{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# General material models"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "from sigmaepsilon.solid.material import ElasticityTensor\n",
    "from sigmaepsilon.math.linalg import ReferenceFrame\n",
    "from sigmaepsilon.solid.material.utils import elastic_stiffness_matrix\n",
    "from sigmaepsilon.math.logical import isposdef, issymmetric\n",
    "from sigmaepsilon.solid.material import (\n",
    "    ElasticityTensor,\n",
    "    LinearElasticMaterial,\n",
    "    HuberMisesHenckyFailureCriterion,\n",
    ")\n",
    "\n",
    "hooke = elastic_stiffness_matrix(E=210000, NU=0.3)\n",
    "assert isposdef(hooke)\n",
    "assert issymmetric(hooke, 1e-8)\n",
    "\n",
    "yield_strength=355.0\n",
    "\n",
    "frame = ReferenceFrame(dim=3)\n",
    "stiffness = ElasticityTensor(hooke, frame=frame, tensorial=False)\n",
    "failure_model = HuberMisesHenckyFailureCriterion(yield_strength=yield_strength)\n",
    "material = LinearElasticMaterial(stiffness=stiffness, failure_model=failure_model)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[ 0.00169048, -0.00050714, -0.00050714,  0.        ,  0.        ,\n",
       "         0.        ]])"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "material.calculate_strains(stresses=np.array([yield_strength, 0.0, 0.0, 0.0, 0.0, 0.0]))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00454578, 0.00218466, 0.00447378, 0.00593879, 0.00546288,\n",
       "       0.00251926, 0.00672043, 0.00349326, 0.00330169, 0.00461547])"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "material.utilization(stresses=np.random.rand(10, 6))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1, 6)"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "material.calculate_stresses(strains=np.random.rand(6)).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10, 6)"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "material.calculate_stresses(strains=np.random.rand(10, 6)).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "100.0"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stresses=np.array([yield_strength, 0.0, 0.0, 0.0, 0.0, 0.0])\n",
    "strains = material.calculate_strains(stresses=stresses)\n",
    "material.utilization(stresses=stresses) * 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([1.        , 1.        , 1.        , 1.73205081, 1.73205081,\n",
       "       1.73205081])"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "strains = material.calculate_strains(stresses=np.eye(6) * yield_strength)\n",
    "stresses = material.calculate_stresses(strains=strains)\n",
    "material.utilization(stresses=stresses)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(2.56195691e-15)"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "strains = material.calculate_strains(stresses=np.array([10*yield_strength, 10*yield_strength, 10*yield_strength, 0.0, 0.0, 0.0]))\n",
    "stresses = material.calculate_stresses(strains=strains)\n",
    "material.utilization(stresses=stresses)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Utilization for a single state of strain:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00173154, 0.00161796, 0.00027652, 0.00169012, 0.00167926,\n",
       "       0.00118488])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "strains = 2*np.random.rand(6)/1000\n",
    "strains"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "122.73374966882162"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "stresses = material.calculate_stresses(strains=strains)\n",
    "material.utilization(stresses=stresses) * 100"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Utilizations for several states with bulk evaluation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.00085395, 0.00134484, 0.00071666, 0.00105298, 0.00071055,\n",
       "       0.00113623, 0.00121962, 0.00046218, 0.00080682, 0.0010324 ])"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "material.utilization(stresses=2*np.random.rand(10, 6)/1000) * 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(10,)"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "material.utilization(stresses=2*np.random.rand(10, 6)/1000).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0.0010681 , 0.001052  , 0.00089471, 0.00078132, 0.00098108,\n",
       "       0.0005937 , 0.00108656, 0.00080096, 0.00104349, 0.00110625])"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "material.utilization(stresses=tuple(2*np.random.rand(10)/1000 for _ in range(6))) * 100"
   ]
  }
 ],
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