2022-04-07 18:46:57 +02:00

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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Description\n",
"\n",
"This notebook intends to gather all the functionalities you'll have to implement for assignment 2.2.\n",
"\n",
"# Load libraries"
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import igl\n",
"import meshplot as mp\n",
"import time\n",
"\n",
"import sys as _sys\n",
"_sys.path.append(\"../src\")\n",
"from elasticsolid import *\n",
"from elasticenergy import *\n",
"from matplotlib import gridspec\n",
"import matplotlib.pyplot as plt\n",
"\n",
"shadingOptions = {\n",
" \"flat\":True,\n",
" \"wireframe\":False, \n",
"}\n",
"\n",
"rot = np.array(\n",
" [[1, 0, 0 ],\n",
" [0, 0, 1],\n",
" [0, -1, 0 ]]\n",
")"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Load mesh\n",
"\n",
"Several meshes are available for you to play with under `data/`: `ball.obj`, `dinosaur.obj`, and `beam.obj`. You can also uncomment the few commented lines below to manipulate a simple mesh made out of 2 tetrahedra."
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {
"scrolled": false
},
"outputs": [],
"source": [
"v, _, _, t, _, _ = igl.read_obj(\"../data/beam.obj\")\n",
"aabb = np.max(v, axis=0) - np.min(v, axis=0)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Linear/Non-Linear Elastic Solid\n",
"\n",
"## Instantiation\n",
"\n",
"We first specify the elasticity model to use for the elastic solid, as well as pinned vertices, and volumetric forces."
]
},
{
"cell_type": "code",
"execution_count": 6,
"metadata": {},
"outputs": [],
"source": [
"rho = 131 # [kg.m-3]\n",
"young = 10e6 # [Pa] \n",
"poisson = 0.2\n",
"force_mass = np.zeros(shape = (3,))\n",
"force_mass[2] = - rho * 9.81\n",
"\n",
"minX = np.min(v[:, 0])\n",
"pin_idx = np.arange(v.shape[0])[v[:, 0] < minX + 0.2*aabb[0]]\n",
"\n",
"ee = LinearElasticEnergy(young, poisson)\n",
"neo_ee = NeoHookeanElasticEnergy(young, poisson)\n",
"solid = ElasticSolid(v, t, ee, rho=rho, pin_idx=pin_idx, f_mass=force_mass)\n",
"neo_solid = ElasticSolid(v, t, neo_ee, rho=rho, pin_idx=pin_idx, f_mass=force_mass)\n"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Validate Elastic Energy Gradient (Elastic Forces) using Finite Differences on Elastic Energy"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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tYmKIJ3Basa+C6HBjZ69r7TrRzuJphXxi1nie2XyclY9ujNk+QRCix+H2cMeTW2jocPD7mysYZzXEIy6pGOJ/KJ7LS04qzGLTP32Kz55ZFtxXkmulwZ8YbrG7cLi9lOX3eAKF2RYKs9I52NAjAs2dTk62d/PpuRO4//qF3H7haTR0OPB6B5wbJwhCAtFac8/zO9l8tIVfXruABZMLkm2SITCECMSbXGs6SvXECEvyMqj3P8BrW31x/4kF1l7nTC/O5nBjTzgoMG/gjLI8AAqy0vFq6Oh2J9p8QRDC8ODbh3j+oxN861OzuOKsick2xzAYIlimlFoBrJg5c2ZCrl+amxGcNVzX5vMIQj0B8OUF3t7fENzuEYFcAAqzLAC02J3kZ/X0JX9zXz3feWY7k8ZlMac0h7MnF3L9ksm9REgQhNh4bfdJfv7Kx1xxVhnf/OSsZJtjKAzhCcQzHBSOkrzAXAFH0BMoC+MJ1Hc4sPnbTuypbac0L4OiHF+JaWG278Hf0meVsq3HWmm2O8m2mHl9zyl+8JedHGmyJ2QcgjAW2VPbzrf+tI2zyvP5z2sWyBesYWIIEUg0pSGzhmvbukg3K4qze3e2njHenxz25wX21LUHQ0EABX5PoNXu6nVec6eDgsx0nrr9XO6//hwAGsK0rhYEYfjUd3Rz25pN5FnTeejmCqzp5mSbZDgMIQLxrA4KR2DWcEO7g7rWbsryM/vVFU8v9peJNtpwur0cbLD1EoHQcFAozZ1OxmX7XivK8f3bZBMREIRY6Xb5KoFa7C4eXllBaZ516JOEfhhCBBIdDgrMGj7V3t1voliAqUVZKAWHGjo5UN+By6OZ20sEAuGg3p5Ak62/CDR2ysL2ghALWmu+/+cdbD3Wyq+uXcD88sQ8G8YChhCBRGNNN5OfmU59h4Pa1m4mhukyaE03U16QyeHGTvbW+foIhXoCedZ0TMrXsjaUFnuPCIzLEk9AEOLBA29W88K2Wr572Rw+E1LuLQwfEQE/pXkZ1LV1caq9O6wnAIEy0U721rVjTTcx3T+JDHwN6gqyLAOEg3yeRprZRGFWOk028QQEIVr+urOO/3xtP587eyJfrZyRbHMMj4iAn9I8K3tq23F7da+WEaHMGJ/DoQYbe2rbmTMhr99qYwVZ6b0Sw16vpsXuosjvCQAU5WTQ1Dl8T8Dr1Xztjx/x5sf1wz5XEEYLu0608Y/PbGPhlAL+/fNnSSVQHBAR8DM+N4Na/xyBiYN4Ap1OD1uOtjDXPz8glMI+nkBblwuPV1MYKgLZFhqj8AQ2Hmnm5Z11PPru4WGfKwijgVPt3dy2ZjPjsiw8eNMiqQSKE4YQgURXBwG9Kgv6ThQLcJq/TNTp8fbKBwQozErvlRhu8ucHQj2B4pyMqHICL273rdL5waEm7C5pTSGMLbqcHm5/YjPt3S4eXrk4WNEnxI4hRCDR1UHg6yQaoG/LiAChOYC5YUSgIMtCa4gnEPAKxvUKB1mC4hApLo+X9TvrOK04G5dHs6PRM6zzBcHIaK357nPb2Xmijf++biFzJ/b/2xOixxAiMBIEPIFMf6VQOCbmZ5KR5vsvO31AT6DnAR9IAPcSgewMWu2uYS1Q8251Iy12F99bfjrFORl8dEr6Ewljh//+2wFe2lHH95efzqVzS5NtzqhDRMBPwBMoK7AOmGwymRTTi7OZWpRFTkb/tksFWRa6XV66Xb5v6s2BcFBOb08A+peSDsa67bXkWtNYdvp4PnVGCTsaPDjc4g0Io58Xt9fyX28c4OpzyrnjotOSbc6oRETAT8ATmDhAPiDAVy6ewV3Lwjey6ztruNlfBRTYD1AcmDAWYXK42+Xhtd2nWD5vAhlpZi6dW0q3Bz441BzR+YJgVLYfb+U7z26nYmoh9119plQCJYikdhFVSpmAnwJ5wGat9Zpk2RKYNTzQHIEAgy1WPS7QRK7TRVl+Jk2dvsZxoVUMgYZzkZaJVu2rx+ZwB1dEu2BmMRlmeH3PSS6ePX6IswXBmNS1dXH7E5sZn5vBgzctIiNNKoESRdSegFLqUaVUvVJqV5/9y5VS+5RS1Uqpu4e4zFVAOeACaqK1JR5Y08187uyJMcUce5rI+b7lt3Q6GRcSCoKeSqFIJ4y9uL2O4hwL551WFLRzfrGvI6ksYCOMRuxON7et2Uynw80jKxcHvzgJiSEWT+Bx4DfAE4EdSikz8ABwKb6H+ial1DrADNzX5/xbgTnA+1rrB5VSzwF/i8GemPmv6xbGdH4g7NPsF4GmkNnCAQIf6MYIykQ7HW7e2HuKLy6eTJq5R6/PKTGzZaeD57bUUN1g49XdJ1k+bwL3XH5GTPYLQrLxejXf/tN29tS188jKCuZM6D8fR4gvUXsCWuu3gb6B6SVAtdb6kNbaCawFrtJa79RaX9Hnpx6fULT4zzV8prNvE7nmTifjsnpXGuVZ00g3q15lom6PlyffP0KXs/d/QdW+BhxuL5f36Y2yYHwaZpPie3/ewWPvHkZreOSdwxxvlnUKBGPzq9f388ruk/zT5WdwyelSCTQSxDsnUA4cD9muAZYOcvzzwP1KqQuBt8MdoJRaDawGKC0tpaqqKmrjbDZbTOcPhdsfntm6ex+Tuw9T12ynAHu/e+akwa4DR6myngRgV6Ob/9zsYM++A1w2rUc01mzrJs8C9qM7qDoWkhRzdnLbfCtur+ac0jQcHs333tL88KkNfHm+sVznRL8nI8loGUuyxvFerZuHdji4aFIaM9xHqao6FvM1R8t7AokbS7xFIFz6fsDAtdbaDqwa7IJa64eUUnXAitzc3EWVlZVRG1dVVUUs50dCdtUrFJRM4uKLz8D2xivMmzmFysreYZqJOzZgybVSWbkYgIPvHAb2sLU1g59dfCFKKbpdHr7299e58uwpXLLszH7juOeK3uPY5tjFUx8e494vLWFSYVYihxhXRuI9GSlGy1iSMY4tR1t4/I0PWDp9HA+vWoolLT6Fi6PlPYHEjSXeJaI1wOSQ7UlAbawXHYkZw/EiMGvY7vTgdHt7TRQLUJST0WtNgep6X2vqj092sLvWt3bxu9WNdDo9LJ8/IaL73lk5A5NSPPDmwTiMQhBGjpoWO3c8uZmyfCu/u3FR3ARAiIx4/29vAmYppaYrpSzAdcC6WC86Er2D4kVhtm/WcGCiWDgRKM629OofVF1v4/QJuVjSTDy72RdN++uuk+Ra04JVQUNRlp/JFxdP5tnNx6lpkdyAYAxsDl8lkMPt5ZGVi3s1WxRGhlhKRJ8G3gfmKKVqlFKrtNZu4C7gVWAv8IzWenesRhrJE/B1EnUFE7/jssJ5ApZgiajWmv2nbCycUsin55bywvZa7E5fVdClZ5QO61tRwBu48eEPuW3NJr7z7HZe2VUXn4EJQpzxeDXfWruNA/U2HrjhHGaW5CTbpDFJ1DkBrfX1A+xfD6yP2qIwKKVWACtmzgw/UzeVKMyycLzZHpwt3HeeAPjCQV0uD3anm06Hh7YuF7NKcphRksNLO+q49+W9tNpdXBZhKCjAxIJM7v2H+fxl6wlqW7v58FAz71U3sny+rLwkpB7/8erHvLH3FD+5ch4XycTHpGGI4JuxPAFfO+nAN/2icDmBkAlj1fU2AGaV5vCJmcWU5Vv544fHyEw3RzUj+JqKyTx1+7ms/+aFfOOTs6ht6w6GpgQhVXh283EefOsQN507lZXnT0u2OWMaQ4iAkXICBVkW2rtdNPhj/mFzAiETxgJJ4VkluZhNiqvP8bWlWHb6+JgXzZhX7ut0uutE6v+/CWOHTUea+cFfdvKJmcX8y4q5yTZnzGMIETCaJ6A1HGnsxGI2he02Gugk2mRzcqDeRk5GGqV5PmG4tmIy1nQTVy+cFLMt8yb6/r921YoICKnBsSY7dzy5hcmFWTxwwzmkmw3xCBrVGOIdMJInEKhuONjQSWF2etjOh6FN5A6csjGzJCd43NSibLb9y6f5VBz6pudnpjO1KKufJ/DkB0f5/G/fi/n6gjAcOrpdrFqzCY9X88gti8nPCr9uhzCyGEIEjOQJBJrIHWyw9esbFCCQE2i0OalusDGrT1VEPNdOnT8xn10n2nvte25LDVuOttDW5RrgLEGILx6v5utPb+VwYye/vfGcXqv0CcnFECJgJAL9g1rtrrBJYfA95HMy0jjYYKOhw8Gs0sSVxs0rz+NYs522kH5GO2paAaTXkDBi/Gz9Xqr2NfCTq+Zx/oziZJsjhGAIETBUOChkXkC4pHCAohwLH/oXhplVkrhOifP9eYHd/rzAO9WNaH8jj6NNIgJC4nl64zEeeecwt5w/jS8tnZpsc4Q+GEIEjBQOCp3xOKgIZFs40doFkNBJMvPLeyeH397fEExWH23u7HVsk83BmveOoLWsUyDEh/cPNvHP/7eLi2eP54eflVbnqYghRMBIZFvMpJt9Sd7BPQFfvsCabqK8YPAlLWNhXLaF8oJMdp1oR2vNhgMNXDxnPEXZln7hoGe31PCjdbuDcxeGosvp4ZbHNrKzJvU9NGHkOdLYyZ1/3MK04mzuv2FhrzUxhNRB3pU4o5QKJocHE4HAWsMzS3IwmRK7duq8iXnsOtHGvlMdnGp3cPGs8UwpyuoXDtp/0jdnIVIR+OBwE1X7Gnh9z8m42ywYm3Z/JZACHllZQZ5VKoFSFUOIgJFyAtCTHB4oMex7zecJJDIfEODM8nwONXayfqfvYX3h7GKmjgsjAvXDE4H3Dzb5jm+I7HhhbOD2eLnrqa0cbbLz2xsXMbVIKoFSGUOIgJFyAkBEnkBRiCeQaAJ5gSfeP8Ls0hzK8jOZMi6LurYunG4v4CvhCzz8D0b4UH+3uhGIXDSEscG96/fy9v4G/u1z8zk3wi64QvIwhAgYjYAnMJgIBF4bCREItI9otbu4aJavH9GUomy8mmBy+niznW6XTxAi+Wbf0ulkT1071nQThxs7cXu8CbJeMBJPbzzGY+8e4csXTOO6JVOSbY4QASICCaAwAk9gyfRxXHJ6CUunj0u4PSW51mBbikC3xqlFvtXHjjb5KoT2n/KFgs6ZUsDB+k683sErhD441ITW8A8Ly3F5NMdkzsGY54NDvkqgi2aP558ul0ogoyAikABK8qxkpJmCYaFwlOVn8ugtiwc9Jp7Mn5hPRpqJJX7RmTLOJwKBh/cBf0hn+fwJdLk81LZ1DXq99w42kWUx8/lzfD2OJCQ0tjnWZOfOP2xhalEWv5FKIENhiHfKaInhVRdM55k7zsOc4Kqf4fCPl87m1188O9iSoiQ3A2u6KZgc3n+qg/KCTBZMKgCGfqi/e7CRJdPHMWeCL7F9QERgzNLR7eK2Jzbh1fDwysVSCWQwDCECRksM52els2ByQbLN6MX88nwuP7NncRmlFFPGZQU9gf2nbMwqzQnmKEJFoK6tixt+/wH7/CWkJ9u6OdTQyfkzisi1pjMhz8rBKERg05Fm9jZ5YhmWkGQ8Xs03127jYEMnv/2S9AQyIoYQASExTBmXzbEmOx6v5mCDjTmluRTlZFCYld6rQmjdtlreO9jE6ic302Z38f4hX1VQoAfMzJKcqMpEf/7Xj1mzxzH0gUJKorXmx+t28/eP6/nxlfM4f6b0BDIiIgJjmIAncKSpE6fby6xSX2hnZklOL0/g7x/XU5KbQW1rF19fu5UNBxopyEpnblle8PiD9bYB201sO97Kybbufvvr2ro51anpdLgTMDoh0fx+wyGe/OAod1x0GjedKz2BjIqIwBhmalEWXS4P7/nr/Wf7u5mGikBbl4vNR1v4wqJJ/OtV83l7fwPPf3SC804rCs50nlmSQ6fTQ12fB73Wmv/52wE+98C7/OLVfb1e83o19R3daGBvXe9W10Lq89KOWn62/mM+e1YZ319+erLNEWIgqSKglLpQKfU7pdTDSilZ5WSEmeIvE319bz3QM2dhxvgc/zrJDjYcaMDj1VxyegnXL5nCDUt9td/nz+iZBBQ4LzQ57HB7+PYz2/nV6/tJM6l+fYqa7U5cHp/nsLtWRMBIbD/eyref2c7iaYX88poFCW97IiSWqEVAKfWoUqpeKbWrz/7lSql9SqlqpdTdg11Da71Ba/0V4CVgTbS2CNEx1V8m+sHBJiaPyyTL4usuGpoc/vvH9RRkpbNwSiEAP14xj3v/YT5Xn9Oz/GXfZLLXq7n18U38ZesJvvPp2VxxVlm/ktPQ8JCsgWwcGm0OvvKHLYzPyeDBmyriugCSkBxi8QQeB5aH7lBKmYEHgM8Ac4HrlVJzlVJnKqVe6vNTEnLqDcDTMdgiREF5YSZKgdPjZXZID6PAQ31/vY239jVw8ezxwXJXS5qJLy2dSnbI2slF2RYKstKDIvDK7pO8W93Ev141j7sumUVZQSYn27rxhExAO9XuE4HsdPEEjILL4+Vrf/yI5k4nD960aNDJkIJx6L8KeoRord9WSk3rs3sJUK21PgSglFoLXKW1vg+4Itx1lFJTgDattTwJRpiMNDMT8zM50doVTAoDTMzPJDPdzF8+qqGp08klp5cMchVfueksf3LY49X8+vX9zBifHVxAZGK+FbdX02hzUJpnBeCkXwTOGm9m08kOHG4PGWnyrTKVuW/9x3x4uJlff3FBsB+VYHyiFoEBKAeOh2zXAEuHOGcV8NhALyqlVgOrAUpLS6mqqoraOJvNFtP5qUI8x5FncnAC8LbUUFXV0xK6JFPz0bFWFGCu309V1YFBr5PldvDRKTe/+NPfOFDv4M4FGWx4+y0AGut91T8v/f1dZhT4HvQfHnCigNk5bt73Kp5+uYpp+cYWgdH8+XrzmIs1e5xcOjWNwrZqqqqqk2PcMBkt7wkkbizxFoFwGaJBm9BorX80xOsPAQ8BVFRU6MrKyqiNq6qqIpbzU4V4juOvjTvY23ycKy9e3Ovb3cKTWzm6rZZFUwu54tPnD3mdavMh3np5Ly8eNTG7NIfvfvGiYMKwpLad//5oA2Uz5lLpn7C2vnE743MbOKPUBPu7yJw4i8rFxm44Nlo/X3/be4onX93Msjnj+e3NFYZqCTFa3hNI3Fji/W7WAJNDticBtbFe1GhtI4zE/En55FnT+nUzDWwvGyIU1Pf4E61d/OOnZveqGJlY4AsB1bb2JIdPtjuYkG+lJEuRk5HGrhMSDUxFth9v5a6ntjJvYj6/ueEcQwmAEBnx9gQ2AbOUUtOBE8B1+JK+Qopyw5IpXLlgYr8qj3OmFJJuVlw2b0JE1wnkFOaW5fU7Jz8zncx0c695BKfauplSlIVJuZlblsfuWhH4VON4s51VazZRlGPhkVsqehUDCKOHWEpEnwbeB+YopWqUUqu01m7gLuBVYC/wjNZ6d6xGGq13kJEwmxT5mf0bfp0/s5iP/vnSiNc7mJhv5cZzp/DTz83vVzeulKKswEpdW6gn0M0Ef5J4Xnkee+s6elUPBdh1oo37/zZ4PkKIP50ON7c/sRmn28vjX15CSa412SYJCSKW6qDrB9i/HlgftUVhUEqtAFbMnDkznpcVhiB3GN0glVL82+fOHPD1ifmZ1Lb6PIFul4e2LhcT8v0iMDGfLtcRDjfamNlnuc1/fXEPG480c8fFM7CkSShiJPBqzT/+aRv7T3Xw+JeXjMjCR0LyMMRflXgCxqcsv8cTCEwUC5SLzvevfNY3L7DrRBsbjzQDvvYVwsjwl2oXr+05xQ8/Oze4CJEwejGECEhi2PiUFWRS3+HA6fYG5wgEwkEzxudgSTP1yws8+u7h4O8iAiPD/209wYsHXXyxYjJfvmBass0RRgBDiIB4AsanvMCK1r6ZwoHZwhPyfUtepptNnDEhl4+OtQY7kdZ3dPPi9lpmjPf1p2/rcibH8DHEe9WNfPe57Zw+zsRPPzcfpaQn0FjAECIgnoDxKcvPBHzto/uGgwA+PW8CW4628NOX9qK15g8fHMPt1Xz9klmAeAKJZt/JDu54cgvTi7P5+kKr5F/GEIao+dJavwi8WFFRcXuybRGiIzBXoK6ti5Pt3WRbzL0Sz1+tnEFDh4NH3z2M0+PhlV0nuWROSXCFNhGBxFHf3s0tj20k02LmsS8v4cC2D5NtkjCCiNwLI0LAE6ht9YWDSvN7lxwqpfjRirncfuF0/vDBMRptTr58wfRg+WqbPTIRaOl08u0/baOhQ1YsiwStNd//8w5a7E4e+/Jiygsyk22SMMIYQgQkHGR8sjPSyLOm+TyBtp45AqEopfjB5Wfw/y6dzYoFE7lgZhF5Vp+z2tYV2epjj757mOe3nmDL0ZZBj3tl18leM5jHKs9uruHNfQ18f/npzJsoObexiCFEQBLDo4OJBZl+T8ARVgTAJwRf/+Qs7r9+IUop0swmcjLSIgoH2Z1unvzgKAC2QZasbLO7+MoftvBYSPXRWOREaxc/fWkPS6ePY+V505JtjpAkDCECwuigLN/KidausOGgwcjPTKc1guqgZzYdp9UfNrJ1Dywa22paAahpGbuegNaau/+8A4/W/OILsjrYWEZEQBgxygoyqa7vwO3VA3oC4cjLTKd9CE/A7fHy8DuHWTDJ5y0O5glsO9YK+L4Jj0W01vzq9f1sONDIDy4/I7jMqDA2MYQISE5gdFBekBlcV7h0GCJQkJk+ZDjold0nqWnp4s7KmWSkmegYTASO+/IFJ8agJ+D1an7y4h7u/3s11yyaxJeWGrt9txA7hhAByQmMDspCQkAThhkO6isCx5rs3PmHLfzq9f28c6CRh94+xGnF2Vw6t5Rcaxq27vAioLVm2/FWlIKmTid2Z2QJ59GA2+Plu8/t4PH3jnDrBdP5+efPkglhgjHmCQijg0CZKDCscFA4EXjrQAN/3XWSV3afxD/JmJ/9w5mYTb71CQYKBx1tstNid7F0+jg+PNxMbWtXv6Z1o5V/e3kvf/6ohm9fOpuvXzJTBEAARASEESQwYcykoDgn8kXK87P6i0BDhwOlYOs/X8q2460cb7ZzTcUkAHIG8QS2HW8F4IqzyvjwcDM1LWNDBN7cVx/0AL7xyVnJNkdIIUQEhBEjEAIan5sxrBWq8jPT6XZ56XZ5govfNHQ4KMq2UJBloXJO79XPcjLSBswJbDveSpbF7Fsx7YXdYyI53GRz8L3ndjCnNJfvLZ+TbHOEFMMQOQFJDI8OMtLMFOdYhhUKAl91ENCrQqihw0FxTkbY43My0gf0BLYeb+XM8nzK8jNJM6mEJYf3n+rgG09vxen2JuT6kaK15p7nd9Jmd/Ff153dbwU5QTCECEhiePQwvzyfuRPzhnVOsHVEqAjYHIzPDS8CudbwOQGH28Pe2nbOnlKA2eRb7SxRcwX+vKWGddtrOdZsT8j1I6HT4ebfX/mY1/ac4nvL53BG2fD+34WxgYSDhBHl4Zsrhp2QLAgjAo0dDmYUZ4c9fqDE8O7adpweLwv9TenKCzITFg7a5F8Mp7lz5Ftguzxe1m46zn+/cYBGm4OrF5Zz6wXTR9wOwRiICAgjynByAQH6egJa66E9gTDhoMAksbMnFwJQXpDFu9WNw7ZnKLpdHnae8IUukyEC33l2Oy9sq2XJ9HE8dPMizplSOOI2CMZBREBIefqKQHu3G6fbO6AI5FjTcHq8ONweMtJ6YuDbjrcyIc8aTFCXF2ZyqqMbp9sb1/75O2ragpPiRloEth9v5YVttdxZOYPvXTZHykCFITFETkAY2wREINAXKNAmekBPIMP33aajjzew7XgrC6cUBLcnFWaidc+ax/Fi89Hm4O8t9pETAa01P3/lY4qyLXxtmcwDECIjqSKglJqilFqnlHpUKXV3Mm0RUpe8Pp5AUAQGqg7yt58ODQl1dLs41mznzEk9xQWT/L3za1rim7zdfKSFmSU5ZFnMI+oJbDjQyHsHm7jrkpnkZIiTL0RG1CLgf3DXK6V29dm/XCm1TylVHcGDfTbwstb6VmButLYIoxuzSZEb0k66wTa4J5CT4RON0ORwk833MC7N7SlPLS/0i0Ack8Ner2bzkWYqphYyLtsyYiLg9Wr+/a8fM6kwkxukH5AwDGLxBB4HlofuUEqZgQeAz+B7qF+vlJqrlDpTKfVSn58SYCtwnVLq78CbMdgijHLys3o6iQ4VDsoJEw5q9odlxmX3zFQuy89Eqfg2kqtusNHe7aZi2rgRFYE/f1TDnrp2/t+nZ/fKgwjCUETtM2qt31ZKTeuzewlQrbU+BKCUWgtcpbW+D7ii7zWUUt8BfuS/1nPAY9HaI4xuQvsHNXQ4SDerYK6gL7mBcFCIJ9DqF4GCrJ5zLGkmSnIzepWJPrzhEJPHZXHZvAlR2RkoDa2YWshLO2qDHkgodqebLEvs4RqtNVX7G/j924d472AT88vzuGpBeczXFcYW8Q4clgPHQ7ZrgKWDHP8K8GOl1A3AkXAHKKVWA6sBSktLqaqqito4m80W0/mpwmgZB0Q+Fm93F8fsvmN3HnCQmw5vvfVW2GNPdfpm6W7atpP0+r0AvH/CJyAHdm2l7VCPA5xrcrH7cC1VVS00d3u5t6qL+cVmMhqGN6s5MJaXd3xMnkVxeOdGnB1Oaps9vcZX0+HlX97r4vuLrcwZF9s39t9u6+bDkx4KMxTXzkln2WQ3b78d/v9kOIzFz5cRSNRY4i0C4coR9EAHa613AV8Y7IJa64eUUnXAitzc3EWVlZVRG1dVVUUs56cKo2UcEPlY/lSzhQP1NiorL+axQxuZbHJSWfmJsMc22hyw4Q0mT59JpX/ZxOoNh2DnXi5bdmEvD+L5uq1sPd5CZWUlv3ptH5pq3OnZVFZeGNVYjnd7uWB2McuWLeLdzj1sbTjWa3zrttfifXcrux3juKNy4bDvEaCmxc6Hr7zJzedN5YefnRvXEtex+PkyAokaS7yrg2qAySHbk4DaON9DGIP0DQcN1DcIQnICIeGgFrsTs0kFF64PUF6YSV1rN90uD09v8jmx9e3RlYy2dHs53tzFoqm+yVmF2Ra6XB66nJ7gMSfbfKGnV3efjGjd5IF4/qMTAKy+6LS4CoAw9oj3p2cTMEspNV0pZQGuA9bFelHpHST0EoFBZgsDZKSZSDerXiWizZ0uCrPS+9XOlxdk4vZq/vjhMRo6HCyYlE9Tp3PQxm/NnU4ONtj67T/Q6jtn8bRxABT5k9DNIXMFTrb5WmA73F5e2hHd9yOtNX/+qIbzTitiUqEsDSnERiwlok8D7wNzlFI1SqlVWms3cBfwKrAXeEZrvTtWI6WLqJCflY7T7aXT4aZpCBFQqv/CMq12JwVZ/dcwCJSJPvBmNZMKM7mmwufINvrLUMPxkxd3c8tjG/vtr7X5RCDQqK3QLwItIRVCp9q7mV6UzZzSXJ7dXDPgPQZj89EWjjbZ+cKiSVGdLwihRC0CWuvrtdZlWut0rfUkrfUj/v3rtdaztdYztNb3xsNI8QSEQBz/cGMnXj1weWiAvgvLtNidjAsjAoEJY82dTm5YOiW4BOapAUJCWmveO9hEXWs3WvdOd7U7NYVZ6cHwTMATaAoRgbq2LkrzrFxTMYltx1upru8YdBzheG5zDdkWM585M7oKJkEIxRDBRPEEhIAIBMIwA80WDpCTkd47J9Dp6lUeGiDgCVjMJq6tmExpXkAEwnsCR5rsNHQ4cHs17V2921K0OzRFIXaF9wQclOVb+dzCctJMatjeQJfTw8s767j8zLK4lJkKgiFEQDwBISACB075RWAITyA3o78nUBjGE8iypFFekMkVC8oozsmgJM933YaO8J7ApsM9fYEaO3sLRYdTB7/9Q39PwOvVnGrvpjTfSnFOBstOL+H5rSdweyJfeObV3SexOdx8XkJBQpwwhAgIQkAEqusjE4GckIVltNY+EcgOv67xX752Pj/7hzMBKMrOwKQG9gQ+DBGBvhPB2p26V9VSnjUds0kFPYHGTp8HEVhZ7ZpFk2jocHDTIxt5YdsJul0ehuLPH9UweVwmS/zJZ0GIFUOIgISDhL7hoMFKRKH3wjKdTg8ujy9eH46SXGtw2UWzSTE+N2PAnMDGI01MLfJV5DT1SR63OzVFOT1CYzIpCrPSg57AqTbf8YFW1p86o5TvLZ/DsWY731y7jSX3vsEDb1YPWpm0t66DC2YUYzJJh1AhPhhCBCQcJARE4EhTJ9kWM9lDdMnMsaYFewcFvomHCweFozTPSn1Hf0+grq2L481dfGZ+GQCNIbF+l8dLp8vnSYRSmGUJ3v+kX1gCnoDJpPhq5Uw2fG8ZT922lCXTi/jFq/u4/H828P7Bpn7311rT1jWwRyMI0WAIERCEXGs6SoHLoykeIhQE/pyAwzevINDTP9KHZ8kAnsBGfyjosnmlgG+JywCBB32oJwD0aiIXmCgWqEAKYDIpzp9ZzMMrK3j0lgocbg/X//4DXtlV1+s4u9+jKRigZ5IgRIMhREDCQUKgnTQMXRkEvnBQt8uLy+Olxb8YzUDhoL6UDOAJbDrSTE5GGmeW5/vDPD3HNPrzA8XhRMDe4wmYTapXBVFfLjm9lNe+dTEWs4mt/uUwA7T6J8uFq3IShGgxhAhIOEgA34QxGDopDD0Ly3Q63D3hoAg9gdJcK81hZg1vPNzMoqmFpJlNFOVk9EoMBwSh7wO+tyfgoCQ3A/MQ8fxMi5mCrPR+q5IFOqHmZ0o4SIgfhhABQYCevEBEIhCypkAwHBRhTiBYJmrrHe7Zf8rGkuk9LSF6iYD/96Ls/p5Aq92Jx6s52d4VTAoPxbhsS9CDCdDm3x6ohbYgRIMhREDCQQKEiEAE4aDQNQVa7C6UivzhWeoXgdC8QGCdgIAIFOdm9JonEGgzEc4T8Grf0pgn27qDSeGhKMhKD37zD9Am4SAhARhCBCQcJMBwPYGeJSZbOp3kZ6YPGYYJUOJfgrI+ZK7AxsPNWNJMnOVfo7i4ryfQ6cSs6NelNLCSWXOnk1Ptjog9gcKs/p6A5ASERGAIERAE6ImFDycnYPOHgyINBUFPOKg+ZNbwpqMtnD2pILh0Y1FOBm1drmDeoMnmINei+nUpDYjA8WY7Nod7GJ6ApZ8n0OoXhQLJCQhxRERAMAxR5QQcARGI/NtzUbYveRsIB3W7POw+0caiaYU9x/irgAL5hiabkzxLf08jID576toBhuEJpNNqd/VqUtfa5cSSZsKaLn+2QvyQT5NgGAIiMNRsYQjJCXS7ael0DcsTMJsU43MyguGgHTVtuL2aRVNCRMA/KSyQC2jsDC8CAbHYU+sXgQg9gcIsC26v7tUEr83uoiCz/5oIghAL0oZQMAyXnzmBLpen32SrcAQ8AZvDRavdGezxHykleRmc8s8V2HK0BYBzpvaIQGA+QCAv0NzpYFIYs6L1BAJx/9ZOF3lW/+/28J1QBSEWDOEJSHWQADC1KJtvXzo7om/CWRYzSvk8gWa7k3HZw3t4luRag8tMbjnawmnF2cH4PvRUAQXmBwwUDrKmm8m2mDnS1AkQbFU9FAHxCJ0r0NblkvJQIe4YQgSkOkgYLoHVxRpsTrpd3rCrig1GaV4G9R0OtNZ8dKyllxcAPWGeJpsTu9ON3ekJKwLgm6SmtS/OH2hUNxSFftEKFYHWLpdMFBPijiFEQBCiITcjjZoWO0Cvb/GRUOKfNbz/lI3mTicVfUQgNyMNi9lEo80ZDAkNJAKBCWSRegFAULRaQ8pE2+xOCQcJcUdEQBi15FjTONbsE4HhVAdBz4SxV3adBGBRHxFQSlGUY6HJ5gi2is4dxBOA/o3jBiNcOKi1yyXN44S4IyIgjFpyMtI40eLr3Dn8cJDvgf3XXXXkWdOYMT6n3zFFORYabY7gugJ5GeFFIOCFRJoUBl8llFIEJ4w53B7sTo94AkLcSaoIKKXmKqWeUUr9Vin1hWTaIow+cqzpuL2+OvvhhoMCcxE+PtnBOVMLwy7iUpyTQVPn0OGgwAL3wwkHmU2KPGtP64hAy4j8YYqZIAxF1CKglHpUKVWvlNrVZ/9ypdQ+pVS1UuruIS7zGeB+rfWdwM3R2iII4cgNWXhmuN+gQx/YofMDQinK9nUSDfQQGigcNC5n+OEg8IWwAp6ANI8TEkUs8wQeB34DPBHYoZQyAw8AlwI1wCal1DrADNzX5/xbgSeBHymlrgSKYrBFEPqREyoCw6yqKcq2YDYpPF7dLx8QoNgfDmrscJJtMZNhjp8nAL1bRwSbx4kICHEmahHQWr+tlJrWZ/cSoFprfQhAKbUWuEprfR9wxQCX+ppfPJ6P1hZBCEegf1BuRhqWtOE5vSb/rOEGm4MFkwvCHlOUY8Hh9nKs2T7oQjGzJ+RiMZuYVZo7LBsKs9KD7ayDfYMkJyDEmXjPGC4Hjods1wBLBzrYLyI/ALKBXwxwzGpgNUBpaSlVVVVRG2ez2WI6P1UYLeOAxI6lsc73Ldpq8kR1j2zlJCNHsen9d8K+3nDC92DefqSeXIvCZhv4Pv/7SSsHtn3IgWHc39HhoK7Zd80P/Pf6eMdHNFcnNpUnn6/UJFFjibcIhPOHdZh9vhe0PoL/AT/IMQ8ppeqAFbm5uYsqKyujNq6qqopYzk8VRss4ILFjqTYf4oWDe5lYlEdl5SeGff742W2YlBq45cS+en6/cxMNXZoF08aTk9MZ17G83bGH7Y3HqKyspHrDIdi5l8uWXZjwvIB8vlKTRI0l3l8paoDJIduTgNpYLyozhoVoCDSRG255aIB5E/MH7TkU2sgu0FAunhRmpdPp9OB0e2nrcmFSvZPdghAP4i0Cm4BZSqnpSikLcB2wLtaLSu8gIRoCC8sMd6JYpBTlWML+Hi8KsgOzhp202l3kZaaHLVUVhFiIpUT0aeB9YI5SqkYptUpr7QbuAl4F9gLPaK13x2qkeAJCNAQSw5EuMD9cwjWUiycB8Wqxu2S2sJAwYqkOun6A/euB9VFbFAal1ApgxcyZM+N5WWGUEygRHc5aAsMhI81MrjWNjm63r7V0a3yvH9o6oq3LJRPFhIRgiLYR4gkI0ZCbYE8AevICickJ9ISD2uxO8QSEhGAIEZCcgBANU8Zl8cnTSzjvtMTNQwwsLpOInEBPO2l/OEjmCAgJwBAiIJ6AEA3WdDOP3LKYmSX9m7/Fi4AHkBARCAkHtdolJyAkBkOIgHgCQqoSePiPS0C83ppuxppuosnmpL1bcgJCYjCECIgnIKQqy+dPYOV5U0kzJ+ZPqTDLwtEmO1pL8zghMcjME0GIgQtnjefCWeMTdv2CLAtH/esTSzhISASG8AQkHCSMVQqz0jnqXx1NEsNCIjCECEg4SBirFGZZcLq9gIiAkBgMIQKCMFYJffDnD3NNBEGIBBEBQUhhQmc7iycgJAJDiIDkBISxSm9PQERAiD+GEAHJCQhjlYAnkG0xk56gMlRhbCOfKkFIYQKtI6JdE0EQhkJEQBBSmMDDX0JBQqIQERCEFCYQDpKksJAoDCECkhgWxiqBhWVEBIREYQgRkMSwMFbJs6ZjUjJHQEgchhABQRirmEyKz58ziYtnJ64/kTC2kQZygpDi/OKaBck2QRjFiCcgCIIwhhkxEVBKnaaUekQp9VzIvmyl1Bql1O+VUl8aKVsEQRAEHxGJgFLqUaVUvVJqV5/9y5VS+5RS1Uqpuwe7htb6kNZ6VZ/dVwPPaa1vB64cluWCIAhCzESaE3gc+A3wRGCHUsoMPABcCtQAm5RS6wAzcF+f82/VWteHue4kYKf/d0/kZguCIAjxICIR0Fq/rZSa1mf3EqBaa30IQCm1FrhKa30fcEWE96/BJwTbkPyEIAjCiKO01pEd6BOBl7TW8/3bXwCWa61v82/fBCzVWt81wPlFwL34PIeHtdb3KaWy8XkY3cA7Wus/hjlvNbAaoLS0dNHatWuHN8IQbDYbOTk5UZ+fKoyWcYCMJRUZLeMAGUuAZcuWbdFaV4R9UWsd0Q8wDdgVsn0Nvod5YPsm4P5IrxfNz6JFi3QsvPnmmzGdnyqMlnFoLWNJRUbLOLSWsQQANusBnquxhGBqgMkh25OA2hiuNyDSNkIQBCExxBIOSgP2A58ETgCbgBu01rsTYyoopRqAoyG78oG2AbYDv4fuKwYao7x933sN55hw+yOxfaDfYxnHYHZG8noqjSWW9yTca8PZNvLnq+9237Ek+vM12DGj+fMVbt9IjWWq1jr8tPOBXITQH+BpoA5w4fMAVvn3X45PCA4C/xTJteL5Azw00Hbg9z77BnSJhnuv4RwTbn8ktg8ypqjHEclYBns9lcYSy3sylN2j+fM11FgS/fmK51iM9PlK5lgG+4m0Ouj6AfavB9ZHco0E8eIg2y8OcEy87jWcY8Ltj8T2wX6PhaGuM9jrqTSWWN6TcK8NZ9vIn6++20Yei5E+X+H2jeTffVgiDgeNBpRSm/VAGXIDMVrGATKWVGS0jANkLJEw1mrzH0q2AXFitIwDZCypyGgZB8hYhmRMeQKCIAhCb8aaJyAIgiCEICIgCIIwhhEREARBGMOICABKqblKqWeUUr/190QyLEqpKUqpdf7234O29051lFIXKqV+p5R6WCn1XrLtiRallEkpda9S6n6l1Mpk2xMLSqlKpdQG//tSmWx7YsW/pskWpVSkTS9TEqXUGf735Dml1J3DOdfwIhCPtQ6Az+Dre3QncHPCjB2COI1lNvCy1vpWYG7CjB2COK1BsUFr/RXgJWBNIu0diDi9J1cB5fRMtkwKcRqLBmyAFeOPBeD7wDOJsTIy4vS3stf/t3ItMKwyUsNXBymlLsL3oXxC97S0MOObyRxc6wC4ngHWOvD/+yPADpyvtb5gBEzvR5zG4gGew/fH+qTW+rGRsb438RiL9q9BoZR6BrhNa90+QuYHidN7civQorV+UCn1nNY6Kd5mnMbSqLX2KqVKgV9prZOyImCcxnIWvlYMVnzjemlkrO9NvP5WlFJXAncDv9FaPxWxAYmYhjzSP/TvcHoe8GrI9j3APRFcxwy8YOSxAN8BLvL//pyRx+I/ZgrweyOPA7gRuNb/+5+MPJaQ4yxG/3zha23/X8BrwAuAyahj6XOtl4dz70hXFjMa5cDxkO0aYOlAB/ub4/0AyAZ+kVDLhs+wxgK8AvxYKXUDcCSBdkXDcMcCsApIijczCMMdx/PA/UqpC4G3E2lYFAz3b+Vq4DKgAN9aIKnEsMaitf4nAKXULfg9nIRaNzyG+75U4luuN4NhtvIZrSKgwuwbMO6ltT6Cf+GaFGS4Y9kFpGpye1hjAdBa/yhBtsTCcN8TOz4xS0WGO5bn8YlaKjLszxeA1vrx+JsSM8N9X6qAqmhuZPjE8ACM2FoHI4CMJfUYLeMAGUuqMmJjGa0isAmYpZSarpSyANcB65JsU7TIWFKP0TIOkLGkKiM3lmQmduKUUEnJtQ5kLKNjLKNlHDKW1P1J9lgMXyIqCIIgRM9oDQcJgiAIESAiIAiCMIYRERAEQRjDiAgIgiCMYUQEBEEQxjAiAoIgCGMYEQFBEIQxjIiAIAjCGEZEQBAEYQzz/wH+2y6IsMsU5gAAAABJRU5ErkJggg==\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fd_validation_elastic(solid)\n",
"fd_validation_elastic(neo_solid)"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Validate External Energy Gradient (External Forces) using Finite Differences on External Energy"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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\n",
"text/plain": [
"<Figure size 432x288 with 1 Axes>"
]
},
"metadata": {
"needs_background": "light"
},
"output_type": "display_data"
}
],
"source": [
"fd_validation_ext(solid)\n",
"fd_validation_ext(neo_solid)"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3 (ipykernel)",
"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": "3.9.7"
},
"toc": {
"base_numbering": 1,
"nav_menu": {},
"number_sections": true,
"sideBar": true,
"skip_h1_title": false,
"title_cell": "Table of Contents",
"title_sidebar": "Contents",
"toc_cell": false,
"toc_position": {},
"toc_section_display": true,
"toc_window_display": false
}
},
"nbformat": 4,
"nbformat_minor": 4
}