV91m2rO4vXwAU3I/azi52lT/k3LHnqccxR/3s8+ux9XbDBs\nz1HIfjSHknc38sUnSKfMW0DaK4gz9kY9zPswd/EXhpoGo6S6WMkr9PDk9YvzL5B+Zvxzhm0kKeem\n3R2dSB89dZz0qSV8rno+wz7ITV9nGmoMf4aP9cv3kkn3eKw/aTVP8vwlPo72LdoaapQ7uA1tWLGW\ntOoPfHz8U6TnJHMOIJRptPsk8NzfAPBd8tekX37vNdKTpn2s7CTvo1ctX2WxidfvLO93eZny/ap4\n/xxF3E7V74M/v/C8ocaUqVNIJ4wYRjp1caqyTf58uU3JWXxslKHGZ29zO1O3MewFnld70dS5pLsM\nYZ/xD1/wXNFeIX6GmsPGVc5J3tA3HG9EP2VYxyoN/tL1mrdhhYJJW/Qr/ZciTxYFQRAEQXA/bsAn\ni4WFhUhKSsKOHTsQEhKCkSNHomfPnqbrZmRkID09HcXFxYiJicGYMWPg7f1rt23ZsmXIzMzE4cOH\n0aNHDzzzzDP02VWrViEtLQ3nz59Hu3bt8PTTT6NOnToAgPT0dGRlZeH06dOoVasW+vbti8GDB191\nv2WAiyAIgiAI7kf57/y/EyQnJ8PHxwfJycl47rnnkJycbDrD2LZt25CWlobXX38d06ZNw8mTJ7Fw\n4cKK5WFhYUhISECvXr0Mn921axe++uorvPzyy5g5cybq1auHjz/mJ+fPPfccZs2ahVdffRXfffcd\n1q9ff9X9ls6iIAiCIAhuR/nv/J8Om82GzZs3Y8SIEfDz80O7du3QtWtXrF271rBuVlYWevfujcjI\nSAQFBSEhIQGZmZkVy6Ojo9GtWzcEBwcbPpuTk4OYmBhERkbC29sbCQkJ2L17N06e/DU+avDgwWje\nvDk8PT3RqFEjdO3aFbm5xhitqmhfQ1f1ZZj503Rz0Vr1n+nmpa1JTdW3ZbZNXQ3d3M+qP80Zn53u\nOFyRb2fV42b1XJrNE6zLONT5IHXzcpttw2o7c2Z+anUbOj+n2gacuZ66dmbVr6nzPAL6LFSdT/J6\nUFhUmcV39+C+tMzhYI/VDymZpNsNNPqSdqfxHMrqHL3qPM2hN9Unrc5nPOvfn5KOva+3oeaqmTwf\ncfQIzlHcfyyfdNP6jUlv28Z5eTM+nW6o8Zfx40l/9PFHpD2VebR9m4aQ3rQ4k3Svh43ePrUNeQWz\nV0+da/i9j3heZ9UTFzvkMUONd/75T9LdlSzN7HmcpXnoBLfBtt3Zq7nzP5xPuHIJfx4AvOpyXuSB\no/mkB8ZzPmHadPaxxo26l/Sq1GWGGmquYukpnmc7btQg0uu+YS+fRxD/SZ78keKjBJDw8HDSKfN5\nP/sN4RpHThwlvS2NnyDNnT3HUMO3GbebsjNXSPv5cpuIGhRNOudr7vx4Ke2y+wNxhpoLp1buR4fI\nNi7xLN5or6GPHz8OLy8vNGhQmcnavHlz7Nq1y7DukSNHEB1deV6bNWuGCxcuoLCw0LSDWBUPDw/6\nXv/t50OHDqFevXq0bnl5OXbv3o2+ffl7V0WeLAqCIAiC4H7cYK+hbTYbAgL4Hy3+/v6w2Wym6wYG\nVobo//Y5s3VVOnfujI0bN+LQoUOw2+1ISUkBANjtdsO6ixYtAgDExcVddZsywEUQBEEQBDfk93+0\nWNVXGBUVhaioqArt7++PK1f4KW1RURH8/ZUZcUzWLSoqqvi9jptvvhnDhg3DBx98gKKiIgwaNAgB\nAQEIC+OZjZYtW4bs7GxMmDChYuBMdUhnURAEQRAE9+MPeA09fPjwapc1bNgQZWVlKCgoqHgVffDg\nQVOLUpMmTZCfn4+YmJiK9UJDQ7WvoH+jX79+6NevHwDg2LFjSE1NJYvR6tWrkZaWhgkTJhg6kWbI\na2hBEARBENyPG+w1tL+/P6Kjo7FgwQIUFxcjNzcXOTk5iI2NNawbGxuL1atX48iRIygsLERqaiq9\nKnY4HLDb7XA4HHA4HCgpKanwG5eUlODQoUMoLy/H6dOnMWPGDAwaNKjitXZ2dja++uor/P3vfzd4\nGKvD0pNFsxBS1aCvDgLQmfx1od3OBIHXZGCBroZq8ndmQMTVcGYAhS4wW0U9LrP1dQNU1M/ozuX1\nGPygG5xidv10A3PUQUy6gSTq512xDWfaiG6wj4or7h8VXRtxRaC5DntppZdGHWChuw/2rt9p+F3H\nB7qT3vYZDyRQRy6e28GDACKj40h36cvbWzHtP4aatz3CAz/q1okgvflL3oebn+hA2nGllD/fhgfA\nAMCGnTxwp+T0ZdLDH+SA5QUfcHh1eSmf2yIbvxIDgOOnd5Nu2/c20unZS0nHxN5BOvPTDNJrtxlD\n06N63kp63YIVpJ+d8CLp5LmfkS6383F41+FXc47LHHYNAPGPDiH99ZyFpAeMvI/0PaM5d27F3HTS\ntbsav5eKi4tJ2w9eJJ29ZBXpjnF8bu0lvN97Vm011Fj0GQfCd7+X212DMP7jv/TLNNIePvw3uvSM\n0QM34lmlHU3n0O3Ietw2v/j356TLbdyWh774GOm0hYsNNb2qBJZ7+rvqpecNNsIFQGJiIpKSkpCY\nmIiQkBCMGTMGkZGROH36NMaPH49JkyYhPDwcnTt3xuDBgzFhwgTY7XbExMTQU8uUlBSkplYGsGdn\nZ2PYsGEYOnQo7HY7pkyZgoKCAgQEBKBXr1548MEHK9ZdsGABCgsL8corr1T8LjY2FomJidXut7yG\nFgRBEATB/bjx+ooIDg7GSy+9ZPh9REQE5szhkenx8fGIj483rAv8+rq7ulfeQUFBmDhxoukyAJg6\ndaqFPf4V6SwKgiAIguB2XIeZSf9/i3gWBUEQBEEQhGrRPlms6leqibdP9cBZ9Vg54/tSa+q8fzqf\npTP7ofrV1Bo1CdRW98tqoLZZgLO6jq6GDmdCn3XnRuc3dCbgXOdbtRrKrX7ebBu6a6wLH3cm1F5X\nw2o7M/MbqttwJgT9auu7gqperdVffkvLHn2efTSq56rvMA4hBoCVGRzK7NeiNuk187lGhwHdSJ+5\ncJa0lxIrUV7MwdMAEOgfSNpmZy+Yut/fL80k3e/ZBNIr539jqHHUYx/pPo9yUPT5wgukVS+fVzhn\nvG3f/ZOhhuM8++6eHctzzk6eOIn0c399gfTGthz6/MPOHEMN9fWgl7Kfew/vJ92iXWvSuct4mx7g\ndj4wkc8lAHwz52vSgx8bSjp9birpB8c8QrpDP24judnbDTXKy/je8PDm/XrgUX5tmPY1e19VL+2D\nT7N3EAC+/GAm6Y1Ls0nf9WoP0mXnuB2WFbIvsvMo9jwCxsDy8Fv5OyFrKwfIlzvUC8ptPe84fxf6\nNDKO6PXyrbzH/P+/OYyvGXm06DLkNbQgCIIgCO6H9BVdhryGFgRBEARBEKpFniwKgiAIguB+yGto\nl2Gps1gTb58ue071eak1nPFJ6vIKdb48sxw3q15LHWbHoeb4qehy/XTHbVZXV1O3DzofpTM1dB5G\nZzIt1f2y2s50vj2gZr7Tqrgin1Dnt62Jd1b9jCuyMq+VBuGV2XAeIb60bP7nnPE27pXnSc943xgD\n8chzT5KeN419Xqqn6pf17N179B/sLXvtH2+QDurawFBz+14l77GUr4VnEB9X/wSOxFiWsoTXDzB+\nPTuusN+sWQO+vjPfTyLd4u6OpAuLOJexWwfO+QOA5Us4R/GTVD533g2CSCfNmk564L3sIc3N32uo\ncdlWRNojnDMpVy3ifVA9cbW6NiJdVsy5fqvXrTHU9G7I+52zhz2HdW/l74zd+XtI/7x8C+mYIb0M\nNTYsWmX4XVX2H8snHdA4hHRocCjpXw6xdxMAHMqxqm3iwuVLpNVsTQ9fL9JRLdoZalwqKiS95dt1\npHMOnCI95qVnSc/85FPSP+fu4n3wNvYlbIcr/bZ2e6FheY2QvqLLkCeLgiAIgiC4HdJXdB3SWRQE\nQRAEwf2Q19AuQzqLgiAIgiC4H9JXdBnazmJVz5uZ/0k317DqsdJlujnjw9NxrV5AwLpHUbdNs89b\n9ZtZ9RuaoZtnV+cFVPfJGZ+kbj7pmmRUqjWszg/ujG/Paq6lK7I2VZxpq1XR+T8B19wfrmb6rBkV\nP496fDQt++ztf5P29/Ujbch4A3DkBM/13LJHFOlf0tl/BiUDcecBnh+5eN850i2G8NzGAHBByThs\nUL8+19zL2Y2rN2aRVrMGHRftUPGpx1mOXy5N4eUNOb+u4EQB6bJLvE3vm9m/BgA3deVzdfIs+9Mu\nXT7PH/DjbRw+cYy0Okc2AISW8H5s+ornza4Vw3MPl5VxruWFLL7/h/6V20z6V5yZCBiPvWEX4zWs\nysZ5K0nf8Whf0pu+4XxDAOgzinMvM9OWk/55F3v3ypXMw5f/xn7c1175X5M94/uzQUwr0is3Z3IN\n5f7wrsttqGPL9oYKE959i3Spkr15S78Y0mty+FzU7cjffRcu8r0R2cA47/mBQz9X7rPdmGMq/LHI\nk0VBEARBENwPeQ3tMqSzKAiCIAiC+yF9RZchodyCIAiCIAhCtWifLDozN3NVdD4vq5mHzsw9fK0e\nKzNfl86bp3rmrK7vzGfU47C6PqD30en20+qcy85sU+f9cyb3T+et1HkYVd+eM95L3T6oOHOurM4F\nrZ473T46M1+4znupnqvrMTd065srs96272NfV9kl9kut/2kz6fue5ExEAPgmg+dV9lR8dd4R7Nvq\nHh9L+ot/f07arw3PVVuw39hGPWtxjuLBS/mkPXx4H7rezBmHFy6xr2tLEvvdAKBeAvsJG0Vw3uPO\nH3he5i49+pH29uSv/IzPjd4+NaPS4WD/2BfT5/ByJfcvKr4tb9Dk+3XuxGTSI8Y/Tjp1wSLeRAm3\nOZ+6PMf1NxkZpMc9x7l/ADDt3Y9Ib13PvlV1Hmd1/uIfN/xA+v7Rwww10ufz+eydMID0oQJuN3uW\nbyVdXMJt3dPH+DzHpz633dN72SN6WskwVDMNI29vQ/rbDSsMNTrefgvpnL2ZpIOUedB/XLiW9Ph3\nXiE99RP2Hecd+8VQ8+4h/Sv3MaCeYXmNkCeLLkNeQwuCIAiC4HaUS2/RZUhnURAEQRAE90P6ii5D\nOouCIAiCILgf0ll0GZY6i2b+J6s+O132nDNePxV1mzo/oTNYzSPU1TTbB7WGM35Nq+s7c/6qosvF\n1PndnN0vK/tghlpD51HU7YO6PqD3D+qyG1Wc8d/q2lFNroeK1TxI3b3gCrq061zx8xezeS7ogA6c\n0/dj1iZe3i/OsD01j7BWIPvP/Jtzztu6+ezbclxhH16He7qS3j6XMxIB4LbHeK7gvXk8r69vY96H\nPQd5zuSq82MDgHc9nssYAM6t53baaRR7GAO7NiSdd4zXbxjB2Y9+bcMMNZZv4szDOrVqk+7Srzvp\nDZ99Rzr/OLdBNRcTML4eLDh7knSbLh1I/5zBfkH1+tx0F3vs9h/JM9Q07IMyZ3JZIW8TyvI74/uQ\nTpvNvkoA6DuC5/uOqM3nd/ncdNKNe95Eesm6ZaQ79Yo21Ngyl6+PQ8lqHDRmKG/z3wtIH87OJd1m\nZEtDDW8v7ho0HXQz6awZPI95eRlfz115XKNpFNewl/I+A5ylqeZq1hzpLboKebIoCIIgCIL7IX1F\nlyGdRUEQBEEQ3A/pLLoM6SwKgiAIguCGSG/RVUhnURAEQRAEt0Nm+3Md2s5iVXO7MwNF1MEJasCy\n1ZBhZwY7WB3EYTW0G9APCtDtd00Gguj205mBJNd6PXTrm7UJdb+v9TjMrq+6jm5Ai26QhjpAxqyu\nbsCL1YEjZnh6coCueu6s3i/ODE75PQaw6Ni5f3fFz/7NeEBFiRLK3b59O9Lrlq4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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": 13, "metadata": { "collapsed": false }, "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": 14, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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bWcqUyB/94DGLg8dEnj8f+Q0K5wcdTMS2AQAwC8HRVARHAABgXbyOx1QERwAA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\n4kJwBAAAQFwIjgAAAIjL/wMPDrq5cKZvOgAAAABJRU5ErkJggg==\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": 15, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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hKpmZmQgMDERYWBjS09Ph7u6OIUOGoF69h9PaXrlyBSEhIYiMjERycjLKlCmD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\n6RVzdebj7Whfepba78HSuV/d/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"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": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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3erfUxc70yLeAWKNmrwxezi9htpIGfJNdam2s24VsjzRi1j2zrKw7TmzxmkOl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\nNf7CDHOAYQZk5FRGRh2Ugvi3bjZhN5YaNc1OyzZNrUaJSWu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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": { "kernelspec": { "display_name": "Python 2", "language": "python", "name": "python2" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 2 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython2", "version": "2.7.11" } }, "nbformat": 4, "nbformat_minor": 0 }