{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Symbolic Stress Notebook"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sympy as sp\n",
    "\n",
    "\n",
    "from mechpy.core.symbolic.stress import (\n",
    "    SymbolicStressTensor,\n",
    ")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Symbolic Stress"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Init Method"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\sigma_{11} & \\sigma_{22} & \\sigma_{33} & \\sigma_{23} & \\sigma_{13} & \\sigma_{12}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[\\sigma_11, \\sigma_22, \\sigma_33, \\sigma_23, \\sigma_13, \\sigma_12]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s_11, s_22, s_33, s_23, s_13, s_12 = sp.symbols(\n",
    "    \"\\\\sigma_11 \\\\sigma_22 \\\\sigma_33 \\\\sigma_23 \\\\sigma_13 \\\\sigma_12\"\n",
    ")\n",
    "data = sp.NDimArray([s_11, s_22, s_33, s_23, s_13, s_12])\n",
    "sigma = SymbolicStressTensor(data)\n",
    "display(sigma.data)"
   ]
  },
  {
   "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": [
       "$\\displaystyle \\left[\\begin{matrix}\\sigma_{1} & \\sigma_{2} & \\sigma_{3} & \\sigma_{4} & \\sigma_{5} & \\sigma_{6}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[\\sigma_1, \\sigma_2, \\sigma_3, \\sigma_4, \\sigma_5, \\sigma_6]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'standard'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\sigma_{11} & \\sigma_{12} & \\sigma_{13}\\\\\\sigma_{12} & \\sigma_{22} & \\sigma_{23}\\\\\\sigma_{13} & \\sigma_{23} & \\sigma_{33}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[[\\sigma_11, \\sigma_12, \\sigma_13], [\\sigma_12, \\sigma_22, \\sigma_23], [\\sigma_13, \\sigma_23, \\sigma_33]]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stress_tensor = SymbolicStressTensor.create()\n",
    "display(stress_tensor.data)\n",
    "display(stress_tensor.notation)\n",
    "display(stress_tensor.to_general().data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Voigt Notation"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\sigma_{11} & \\sigma_{22} & \\sigma_{33} & \\sigma_{23} & \\sigma_{13} & \\sigma_{12}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[\\sigma_11, \\sigma_22, \\sigma_33, \\sigma_23, \\sigma_13, \\sigma_12]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/plain": [
       "'voigt'"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\sigma_{11} & \\sigma_{12} & \\sigma_{13}\\\\\\sigma_{12} & \\sigma_{22} & \\sigma_{23}\\\\\\sigma_{13} & \\sigma_{23} & \\sigma_{33}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[[\\sigma_11, \\sigma_12, \\sigma_13], [\\sigma_12, \\sigma_22, \\sigma_23], [\\sigma_13, \\sigma_23, \\sigma_33]]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stress_tensor = SymbolicStressTensor.create(notation=\"voigt\")\n",
    "display(stress_tensor.data)\n",
    "display(stress_tensor.notation)\n",
    "display(stress_tensor.to_general().data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Custom name"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sigma^{1}$"
      ],
      "text/plain": [
       "\\sigma^1"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\sigma^{1}_{11} & \\sigma^{1}_{12} & \\sigma^{1}_{13}\\\\\\sigma^{1}_{12} & \\sigma^{1}_{22} & \\sigma^{1}_{23}\\\\\\sigma^{1}_{13} & \\sigma^{1}_{23} & \\sigma^{1}_{33}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[[\\sigma^1_11, \\sigma^1_12, \\sigma^1_13], [\\sigma^1_12, \\sigma^1_22, \\sigma^1_23], [\\sigma^1_13, \\sigma^1_23, \\sigma^1_33]]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "name = sp.symbols(\"\\sigma^1\")\n",
    "display(name)\n",
    "stress_tensor = SymbolicStressTensor.create(name=name, notation=\"voigt\")\n",
    "display(stress_tensor.to_general().data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\sigma^{1}_{11} & \\sigma^{1}_{22} & \\sigma^{1}_{33}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[\\sigma^1_11, \\sigma^1_22, \\sigma^1_33]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\sigma^{1}_{23} & \\sigma^{1}_{13} & \\sigma^{1}_{12}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[\\sigma^1_23, \\sigma^1_13, \\sigma^1_12]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\frac{\\sigma^{1}_{11} + \\sigma^{1}_{22} + \\sigma^{1}_{33}}{3}$"
      ],
      "text/plain": [
       "(\\sigma^1_11 + \\sigma^1_22 + \\sigma^1_33)/3"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(stress_tensor.normal_components())\n",
    "display(stress_tensor.shear_components())\n",
    "display(stress_tensor.pressure())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Tresca and Von Mises"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\sigma_{11} & \\sigma_{22} & \\sigma_{33} & \\sigma_{23} & \\sigma_{13} & \\sigma_{12}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[\\sigma_11, \\sigma_22, \\sigma_33, \\sigma_23, \\sigma_13, \\sigma_12]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "stress_tensor = SymbolicStressTensor.create(notation=\"voigt\")\n",
    "display(stress_tensor.data)\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "subs using keys"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}\\sigma_{11} & \\sigma_{11} & \\sigma_{11} & 0 & 1 & \\sigma_{12}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[\\sigma_11, \\sigma_11, \\sigma_11, 0, 1, \\sigma_12]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "s_11 = stress_tensor[0]\n",
    "subs = {\n",
    "    1: s_11,\n",
    "    2: s_11,\n",
    "    3: 0,\n",
    "    4: 1,\n",
    "}\n",
    "stress_tensor.subs_tensor_components(subs)\n",
    "display(stress_tensor.data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "subs using symbols"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\left[\\begin{matrix}0 & 0 & 0 & 0 & 1 & \\sigma_{12}\\end{matrix}\\right]$"
      ],
      "text/plain": [
       "[0, 0, 0, 0, 1, \\sigma_12]"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "subs = {\n",
    "    s_11: 0,\n",
    "}\n",
    "stress_tensor.subs(subs)\n",
    "display(stress_tensor.data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle 2 \\left|{\\sqrt{\\sigma_{12}^{2} + 1}}\\right|$"
      ],
      "text/plain": [
       "2*Abs(sqrt(\\sigma_12**2 + 1))"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "text/latex": [
       "$\\displaystyle \\sqrt{3 \\sigma_{12}^{2} + 3}$"
      ],
      "text/plain": [
       "sqrt(3*\\sigma_12**2 + 3)"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "display(stress_tensor.tresca())\n",
    "display(stress_tensor.von_mises())"
   ]
  }
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