{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Symbolic Strain Notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "\n",
    "from mechpy.core.symbolic.strain import (\n",
    "    SymbolicStrainTensor,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Symbolic Strain"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Init Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\epsilon_{1} & \\epsilon_{2} & \\epsilon_{3} & \\epsilon_{4} & \\epsilon_{5} & \\epsilon_{6}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[epsilon_1, epsilon_2, epsilon_3, epsilon_4, epsilon_5, epsilon_6]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "e1, e2, e3, e4, e5, e6 = sp.symbols(\"epsilon_1 epsilon_2 epsilon_3 epsilon_4 epsilon_5 epsilon_6\")\n",
    "data = sp.NDimArray([e1, e2, e3, e4, e5, e6])\n",
    "strain_tensor = SymbolicStrainTensor(data)\n",
    "display(strain_tensor.data)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Create Method"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Default Notation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\epsilon_{1} & \\epsilon_{2} & \\epsilon_{3} & \\epsilon_{4} & \\epsilon_{5} & \\epsilon_{6}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[\\epsilon_1, \\epsilon_2, \\epsilon_3, \\epsilon_4, \\epsilon_5, \\epsilon_6]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'standard'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\epsilon_{11} & \\epsilon_{22} & \\epsilon_{33}\\\\\\epsilon_{22} & \\epsilon_{23} & \\epsilon_{13}\\\\\\epsilon_{33} & \\epsilon_{13} & \\epsilon_{12}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[[\\epsilon_11, \\epsilon_22, \\epsilon_33], [\\epsilon_22, \\epsilon_23, \\epsilon_13], [\\epsilon_33, \\epsilon_13, \\epsilon_12]]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "strain_tensor = SymbolicStrainTensor.create()\n",
    "display(strain_tensor.data)\n",
    "display(strain_tensor.notation)\n",
    "display(strain_tensor.to_general().data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Voigt notation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\epsilon_{11} & \\epsilon_{22} & \\epsilon_{33} & 2 \\epsilon_{23} & 2 \\epsilon_{13} & 2 \\epsilon_{12}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[\\epsilon_11, \\epsilon_22, \\epsilon_33, 2*\\epsilon_23, 2*\\epsilon_13, 2*\\epsilon_12]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'voigt'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\epsilon_{11} & \\epsilon_{22} & \\epsilon_{33}\\\\\\epsilon_{22} & \\epsilon_{23} & \\epsilon_{13}\\\\\\epsilon_{33} & \\epsilon_{13} & \\epsilon_{12}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[[\\epsilon_11, \\epsilon_22, \\epsilon_33], [\\epsilon_22, \\epsilon_23, \\epsilon_13], [\\epsilon_33, \\epsilon_13, \\epsilon_12]]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "strain_tensor = SymbolicStrainTensor.create(notation=\"voigt\")\n",
    "display(strain_tensor.data)\n",
    "display(strain_tensor.notation)\n",
    "display(strain_tensor.to_general().data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Custom name"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\epsilon^{1}_{11} & \\epsilon^{1}_{22} & \\epsilon^{1}_{33} & 2 \\epsilon^{1}_{23} & 2 \\epsilon^{1}_{13} & 2 \\epsilon^{1}_{12}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[\\epsilon^1_11, \\epsilon^1_22, \\epsilon^1_33, 2*\\epsilon^1_23, 2*\\epsilon^1_13, 2*\\epsilon^1_12]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'voigt'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\epsilon^{1}_{11} & \\epsilon^{1}_{22} & \\epsilon^{1}_{33}\\\\\\epsilon^{1}_{22} & \\epsilon^{1}_{23} & \\epsilon^{1}_{13}\\\\\\epsilon^{1}_{33} & \\epsilon^{1}_{13} & \\epsilon^{1}_{12}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[[\\epsilon^1_11, \\epsilon^1_22, \\epsilon^1_33], [\\epsilon^1_22, \\epsilon^1_23, \\epsilon^1_13], [\\epsilon^1_33, \\epsilon^1_13, \\epsilon^1_12]]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "strain_tensor = SymbolicStrainTensor.create(name=\"\\epsilon^1\", notation=\"voigt\")\n",
    "display(strain_tensor.data)\n",
    "display(strain_tensor.notation)\n",
    "display(strain_tensor.to_general().data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\epsilon^{1}_{11} & \\epsilon^{1}_{22} & \\epsilon^{1}_{33}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[\\epsilon^1_11, \\epsilon^1_22, \\epsilon^1_33]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}2 \\epsilon^{1}_{23} & 2 \\epsilon^{1}_{13} & 2 \\epsilon^{1}_{12}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[2*\\epsilon^1_23, 2*\\epsilon^1_13, 2*\\epsilon^1_12]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\epsilon^{1}_{11} + \\epsilon^{1}_{22} + \\epsilon^{1}_{33}$"
      ],
      "text/plain": [
       "\\epsilon^1_11 + \\epsilon^1_22 + \\epsilon^1_33"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(strain_tensor.normal_components())\n",
    "display(strain_tensor.shear_components())\n",
    "display(strain_tensor.volumetric_strain())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "venv",
   "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": "3.10.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}