{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "o1rOnnKOer2R"
   },
   "source": [
    "# Gradient damage as phase-field models of brittle fracture: dolfinx example\n",
    "\n",
    "*Authors: Jack Hale, Corrado Maurini, 2021*\n",
    "\n",
    "In this notebook we implement a numerical solution of the quasi-static evolution problem for gradient damage models, and show how they can be used to solve brittle fracture problems.\n",
    "\n",
    "Denoting by $u$ the displacement field (vector valued) and by $\\alpha$ the scalar damage field we consider the energy functional\n",
    "\n",
    "$$\n",
    "\\mathcal{E}_{\\ell}(u, \\alpha)=\n",
    "\\dfrac{1}{2}\\int_{\\Omega} a({\\alpha})\n",
    "A_0\\,\\epsilon(u)\\cdot\\epsilon(u)\\,dx\n",
    "+\n",
    " \\,\n",
    "\\dfrac{G_c}{c_w} \\int_{\\Omega}\\left(\n",
    "\\dfrac{w(\\alpha)}{\\ell}+\n",
    "{\\ell}\\,\\nabla {\\alpha}\\cdot\\nabla{\\alpha}\\right)dx,\n",
    "$$\n",
    "\n",
    "where $\\epsilon(u)$ is the strain tensor, $\\sigma_0=A_0\\,\\epsilon=\\lambda \\mathrm{tr}\\epsilon+2\\mu \\epsilon$ the stress of the undamaged material, $a({\\alpha})$  the stiffness modulation function though the damage field, $w_1\\,w(\\alpha)$ the energy dissipation in an homogeouns process and $\\ell$ the internal length.\n",
    "\n",
    "In the following we will solve, at each time step $t_i$ the minimization problem \n",
    "\n",
    "$$\n",
    "\\min\\mathcal{E}_{\\ell}(u, \\alpha),\\quad u\\in\\mathcal{C}_i, \\alpha\\in \\mathcal{D}_i,\n",
    "$$\n",
    "\n",
    "where $\\mathcal{C}_i$ is the space of kinematically admissible displacement at \n",
    "time $t_i$ and $\\mathcal{D}_i$ the admissible damage fields, that should respect the irreversibility conditions \n",
    "$\\alpha\\geq\\alpha_{i-1}$. \n",
    "\n",
    "Here we will\n",
    " * Discretize the problme using $P_1$ finite elements for the displacement and the damage field\n",
    " * Use alternate minimization to solve the minimization problem at each time step\n",
    " * Use PETSc solver to solve linear problems and variational inequality at discrete level\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "pnn3YykUer2S"
   },
   "source": [
    "We will consider here the specific problem of the **traction of a two-dimensional bar in plane-stress**, where\n",
    "$\n",
    "\\Omega =[0,L]\\times[0,H]\n",
    "$ and the loading is given by \n",
    "under imposed end-displacement $u=(t,0)$ in $x=L$, the left-end being clamped : $u=(0,0)$ in $x=0$. \n",
    "\n",
    "You can find further informations about this model here:\n",
    "- Marigo, J.-J., Maurini, C., & Pham, K. (2016). An overview of the modelling of fracture by gradient damage models. Meccanica, 1–22. https://doi.org/10.1007/s11012-016-0538-4 "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "XdKu5cCBer2U"
   },
   "source": [
    "## Preamble \n",
    "\n",
    "Here we import the required Python modules and set few parameters.\n",
    "\n",
    "The FEniCS container does not have the `sympy` module by default so we install it using pip."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "id": "XdKu5cCBer2U"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Requirement already satisfied: sympy in /usr/local/lib/python3.8/dist-packages (1.7.1)\n",
      "Requirement already satisfied: mpmath>=0.19 in /usr/local/lib/python3.8/dist-packages (from sympy) (1.2.1)\n"
     ]
    }
   ],
   "source": [
    "!pip3 install sympy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "id": "gVc2omtmfLF6"
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "\n",
    "import dolfinx\n",
    "import dolfinx.plot\n",
    "import ufl\n",
    "\n",
    "from mpi4py import MPI\n",
    "from petsc4py import PETSc\n",
    "\n",
    "import pyvista\n",
    "from pyvista.utilities.xvfb import start_xvfb\n",
    "start_xvfb(wait=0.5)\n",
    "\n",
    "import sys\n",
    "sys.path.append(\"../python/\")\n",
    "from snes_problem import SNESProblem\n",
    "\n",
    "from plots import plot_damage_state"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "k78eeo7yer2Z"
   },
   "source": [
    "## Mesh \n",
    "\n",
    "We define here the mesh and the indicators for the boundary conditions. The function `generate_mesh` uses `gmsh` (https://gmsh.info/)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "id": "S_mNubT0er2a"
   },
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=1024x768 at 0x7F0645466AC0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "L = 1.; H = 0.3;\n",
    "ell_ = 0.1\n",
    "cell_size = ell_/6;\n",
    "\n",
    "nx = int(L/cell_size)\n",
    "ny = int(H/cell_size)\n",
    "\n",
    "mesh = dolfinx.RectangleMesh(MPI.COMM_WORLD, [(0.0, 0.0, 0.0), (L, H, 0.0)], [nx, ny])\n",
    "\n",
    "\n",
    "ndim = mesh.geometry.dim\n",
    "\n",
    "\n",
    "pyvista.OFF_SCREEN \n",
    "topology, cell_types = dolfinx.plot.create_vtk_topology(mesh, mesh.topology.dim)\n",
    "grid = pyvista.UnstructuredGrid(topology, cell_types, mesh.geometry.x)\n",
    "plotter = pyvista.Plotter()\n",
    "plotter.add_mesh(grid, show_edges=True, show_scalar_bar=True)\n",
    "plotter.view_xy()\n",
    "plotter.add_axes()\n",
    "plotter.set_scale(5,5)\n",
    "#plotter.reset_camera(render=True, bounds=(-L/2, L/2, -H/2, H/2, 0, 0))\n",
    "if not pyvista.OFF_SCREEN:\n",
    "    plotter.show()\n",
    "\n",
    "from pathlib import Path\n",
    "Path(\"output\").mkdir(parents=True, exist_ok=True)\n",
    "figure = plotter.screenshot(\"output/mesh.png\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Setting the stage\n",
    "\n",
    "Setting the finite element space, the state vector, test/trial functions and measures.\n",
    "\n",
    "We use $P_1$ finite element (triangle with linear Lagrange polynomial as shape functions and nodal values as dofs) for both displacement and damage. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "element_u = ufl.VectorElement('Lagrange',mesh.ufl_cell(),degree=1,dim=2)\n",
    "V_u = dolfinx.FunctionSpace(mesh, element_u)\n",
    "\n",
    "element_alpha = ufl.FiniteElement('Lagrange',mesh.ufl_cell(),degree=1)\n",
    "V_alpha = dolfinx.FunctionSpace(mesh, element_alpha)\n",
    "\n",
    "# Define the state\n",
    "u = dolfinx.Function(V_u, name=\"Displacement\")\n",
    "alpha = dolfinx.Function(V_alpha, name=\"Damage\")\n",
    "\n",
    "state = {\"u\": u, \"alpha\": alpha}\n",
    "\n",
    "# need upper/lower bound for the damage field\n",
    "alpha_lb = dolfinx.Function(V_alpha, name=\"Lower bound\")\n",
    "alpha_ub = dolfinx.Function(V_alpha, name=\"Upper bound\")\n",
    "\n",
    "# Measures\n",
    "dx = ufl.Measure(\"dx\",domain=mesh)\n",
    "ds = ufl.Measure(\"ds\",domain=mesh)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "mEWA9qYuer2e"
   },
   "source": [
    "### Boundary conditions\n",
    "We impose the boundary conditions on the displacement and the damage field. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def bottom(x):\n",
    "    return np.isclose(x[1], 0.0)\n",
    "\n",
    "def right(x):\n",
    "    return np.isclose(x[0], L)\n",
    "\n",
    "def top(x):\n",
    "    return np.isclose(x[1], H)\n",
    "\n",
    "def left(x):\n",
    "    return np.isclose(x[0], 0.0)\n",
    "\n",
    "blocked_dofs_left_u = dolfinx.fem.locate_dofs_geometrical((V_u.sub(0), V_u.sub(0).collapse()), left)\n",
    "blocked_dofs_right_u = dolfinx.fem.locate_dofs_geometrical((V_u.sub(0), V_u.sub(0).collapse()), right)\n",
    "blocked_dofs_bottom_u = dolfinx.fem.locate_dofs_geometrical((V_u.sub(1), V_u.sub(1).collapse()), bottom)\n",
    "blocked_dofs_left_alpha = dolfinx.fem.locate_dofs_geometrical(V_alpha, left)\n",
    "blocked_dofs_right_alpha = dolfinx.fem.locate_dofs_geometrical(V_alpha, right)\n",
    "\n",
    "zero_u = dolfinx.Function(V_u.sub(0).collapse())\n",
    "\n",
    "with zero_u.vector.localForm() as bc_local:\n",
    "    bc_local.set(0.0)\n",
    "\n",
    "nonzero_u = dolfinx.Function(V_u.sub(0).collapse())\n",
    "with nonzero_u.vector.localForm() as bc_local:\n",
    "    bc_local.set(1.0)\n",
    "    \n",
    "one_alpha = dolfinx.Function(V_alpha)\n",
    "with one_alpha.vector.localForm() as bc_local:\n",
    "    bc_local.set(1.0)\n",
    "                 \n",
    "zero_alpha = dolfinx.Function(V_alpha)\n",
    "with zero_alpha.vector.localForm() as bc_local:\n",
    "    bc_local.set(0.0)\n",
    "\n",
    "\n",
    "bc_u0 = dolfinx.DirichletBC(zero_u, blocked_dofs_left_u, V_u.sub(1))\n",
    "bc_u1 = dolfinx.DirichletBC(nonzero_u, blocked_dofs_right_u, V_u.sub(1))\n",
    "bc_u2 = dolfinx.DirichletBC(zero_u, blocked_dofs_bottom_u, V_u.sub(0))\n",
    "\n",
    "bc_alpha0 = dolfinx.DirichletBC(zero_alpha, blocked_dofs_left_alpha)\n",
    "bc_alpha1 = dolfinx.DirichletBC(zero_alpha, blocked_dofs_right_alpha)\n",
    "\n",
    "bcs_u = [bc_u0,bc_u1,bc_u2]\n",
    "bcs_alpha = [bc_alpha0,bc_alpha1]\n",
    "\n",
    "# setting the upper bound to 0 where BCs are applied\n",
    "alpha_ub.interpolate(one_alpha)\n",
    "dolfinx.fem.set_bc(alpha_ub.vector, bcs_alpha)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "glu29jUver2j"
   },
   "source": [
    "## Variational formulation of the problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "IELp_KKger2j"
   },
   "source": [
    "### Constitutive functions\n",
    "\n",
    "We define here the constitutive functions and the related parameters. \n",
    "These functions will be used to define the energy. You can try to change them, the code is sufficiently generic to allows for a wide class of function $w$ and $a$.\n",
    "\n",
    "**Exercice:** Show by dimensional analysis that varying $G_c$ and $E$ is equivalent to a rescaling of the displacement by a factor \n",
    "\n",
    "$$\n",
    "u_0 = \\sqrt{\\frac{G_c L}{E}}\n",
    "$$\n",
    "\n",
    "We can then choose these constants freely in the numerical work and simply rescale the displacement to match the material data of a specific brittle material. \n",
    "The *real* material parameters (in the sense that they are those that affect the results) are   \n",
    "- the Poisson ratio $\\nu$ and \n",
    "- the ratio $\\ell/L$ between internal length $\\ell$ and the domain size $L$. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "id": "mNpej74per2k"
   },
   "outputs": [],
   "source": [
    "E, nu = dolfinx.Constant(mesh, 100.0), dolfinx.Constant(mesh, 0.3)\n",
    "Gc = dolfinx.Constant(mesh, 1.0)\n",
    "ell = dolfinx.Constant(mesh, ell_)\n",
    "\n",
    "def w(alpha):\n",
    "    \"\"\"Dissipated energy function as a function of the damage \"\"\"\n",
    "    return alpha\n",
    "\n",
    "def a(alpha, k_ell=1.e-6):\n",
    "    \"\"\"Stiffness modulation as a function of the damage \"\"\"\n",
    "    return (1 - alpha) ** 2 + k_ell\n",
    "\n",
    "def eps(u):\n",
    "    \"\"\"Strain tensor as a function of the displacement\"\"\"\n",
    "    return ufl.sym(ufl.grad(u))\n",
    "\n",
    "def sigma_0(u):\n",
    "    \"\"\"Stress tensor of the undamaged material as a function of the displacement\"\"\"\n",
    "    mu    = E / (2.0 * (1.0 + nu))\n",
    "    lmbda = E * nu / (1.0 - nu ** 2)\n",
    "    return 2.0 * mu * eps(u) + lmbda * ufl.tr(eps(u)) * ufl.Identity(ndim)\n",
    "\n",
    "def sigma(u,alpha):\n",
    "    \"\"\"Stress tensor of the damaged material as a function of the displacement and the damage\"\"\"\n",
    "    return a(alpha) * sigma_0(u)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "JHfoqDbLer2n"
   },
   "source": [
    "**Exercise:** Show that \n",
    "1. One can relate the dissipation constant $w_1$ to the energy dissipated in a smeared representation of a crack through the following relation:\n",
    "\\begin{equation}\n",
    "{G_c}={c_w}\\,w_1\\ell,\\qquad c_w =4\\int_0^1\\sqrt{w(\\alpha)}d\\alpha\n",
    "\\end{equation}\n",
    "2. The half-width of a localisation zone is given by:\n",
    "$$\n",
    "D =  c_{1/w} \\ell,\\qquad c_{1/w}=\\int_0^1 \\frac{1}{\\sqrt{w(\\alpha)}}d\\alpha\n",
    "$$\n",
    "3. The elastic limit of the material is:\n",
    "$$\n",
    "\\sigma_c = \\sqrt{w_1\\,E_0}\\sqrt{\\dfrac{2w'(0)}{s'(0)}}= \\sqrt{\\dfrac{G_cE_0}{\\ell c_w}}\n",
    "\\sqrt{\\dfrac{2w'(0)}{s'(0)}}\n",
    "$$\n",
    "*Hint:* Calculate the damage profile and the energy of a localised solution with vanishing stress in a 1d traction problem\n",
    "\n",
    "For the function above we get (we perform the integral with `sympy`)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "id": "ICvBNgFper2n"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "c_w =  8/3\n",
      "c_1/w =  2\n",
      "sigma_c = 19.365\n",
      "eps_c = 0.194\n"
     ]
    }
   ],
   "source": [
    "import sympy \n",
    "z = sympy.Symbol(\"z\")\n",
    "c_w = 4*sympy.integrate(sympy.sqrt(w(z)),(z,0,1))\n",
    "print(\"c_w = \",c_w)\n",
    "\n",
    "c_1w = sympy.integrate(sympy.sqrt(1/w(z)),(z,0,1))\n",
    "print(\"c_1/w = \",c_1w)\n",
    "\n",
    "tmp = 2*(sympy.diff(w(z),z)/sympy.diff(1/a(z),z)).subs({\"z\":0})\n",
    "sigma_c = sympy.sqrt(tmp * Gc.value * E.value / (c_w * ell.value))\n",
    "print(\"sigma_c = %2.3f\"%sigma_c)\n",
    "\n",
    "eps_c = float(sigma_c/E.value)\n",
    "print(\"eps_c = %2.3f\"%eps_c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "bZqaI6gYer2t"
   },
   "source": [
    "### Energy functional and its derivatives\n",
    "\n",
    "We use the `UFL` \n",
    " component of FEniCS to define the energy functional.\n",
    "Directional derivatives of the energy are computed using symbolic computation functionalities of `UFL`, see http://fenics-ufl.readthedocs.io/en/latest/"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "id": "Gc6yeO54er2u"
   },
   "outputs": [],
   "source": [
    "f = dolfinx.Constant(mesh,(0,0))\n",
    "elastic_energy = 0.5 * ufl.inner(sigma(u,alpha), eps(u)) * dx \n",
    "dissipated_energy = Gc / float(c_w) * (w(alpha) / ell + ell * ufl.dot(ufl.grad(alpha), ufl.grad(alpha))) * dx\n",
    "external_work = ufl.dot(f, u) * dx \n",
    "total_energy = elastic_energy + dissipated_energy - external_work"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "5trh5kFJer2x"
   },
   "source": [
    "## Solvers"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "HOXVWrWMer2x"
   },
   "source": [
    "### Displacement problem\n",
    "The $u$-problem at fixed $\\alpha$ is a linear problem corresponding with linear elasticity. We solve it with a standard linear solver. We use automatic differention to get the first derivative of the energy. We use a direct solve to solve the linear system, but you can also easily set iterative solvers and preconditioners when solving large problem in parallel."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Coefficient(FunctionSpace(Mesh(VectorElement(FiniteElement('Lagrange', triangle, 1), dim=2), 0), VectorElement(FiniteElement('Lagrange', triangle, 1), dim=2)), 3)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "E_u = ufl.derivative(total_energy,u,ufl.TestFunction(V_u))\n",
    "E_du = ufl.replace(E_u,{u: ufl.TrialFunction(V_u)})\n",
    "\n",
    "problem_u = dolfinx.fem.LinearProblem(a=ufl.lhs(E_du), L=ufl.rhs(E_du), bcs=bcs_u, u=u,\n",
    "                                      petsc_options={\"ksp_type\": \"preonly\", \"pc_type\": \"lu\"})\n",
    "\n",
    "problem_u.solve()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We test below the solution of the elasticity problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622F2B220>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "load = .6\n",
    "with nonzero_u.vector.localForm() as bc_local:\n",
    "        bc_local.set(load) \n",
    "        \n",
    "problem_u.solve()\n",
    "\n",
    "plot_damage_state(state,load=load)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "yETlzbzzer2z"
   },
   "source": [
    "### Damage problem with bound-constraints\n",
    "\n",
    "The $\\alpha$-problem at fixed $u$ is a variational inequality, because of the irreversibility constraint. We solve it using a specific solver for bound-constrained provided by `PETSC`, called `SNESVI`. To this end we define with a specific syntax a class defining the problem, and the lower (`lb`) and upper (`ub`) bounds. \n",
    "\n",
    "See the [../03-variational-inequalities/VI.ipynb](../03-variational-inequalities/VI.ipynb) notebook for further details"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now set up the PETSc solver using petsc4py (https://www.mcs.anl.gov/petsc/petsc-current/docs/manualpages/SNES/SNESVINEWTONRSLS.html)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "\n",
    "E_alpha = ufl.derivative(total_energy,alpha,ufl.TestFunction(V_alpha))\n",
    "E_alpha_alpha = ufl.derivative(E_alpha,alpha,ufl.TrialFunction(V_alpha))\n",
    "\n",
    "damage_problem = SNESProblem(E_alpha, E_alpha_alpha, alpha, bcs_alpha)\n",
    "\n",
    "b = dolfinx.cpp.la.create_vector(V_alpha.dofmap.index_map, V_alpha.dofmap.index_map_bs)\n",
    "J = dolfinx.fem.create_matrix(damage_problem.a)\n",
    "\n",
    "# Create Newton solver and solve\n",
    "solver_alpha_snes = PETSc.SNES().create()\n",
    "solver_alpha_snes.setType(\"vinewtonrsls\")\n",
    "solver_alpha_snes.setFunction(damage_problem.F, b)\n",
    "solver_alpha_snes.setJacobian(damage_problem.J, J)\n",
    "solver_alpha_snes.setTolerances(rtol=1.0e-9, max_it=50)\n",
    "solver_alpha_snes.getKSP().setType(\"preonly\")\n",
    "solver_alpha_snes.getKSP().setTolerances(rtol=1.0e-9)\n",
    "solver_alpha_snes.getKSP().getPC().setType(\"lu\")\n",
    "\n",
    "# We set the bound (Note: they are passed as reference and not as values)\n",
    "solver_alpha_snes.setVariableBounds(alpha_lb.vector,alpha_ub.vector)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let us known test the damage solver"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622132400>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "solver_alpha_snes.solve(None, alpha.vector)\n",
    "plot_damage_state(state,load=load)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "0udH0Gdfer21"
   },
   "source": [
    "### The static problem: solution with the alternate minimization algorithm\n",
    "\n",
    "We solve the nonlinear problem in $(u,\\alpha)$ at each time-step by a fixed-point algorithm consisting in alternate minimization with respect to $u$ at fixed $\\alpha$ and viceversa, *i.e.* we solve till convergence the $u$- and the $\\alpha$-problems above."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The main idea is to iterate as following solution of displacement and damage subproblem at fixed loading"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration 0\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622F2CC70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration 1\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622F279A0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration 2\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622123070>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration 3\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622F2D9D0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration 4\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F062213B3D0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration 5\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F062213B880>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration 6\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622F2D970>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration 7\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F065FAB2430>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration 8\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622F2CF10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "iteration 9\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622123E20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with alpha.vector.localForm() as alpha_local:\n",
    "    alpha_local.set(0)\n",
    "\n",
    "for i in range(10):\n",
    "    print(f\"iteration {i}\")\n",
    "    problem_u.solve()\n",
    "    solver_alpha_snes.solve(None, alpha.vector)\n",
    "    plot_damage_state(state,load)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We need to add a convergence condition for the fixed point algorithm.\n",
    "We define it the following function"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "alt_min_parameters = {\"atol\": 1.e-8, \"max_iter\": 100}\n",
    "\n",
    "def simple_monitor(state, iteration, error_L2):\n",
    "    #if MPI.comm_world.rank == 0:\n",
    "    print(f\"Iteration: {iteration:3d}, Error: {error_L2:3.4e}\")\n",
    "    \n",
    "def alternate_minimization(state,parameters=alt_min_parameters,monitor=None):\n",
    "    \n",
    "    u = state[\"u\"]\n",
    "    alpha = state[\"alpha\"]\n",
    "    \n",
    "    alpha_old = dolfinx.Function(alpha.function_space)\n",
    "    alpha.vector.copy(alpha_old.vector)\n",
    "    \n",
    "    for iteration in range(parameters[\"max_iter\"]):\n",
    "                              \n",
    "        # solve displacement\n",
    "        problem_u.solve()\n",
    "        \n",
    "        # solve damage\n",
    "        solver_alpha_snes.solve(None, alpha.vector)\n",
    "        \n",
    "        # check error and update\n",
    "        L2_error = ufl.inner(alpha - alpha_old, alpha - alpha_old) * dx\n",
    "        error_L2 = np.sqrt(dolfinx.fem.assemble_scalar(L2_error))\n",
    "        alpha.vector.copy(alpha_old.vector)\n",
    "        \n",
    "        if monitor is not None:\n",
    "            monitor(state, iteration, error_L2)\n",
    "                                 \n",
    "        if error_L2 <= parameters[\"atol\"]:\n",
    "            break\n",
    "    else:\n",
    "        pass #raise RuntimeError(f\"Could not converge after {iteration:3d} iteration, error {error_L2:3.4e}\") \n",
    "    \n",
    "    return (error_L2, iteration)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can test it by solving the problem at fixed problem. We need to reset to zeror the damage field to start"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Iteration:   0, Error: 4.5577e-01\n",
      "Iteration:   1, Error: 1.1046e-01\n",
      "Iteration:   2, Error: 1.4358e-01\n",
      "Iteration:   3, Error: 1.3343e-01\n",
      "Iteration:   4, Error: 1.0460e-01\n",
      "Iteration:   5, Error: 6.6663e-02\n",
      "Iteration:   6, Error: 3.7487e-02\n",
      "Iteration:   7, Error: 1.5170e-02\n",
      "Iteration:   8, Error: 2.0475e-03\n",
      "Iteration:   9, Error: 5.3557e-03\n",
      "Iteration:  10, Error: 6.6910e-03\n",
      "Iteration:  11, Error: 6.4167e-03\n",
      "Iteration:  12, Error: 1.1111e-03\n",
      "Iteration:  13, Error: 6.2454e-04\n",
      "Iteration:  14, Error: 1.4914e-06\n",
      "Iteration:  15, Error: 4.2970e-09\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622F37CA0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "with alpha.vector.localForm() as alpha_local:\n",
    "    alpha_local.set(0)\n",
    "    \n",
    "alternate_minimization(state,parameters=alt_min_parameters,monitor=simple_monitor)\n",
    "plot_damage_state(state, load=load)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Time-stepping: solving a quasi-static problem"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def postprocessing(state, iteration, error_L2):\n",
    "    \n",
    "    # Save number of iterations for the time step\n",
    "    iterations[i_t] = np.array([t,i_t])\n",
    "    \n",
    "    # Calculate the energies\n",
    "    elastic_energy_value = dolfinx.fem.assemble_scalar(elastic_energy)\n",
    "    surface_energy_value = dolfinx.fem.assemble_scalar(dissipated_energy)\n",
    "    energies[i_t] = np.array([t,elastic_energy_value,surface_energy_value,elastic_energy_value+surface_energy_value])\n",
    "    \n",
    "    simple_monitor(state, iteration, error_L2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.00 --\n",
      "Iteration:   0, Error: 0.0000e+00\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622098EE0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.02 --\n",
      "Iteration:   0, Error: 0.0000e+00\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622F36AC0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.03 --\n",
      "Iteration:   0, Error: 0.0000e+00\n"
     ]
    },
    {
     "data": {
      "image/png": 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mXHXVVW+++aZzF/Mbb7wxaNCg6dOn/+hHPwq9ajZhwgT7zhWD4t2iXX7atGmzZs0KKqyUmjp1qnvJsmXLrrvuuunTpz/11FOhx9IpU6aMHj36pz/9qaGPAiAO4QPWT37yExHRWp87d+706dPHjx+fM2fO9u3bIz2a/osvvnjiiScmTZp0//33X7x48Z133nFPB+r3+xctWnTw4ME77rjjuuuuq6io+Oijj37zm9+sWrUqytijdevW7d69e9y4cb179/7GN75RVVVVUlLy+OOPHz169Prrr3fPBLN9+/ZHHnlk7NixhYWFI0eOvHjx4uHDh//1X/91x44d7go3bdpUUlIybty4/v37jxkz5uTJkyUlJbNnz7Ynsmq65q4fQIyUUldfffXEiRP79u27detW9wX6nTt3vv3223feeedTTz31wgsv2MMYRCQrK+s73/nO3XffferUKXcXUdPFu8WdO3euWrXq9ttvnzVr1q9+9auzZ8/ay9u3bz99+vRevXodOnSoR48e9sFz//79r7/++vjx4//5n/950aJFztD4Nm3aTJ48efTo0atWrdq1a5fBjwMgRqpPnz59+vRpvg3YD4cJmhYLAOJSWlpaWloadLwaNGjQk08++de//tUeRZ6ZmZmdnZ2fn9+zZ88OHTqUl5e/9tprr732WtAfcnay+eY3v+n3+w8dOnT48OEOHTr06dOnbdu2a9asOXLkyAMPPBD0qJyHHnooaPB727Ztly5dumbNmueffz6oqVOnTh0zZsykSZPKysoasUVxTc5eUVFx8ODB48ePd+nSpVevXj6fb/78+TfddNOAAQPuueceu7DP5xs/frz9/Iz9+/cfO3asY8eOAwYMyM7OfuuttxYvXszwdiDB7ONV3NM0AEBKGTRokD2NnNa6oqLizJkzBw4c2Lhx48aNG92TAzsqKysXL1783nvv3XrrrT169BgxYkRVVdWhQ4f+9Kc/bdiw4frrr9++fbvZhyjEu8XKysqXX365uLj45ptvvuqqq0aOHHnhwoXt27f/13/91/79+8eNG+d0a4mI/VyyLVu23Hvvvf379y8oKPj000+3bt26YsWKsCM6ACQGPVgAPCBsD1ZaGj58+Pe///2FCxdu2rQp9N28vLxXXnll8+bNv/jFLxLfNgCxsI9XcT8qJ17//d//vWLFiubeCgCkh23btlVVVU2dOjV0LkDLsh555BGllPtBhwBSU7MHrG3btvGUBgCIUXV19bPPPpuVlfX8889PmDChR48eOTk57dq1GzZs2NNPPz1s2LD169eHTh8IINUwBgsAUsu+fftmzZr10EMP3Xfffffdd5+zvKqqatmyZUuXLk1i2wDEiIAFACmntLR05syZhYWFPXr0uPTSSysrK48dO/b+++9fuHAh2U0DEBMCFgCkqL1794Y+ZAyAJzT7GCwAAICWhoAFAABgGAELAADAMAIWAACAYQQsAAAAwwhYAAAAhhGwAAAADCNgAQAAGEbAAgAAMIyABQAAYBgBCwAAwDACFgAAgGEELAAAAMMIWAAAAIYRsAAAAAwjYAEAABhGwAIAADCMgAUAAGAYAQsAAMAwAhYAAIBhBCwAAADDCFgAAACGEbAAAAAMI2ABAAAYRsACAAAwjIAFAABgGAELAADAMAIWAACAYQQsAAAAwwhYAAAAhhGwAAAADCNgAQAAGEbAAgAAMIyABQAAYBgBCwAAwDACFgAAgGEELAAAAMMIWAAAAIYRsAAAAAwjYAEAABhGwAIAADCMgAUAAGAYAQsAAMAwAhYAAIBhBCwAAADDCFgAAACGEbAAAAAMI2ABAAAYRsACAAAwjIAFAABgGAELAADAMAIWAACAYQQsAAAAwwhYAAAAhhGwAAAADCNgAQAAGEbAAgAAMIyABQAAYBgBCwAAwDACFgAAgGEELAAAAMMIWAAAAIYRsAAAAAwjYAEAABhGwAIAADCMgAUAAGAYAQsAAMAwAhYAAIBhBCwAAADDCFgAAACGEbAAAAAMI2ABAAAYRsACAAAwjIAFAABgGAELAADAMAIWAACAYQQsAAAAwwhYAAAAhhGwAAAADCNgAQAAGJaR7AY00lcnGmq5UnX/X2+56z/OuyroXdH1V9fOW/VWFxHlXlc7W6kLriqwrqshWrla6F7X2bqzkaC13D+GFAjUo+r/GPQBXWtp9xKJtq0wS8JupX6TQj6FDrstER38QZydWruiksCOrL+/RZQWVe9TKuUuo5VoUaKUs9naJU4lyt5h2lK1BZQW1xdoL6mtQavaPaGUFldJS7SItkREiSValLacBgT2gVa1m7P/v24VuwGiRcRSgYV2U5Xr01l1W69tQ6BOuyoRkdpPYX9oUa7XVt1OVUc+bXvkeBtBolworag6VZPsVgCelNnR16ZPdrJb0RheDVhV562q866ToFtQfLFcp3T3W0rVvnDilNRb4hS2T7lin+Jcwcsu72Sa2noCP1oqEAGcE11tKqo999adDGsDltJBJVVdjNP20trNuasVV2FXY+pVVdcG98lZapeIqzZVL07VO6WHbreuvA56VyupC09KdFCQqtucs1wrVfuj87lVYBeK0nYB9/cmdvRRzi6vDUOutKSUtr8KJdopYDk72H5XaUtp+5tRSqzAKrr2O9c+O/corZT2iVYilvLb/y58diWiLdGW0pb9WvktEUv89rfqE62U3yeilN8u7xNtiV+JXbNY4q9dUVvit8Teit+nAsFLKe0Tf20BbYkEtijaUuKr/ZJ9SpSIJeJTSon4RJRSPlFKlK92j1qiPvk09/fHewsSpepUTWVZdbJbASCh0uMSoXZ3xwRe6tolfu1aGrRebc+HDvtu3UsV/Fa98irc2lFqa1zJmLYSjwYqbL53PUKHfO2eVpMe3woAeER6BCxbyPkjNDbpCMujrBL/ZsMEl3C1hk91ZjV2C03KXk3XUP0N7rkGC/hNhCetDVRSY6SS9MqCAJAGPBuw/Lq2a8pNB/03Gh1S2N1l5T5FNy0JxdXzFLFwvMsb1HwhKS06SsL842pEJSZ+v4xkQQBAgnk2YNnsmFXvZFj/xGhnI/dVwngv5wVfDQxXv/NuDHVH3a7JGBUt2DWhg6qpVyobXL2hHp2md18Z4dce/90BADSndDlJhGasBjKEDnoR0wU7f1AlkauNVkiUP3RZozQ6QjUb4wPFmkNiElgsEjbMS6dHvyIAeEe6BCwJd1HHPeIqylD34LVCxsuLSEPj3MPXHXZrkcawR2xPpDcaKZUzUMr0ThnIPaZSdMMbSuEvFABaLO8GLC1aB59v6041Uc85daWijdmKaxB6M104i1JtKuekiBIwrN9ENmp4KwnYhogYGgIPAEg87wasWkExK+jP+TCdWK4Vw9QWeSvxCtexEP5smTpRqSVMvpAykcXIEHgAQGpKl0N8mIwV84DxsMOwYh/nHq7K8N1L8QaURgWapPVsNRRcVMPjjZpawMilPSMJLGFD4GO5x5AZsAAg8dIlYEnkAeZh574KvUrYQFVxbTce8Q7JarbbA5v35sHUYCSBJWzSKZ1Ov54A0MKk1xE8ePb2EFHGA8fY4dXooctNHuYVpZ7mXTEGDccvAwVS5dKeEUwNCgDpLb0CloT2J4WdsiF4joZIdw4GCXNKDHNxMNzQK69fHEyL7qtYGJnVM6WmBtWpMykFALQkaRewJMKQdmnMtbwGephimakh8tLIG23MWw1I7uW/pndfmWlFqozQMiWlkhwAwM2zAcuvxd/Q5bqwo92d4BVuGFbEce7SmHwWhbG5Rh3NllEMXP5rshbYCcM1RADwNM8GLJvfH/hfkIb7lhqaoyHqI3HCMnTnYPyjxBrSEk7URhJY4uZVT6VuMABAc/B4wHI02JtlCxO8GnNqjmWmBpHIY+rjv3PQw504qTF6PWG7z8iNiqbUJLsBANBipUvAkpCMFeUJOaFXCUWijXM3dSOhiDRHf1LaT76QMpElpcITA7AAIJV5NmDpcI/KaWCVqLVFENNMCs1952DS5g5tehUJ6Z0yMzVogvJKLIOrCE8A4HWeDVgOd8yK1olVf6FIpPgQPVHFMlNDNMajUlM6qLzQfWXk1oKEPQ45pbq4AABJ5P2AZYuUsVwlGl43tJTZGwkb1UeVulfxGmpY6ra8URI2BB4AkAbSJWBJhIwV6Qk5YYdhRaowlo26xD0/e2MvDjapgyoV4pGJTRjp4vLcbX2xjANMr3wLAB6TRgErihgvEcU7rWj4YuEXp1l3ToKkXXjSMTwE2t9CfisBIK2l16G8gU6s0Afj6HDFgt8J82P8LYv0RpTurubLBQl5dGCsjUkbjEwHADjSK2BJ5H6mWK4J1orlGp+ZZw42VvQNeaO3zMzcoIm69S+VusEAAKnPswFLR5nG0755MMYH6bhWiSBMlgpbd6Q6GpckUjgkJSbAJXBq0ERtyZBYuspqeMYzACSVZwOWza/Fr2O4XBXlKmGDdw4GVxZfV0bks3eUxxE26+j1REiFNohIig3AimVedSZ6AID04PGAZTP0AJyErpgyESRYyjYsREo9OpABWAAAN88GLF2//ydsR5E/Qpl6ZeO8czBskDJ752AD1yujrWpg9HqTmbmAmKicl1JdXACAtOHZgCUi2l8vZkUfShM2tUSc5N3+MbZK4u/0aumn9ISFpxa/pwEAyeLlgGVzx6zQcethhrpHHRpfK+7JQg1pIBE0cfRVGk2+4Lkx3LHNgBXDtciYrlcCAJLM+wHLpmM7p8R852C4TcRRNlo+81oySIJUumwXS+jhOiMAIIhnA1akmBJjhIr3zkEjj8QJV3Mc7zYxmqVIsEuRZogI1xABAM3GswFLRHT9s3WkTiznKmHEPBR1JFbjGmZ8rRTIJakzf2ljnxIJAECCeDlg2dwxy85YDU8c6SoQyyyTYYtEiHNRUkgSA0qi5jMwsB2CEQAgDXg/YNkidk6FzrMQvZ6Y5mUwn1eSPflCYuZ3UOl4Sa4mlnnVjY1ej2FAWIMlAADNz7sBS0eYNKGhTqx6c7g3dHEw3pNVtPKc+BInlm6w2MJKGiZCEfHTTwgAzcy7AUtERLQrZkU5ZYQdhtXoU0ykk1Nj7xxsYLC8R+ZWSNgFULIBACD1eTxg2YIyVtBo9xhPyLHdOdgyT+8JHD2Wnj1GAICWxrMBq8Grew2MXm9oYgaDFwdjGUcfQYNxo8Hokzq3/nGNFADQcng2YEnIo3ICC5t1i5GWezg7eOvRgabENEgrpskgzExDmq6DvQCgxfJywLJpf+D0Xm98VUjw8kd+amHoidTUtKINPpuZZ5rELT3nVY8lYNXE8Nta47WkCwDpyvsBSyI/pNlJTvHdOZgy56imNyRlPkpMLUmd1qY1PzsaAJqfZwNW8Bgqv0hzPl4wQskmPRM6FU5zqdAGAADSjmcDloQ8Kif43UZdfjN352D07OWZ0eskMAAA4uflgGULek5OUKxxj6/yB0WuJt85yAiqBItlrnNDo85jqQcAgEi8H7AkXDBqMCqFuUMs0vSh8benwbUanhq0oRLeuvUvTQdg+XXDvz7+9PgVAwDEyatHf621Dp2WPagTy32V0PRlvhTv30ih6a/QkBpDvW4AgNTh1YBl040bYx73rKQx1ODSxHCTOidSUpq38HUBQOrwdsASd8YKek5OHHcIGr042PDmmlqBkdxDeAIAoPl4NmC5UlED/ViNe1JNtCc3N+3ZzAmQCm2oE0OXXExzncMAzY4EgITwbMCSencFBjJW3R2F4YZhSeiNhIk+bzfcb9T0Aqak7ch0BjwBAJqdlwOWhAtMEnkGrDA9T5EuDkbpvorantSZBR7NjG8aABCFxwOWiPj9tY8ibPK8VoG1It852NT8lIjJFxhclTqYKA0AWizPBix3jKg3HUPMNTRubFYUiUg2pKd0E8tjngEAnuPZgCX1w0aYwVXuOdxjfqJztGfvxNyw5lg9BcXwiehOM8JPCAMAr/FywJLgxxHqSGPb46iu0S1pcpRIqdHrqYbbDAEAnuLZgBV7hGpk2AqqxCOnb480M1nS+HpcTfp+NADwIs8GLAmZU9QfborR0MAR9sZDaYYhWcYrJzwlBNfjAABN5+WA1QiNfLSO6WaEaPL9iUDDagjpAJAoHg9Y2h+IP87gq3pPgI75dNKEfNNgNkqtgd6Gpg9NrQ+VcFyPAwBE5/GAJUF3C7rna4h9kFa0N1Okb8mTgcaLbQYAwAQPB6y65BOapcIMvWqesz1TSTZR+oYwv/bwLxcAoIm8fQ7Q0cezx1ZHo99EYqRGHyIAAHHwdsAKK9wzc5Jx5yASyKOPZ/an4y8gAEA8HLBqU1Tgv06ECjOle1M3EUniTumGRqYDAIDE8GzAkiZfOkqNK08qkaO4WnZQS99PBgBIOV4OWLVco92jvNfoShsvRe5AhKfVePPqJwC0cJ4NWHZ2iZ5gjDwkJ3oDAAAAQng2YDma+oDnqHWi0by5C9P4YYUAgETycsByJaowiSjKCT7S4wjNatkDngAAaMm8HLAiCzNTg+kNNG/9Lunco0K+NIT5RgAg1Xg1YAV6r+z/xBV3GizsxXOVF9sMAED68mrAiiYxVwC9Jp17whLLo5OaAgASycMBq14nVt3SZDQFAADAxcMBCy0CiRkA4EHeDVjhrgMamKkhhvN5DEUUsQAAgBbMuwFLpH6ganikO7daAQCAhPB2wPI0RkoDAJCuPB2w4uq/AgAASBBPBywAAIBURMACWgTNDZkAkEAZyW5AI7XunZV5yi8iKjCUyRJlv1YiIlbtACelasc6+UVUbZ7Ugdv8lFPMfu3+sfY/rsWiRCvXD0q0uN9VgbXc5Z0WBzatdF39Afa8ldrdGKlfILBp19uuGoKvjmoJ3YT9ul5r7e2GlAnetHKtG6Fa57Wu/Xza/W5wtTrCRnWkNgT2qNJ1DbH3gaptWm3NgQ0Gv6tV0FctWqm6naHsmpV2/tpwClhKnH8ZSinlxBSla0SUiF+0/VpELNEi2v6nZ9UWswI7Rlt1m3BeO23Qlr2nlVaBXV73wmmhElHiV4GP5hSr2812hZZyflRi/7tz/uGLsmr/ZSORMjv6kt0EwKu8++vj1YCVlZeRlRfvSjqdZ1VK6w+XbEG5kp2N+LTpk53sJgBINC4RAgAAGEbAAgAAMIyABQAAYBgBCwAAwDACFgAAgGEELAAAAMMIWAAAAIYRsAAAAAwjYAEAABhGwAIAADCMgAUAAGAYAQsAAMAwAhYAAIBhBCwAAADDCFgAAACGEbAAAAAMI2ABAAAYRsACAAAwjIAFAABgGAELAADAMAIWAACAYQQsAAAAwwhYAAAAhhGwAAAADCNgAQAAGEbAAgAAMIyABQAAYBgBCwAAwDACFgAAgGEELAAAAMMIWAAAAIYRsAAAAAwjYAEAABhGwAIAADCMgAUAAGAYAQsAAMAwAhYAAIBhBCwAAADDCFgAAACGEbAAAAAMI2ABAAAYRsACAAAwjIAFAABgGAELAADAMAIWAACAYQQsAAAAwwhYAAAAhhGwAAAADCNgAQAAGEbAAgAAMIyABQAAYBgBCwAAwDACFgAAgGEELAAAAMMIWAAAAIYRsAAAAAwjYAEAABhGwAIAADCMgAUAAGAYAQsAAMAwAhYAAIBhBCwAAADDCFgAAACGEbAAAAAMI2ABAAAYRsACAAAwjIAFAABgGAELAADAMAIWAACAYQQsAABS14QJE9q3bx/LQqSUjGQ3AEi+CRMmrFq16syZM4WFhZ06ddqwYUOyWwSg5crMzHzggQdqampat26dl5dXUlIiInfffXebNm2ys7Nbt269evVqEfn2t79dUVGRlZW1cOFCn8/nXmX27NnJ/hAgYAEAkEpuv/32v/zlL3/5y19ycnIWLVpkB6xWrVodPny4uLhYKTV79ux9+/Zt3Lhx586do0ePvvrqq3v27OleJdmfACJcIgRERGttWZaI+Hy+ZLcFQEvXvXv3HTt2iEh5ebmdrmz2a631iRMnMjMzjxw5IiLHjx/v2LFjpFWQRAQsQM6ePdulSxcR6dq1a7LbAqClO3bsWK9evUQkJyenb9++zvKhQ4faLzp37lxVVeX3+0VEa62UirQKkohLhIAUFxdPmTJl6NChbdq02bZtW7KbA6BFe/vttydNmjR8+PBWrVrt3LnTWX7JJZdMnDixdevWf/zjHwcPHhzLKkgi1adPnz59+iS7GQAQTWlpaWlpKccrtFjOvTjJbggaZh+v6MECACDVrVy58sKFC8luBeJAwPKSESNGtGnT5vjx47t27XJe5+bmOgtTs2HV1dXdu3e/ePHi+++/P2zYsLVr1/br189esn79+qS38+OPP77jjjteffXVUaNGVVdX79279/LLL7/sssu2bNly6tSpRDYvUgs7deqklDp69GibNm3shvXr1y9ZX3rYFmZkZAQ1zPnSE/wVI+lS9jDl5m7k6NGj7d+vrl272keAvn37pkJr3Y10jk5O21Jnl7rb6RzbfT5fSu1MEcnNzbUP9e42N+tuZJC7l2RmZv7pT3+65JJL3K/dC1OzYR9++OHFixe3bNly++23Z2ZmFhYWOktSoZ3nzp07ceKEiGRkZPh8vry8vB07duTm5lZXVye4eZFauGfPnuLiYvsuIbthSfzSw7YwtGHJ+oqRdCl7mHJzt8f5/XKOACnSWnczQtuWIo0Maqfzi59qO1NEnEO9JOpfJgHLe7TWoa/dC5MlSsOysrIqKyvPnDmzevXqzp07O0tSp50isnfv3nXr1nXt2rV9+/YrVqwYMmRIMloX3Cqt9alTp8aMGfPee+8FNSyJX3pQC8M2LIlfMZIuZQ9TbnZ7nN8v5wjgfjfp7GZEaluKNFJcLbF/8VNzZwZp7t3IIHcvuemmm7TWn332WU1NTdeuXe3Xl112mf1iz549qdkwrfXp06ePHz8+bNiw7Ozszz77LCMjw16SCu3cs2fPjTfeuG7duqKiIsuyTpw40a1bN7/ff/To0QMHDqRCC4cPH37w4EF7iLfdsCuvvDJZX3rYFl566aVBDXO+dFPbZZC7V6TsYcrN3cgbbrjB/v3q0aOHfQTo3r17KrTW3cj8/PygtqXOLnW307Is+xffOZymyM602Yf6wsLC5v6XaR+vCFgAPICABcAr7OMVlwgBAAAM4y5Cbyt/O0dExLJEWcpniVLKUmL5xOdTIqKUWJZYqq6AiPh8opRYSlTgf9p+bVn2cm1ZokQsEWVpu6SlRIn2WVpElGhLiYhY9oqilRIl2hJRSisllmhLROqWa0tpS0TVLrTEX/ejiKW0XUyJBOoXqf1Rq8AW7TpF2auIKPHXLpGg1WuXBN5SIkrba9lviRItgUq00k7h2ne1WIHlgR/trViBJcqyl2hlaandhWJ/eksH9qilRbRliVJ+pQL7xhfYnX5LaaW0Esmw/M4SS7RSOsPyKxGfvZby+5TOUH6ltE/5LaV9oi2lM60aS/lr96s/Q/kzVKCeDPH7lN+n/Bmqxi7gE3+WqlaiMwI1+C1lL5EM5bfE71M1PtH2Ep/y+8TvE79P+bPEbom9is4QnalEifhEfEr5RHyifEr5xPIpyyfKEuveh/o19z94eFH52zmiLLEsZSmxLBU4LtnHK+cApURZYin3u3WHKfu4JM7hqPbAZSnnsONeqJX9CymBY5eltKjAEaDeu+7DV+DopAOHAqVV3QFHOwc61+GlroASbR8Y6y+pPci4jjxK6h3KgkvqoIX2Idc5jtXfdO0xyjleiXuh/UKr2pJKabF3s2iltP2WUlpZYil/4LW9VyxtKW0fplwvao9U9v/s44+lnWORT/l9gXf9gR+l9sAVOJrZBxwdOKpYgUONXcxV3lnut49RGbULM1xvuf8/o/YYZR/ifKJ99o8iPhX+kGWJ8ollKetbDzbjrPf0YAEAABhGwAIAADCMgAUAAGAYAQsAAMAwAhYAAIBhBCwAAADDCFgAAACGMQ+Wt+XcUZ7sJkSmRbSIP9nN8CBnz1WLVDSmAou/nZA6OEylPb+IX6SqkWsH5tcz2qKUwFEYAADAMAIWAACAYQQsAAAAwwhYAAAAhhGwAAAADCNgAQAAGEbAAgAAMIyABQAAYBgBCwAAwDACFgAAgGEELAAAAMMIWAAAAIYRsAAAAAwjYAEAABim8vLy8vLykt0MAIimrKysrKyM4xWA1Gcfr/4fgNozL3lWWYQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622F36700>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.05 --\n",
      "Iteration:   0, Error: 0.0000e+00\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622123F70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.06 --\n",
      "Iteration:   0, Error: 0.0000e+00\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F062213BDF0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.08 --\n",
      "Iteration:   0, Error: 0.0000e+00\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F065FA6A4C0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.09 --\n",
      "Iteration:   0, Error: 0.0000e+00\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622F39EB0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.11 --\n",
      "Iteration:   0, Error: 0.0000e+00\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622094880>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.12 --\n",
      "Iteration:   0, Error: 0.0000e+00\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622123730>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.14 --\n",
      "Iteration:   0, Error: 0.0000e+00\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F065FA6A250>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.15 --\n",
      "Iteration:   0, Error: 0.0000e+00\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F065FAB2B50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.17 --\n",
      "Iteration:   0, Error: 0.0000e+00\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622097610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.18 --\n",
      "Iteration:   0, Error: 0.0000e+00\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F062213BBB0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.20 --\n",
      "Iteration:   0, Error: 2.1272e-02\n",
      "Iteration:   1, Error: 1.0410e-02\n",
      "Iteration:   2, Error: 1.3868e-02\n",
      "Iteration:   3, Error: 1.9660e-02\n",
      "Iteration:   4, Error: 2.6020e-02\n",
      "Iteration:   5, Error: 3.2634e-02\n",
      "Iteration:   6, Error: 3.7545e-02\n",
      "Iteration:   7, Error: 3.6467e-02\n",
      "Iteration:   8, Error: 2.7822e-02\n",
      "Iteration:   9, Error: 2.8471e-02\n",
      "Iteration:  10, Error: 2.6135e-02\n",
      "Iteration:  11, Error: 6.8805e-03\n",
      "Iteration:  12, Error: 6.7330e-03\n",
      "Iteration:  13, Error: 4.1048e-03\n",
      "Iteration:  14, Error: 1.0069e-03\n",
      "Iteration:  15, Error: 2.7417e-04\n",
      "Iteration:  16, Error: 1.0177e-04\n",
      "Iteration:  17, Error: 2.6176e-05\n",
      "Iteration:  18, Error: 6.1540e-06\n",
      "Iteration:  19, Error: 1.4352e-06\n",
      "Iteration:  20, Error: 3.3461e-07\n"
     ]
    },
    {
     "data": {
      "image/png": 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79u7du48aNcqblerwA1Brnx9AcymlpkyZctJJJ73yyiv+Xcwvv/zyiBEj7rzzzh//+MeZvWbXX3+9d+dKiJp7Re/4O+64Y9q0aWkHK6UmT54c3PPCCy+ceeaZd9555/33359Zl958881jx4792c9+FtKvAqAZsgesn/70pyJird27d+9XX321ffv2GTNmrFixItfS9F9++eW99947ceLEG2+88eDBg2+88UZwOlBjzKxZsz766KPLL7/8zDPPjEajH3/88W9+85v58+c3Mvbo7bffXrNmzXXXXXfyySdfcMEFsVhs3bp199xzz9atW88555zgTDArVqy4/fbbr7322sGDB48ePfrgwYObN2/+f//v/61cuTJ4wqVLl65bt+66664bOnTouHHjdu7cuW7duunTp3sTWR2+1j4/gCZSSp1yyikTJkwYNGjQe++9F+ygX7Vq1euvv37FFVfcf//9jz/+uDeMQUQKCwu/+93vXnXVVbt27Qo2ER2+5l5x1apV8+fPv+yyy6ZNm/arX/1qz5493v7u3bvfeeedAwYM2LRp04knnuhVnhs2bHjppZfGjx//T//0T7NmzfKHxnfp0mXSpEljx46dP3/+6tWrQ/x1ADSRGjhw4MCBA1vvAt7iMGnTYgFAs9TU1NTU1KTVVyNGjLjvvvv++te/eqPICwoKioqKKisr+/fvX1ZWVldX9+KLL7744otpX+S8ZPOtb33LGLNp06bNmzeXlZUNHDiwa9eub7311pYtW2666aa0pXJuvfXWtMHvXbt2nTNnzltvvfXYY4+lFXXy5Mnjxo2bOHFibW1tC64ogcnZo9HoRx99tH379t69ew8YMMBxnEcfffTCCy8cNmzY1Vdf7R3sOM748eO99TM2bNiwbdu28vLyYcOGFRUVvfbaa88++yzD24EjzKuvmj1NAwC0KSNGjPCmkbPWRqPR3bt3b9y4ccmSJUuWLAlODuyrr69/9tln33nnnUsuueTEE08877zzYrHYpk2b/vjHPy5evPicc85ZsWJFuIsoNPeK9fX1zzzzTHV19UUXXXTSSSeNHj16//79K1as+K//+q8NGzZcd911frOWiHjrkr377rvXXHPN0KFDq6qqPvvss/fee+/VV1/NOqIDwJFBCxaAdiBrC1aHdO655/7gBz94+umnly5dmvlsRUXFc889t2zZsl/84hdHvmwAmsKrr5q9VE5z/fd///err77a2lcBgI5h+fLlsVhs8uTJmXMBaq1vv/12pVRwoUMAbVOrB6zly5ezSgMANFE8Hn/ooYcKCwsfe+yx66+//sQTTywuLu7WrdtZZ531wAMPnHXWWYsWLcqcPhBAW8MYLABoW9avXz9t2rRbb731hhtuuOGGG/z9sVjshRdemDNnTh7LBqCJCFgA0ObU1NRMnTp18ODBJ5544jHHHFNfX79t27Y///nP+/fvz3fRADQJAQsA2qi1a9dmLjIGoF1o9TFYAAAARxsCFgAAQMgIWAAAACEjYAEAAISMgAUAABAyAhYAAEDICFgAAAAhI2ABAACEjIAFAAAQMgIWAABAyAhYAAAAISNgAQAAhIyABQAAEDICFgAAQMgIWAAAACEjYAEAAISMgAUAABAyAhYAAEDICFgAAAAhI2ABAACEjIAFAAAQMgIWAABAyAhYAAAAISNgAQAAhIyABQAAEDICFgAAQMgIWAAAACEjYAEAAISMgAUAABAyAhYAAEDICFgAAAAhI2ABAACEjIAFAAAQMgIWAABAyAhYAAAAISNgAQAAhIyABQAAEDICFgAAQMgIWAAAACEjYAEAAISMgAUAABAyAhYAAEDICFgAAAAhI2ABAACEjIAFAAAQMgIWAABAyAhYAAAAISNgAQAAhIyABQAAEDICFgAAQMgIWAAAACEjYAEAAISMgAUAABAyAhYAAEDICFgAAAAhI2ABAACEjIAFAAAQMgIWAABAyAhYAAAAISNgAQAAhIyABQAAEDICFgAAQMgIWAAAACEjYAEAAISMgAUAABAyAhYAAEDICFgAAAAhI2ABAACEjIAFAAAQMgIWAABAyAhYAAAAISNgAQAAhIyABQAAEDICFgAAQMgIWAAAACEjYAEAAISMgAUAABAyAhYAAEDICFgAAAAhI2ABAACELJLvAgBAB7e/Jhrb5ea7FG2BVlpEaxERpUUrpZUoLVqLEnG8DS2OEq2tVuJoq5V1lHWU1co62kbEajGOsloZR8QR44iNiHHE6uRGxFrH2ogox+iIiURMQcQtctziglgnHescqS/Rsc6Rum66rouuK9X1XZUUqYiIKFEiokXtt/V7jdprivaaTvvc4v1u0dem8EC84ECsMGqc+lgkFtfG1SbmiCs6rlRcKSM6LsoV7Yq44sRFXNGuKGO1a1VclBEdN8pYca02VlwrxijXiLFijLhGxIprxBixVoy1xogxIiLWirXWiIjJ43+5PCood7oMLMp3KVqivQasz1/fm+8iQEQpESksd5KPtXKUqiyvL+8U7abrSyVWagpKYz277uvfadeg4s/6OCrxOlFK1PG99+ep3JAZs0bmuwhHkdgut742nu9S5JXy/u1bpUW0KCVeovIeihbRShydyFiOFsexjrIRbbW2EW0jyjjKRrQRsY4yShmljIhVYrQYR0xErCOmQEyBmIi1BdYWWBUxTqFbUOAWFSiJ2EihshGrC9xCJ1YSiZY6B7o7Byp0XbmjiiWivXSltIjsNnXFroqYTtaVWFzXxR1xI25M6uv1wbhTVx+pjzluzDH1jsRFx7SOKRUXR4lSokWUFUeJEtFWtLHatTpulSs6ZrRrJW60a8U1yjUqbsQ14oq4ItaKa8UVMSLGWteIMdZ6Acs0BCxr8/dfEc3TXgMW2gRrRan6hq/mro5EVEkk2rXwgDjRAomWmMJSKS9TRV3re5Ts7RfRIhKsyACgtahmZxFjjVLKipgWvLi5SEodHR9yODzN+TqlRHnpCgDyRSujxYqIk+x0y1ovGasaeQgcEgELrUuJFRHV+t8GAaCJ/Kzk0I6EVkPAwpFD8xWAlqP+QLtCwEIeMAALwCGoZuYplWP7UJywgxvt9fDwOYcjhL9qAJrtUBVHi0dG6SbkIJdxVzgMfOoBANqINhpo7GEnLZq1jkIELBw25mUBgCyoG49qBCwAQJunD6sNqcU3Mud6WVNPZ0NNWXybbVcIWACA9iN30DoCI6YOv68w85RhnxBtBQELANCeWGl0sFbGU6rVQozKVQ7b6EMcHQhYAIAj5ZBTtGTtCsy2z6oj0WQlIqaJQ+9JUUhFwAIAdFj+6KvWa8cKh/HWcs53MRAeAhYAoI3x2oyaPNdou5uvSjFc/ShAwAIAHAEt/bg5rPCUkmOc1HsJdRPai7L2D2amI6a5QiYCFgCgNTV70ZuWRKosjVjZTtMWV3dueyVCKAhYAIB8a0qoynpI1vHvRzKzhH4pa8I+I/KDgAUAOOJaY9RU087Zuh97jeet9OkbaLzqyAhYAID8UY1NzWD9lq3k/3uTYFklovxjsrzwENfM75gpctXRgYAFAMiT4LRYLRp6lfvMDSFGKRvKub0B74cORzZ5fXLU0Y2ABQDIA9WMWRianI9SD1Q5p1o/QgIxqwlpyyQPpYmrQyBgAQCOhEPO4p5jGHvD3saSVpYVclI0ZVKGZrCBn4eS/dciRXV0BCwAQNuhxA9SqXEqax7JHlJyxLDDmczdW+a5FRZ7Tpy9VU6LvCJgAQCOrEO3ZTXyWpUIOf5ahKmZp/EI5A9v1xLqbAj+uKtwWSvWMG9DO0XAAgC0Jdn7AVUjj7I0WQX2KGUPs3/Q5L5TMT1UNfE6/mEmxwvSdxtaudodAhYAoM1p2Y1/KW1aKuQbEzMu1pIXMfTq6EHAAgDkm27ah1GjLVUt6BxsSgBLW44wyzCsHKPDsvQYkq6OJgQstLqQb94B0CFlTDeaqDj83bmylEoLSjbt4MAVEqds2YqEKenIK0HKnmzb1iaarGyg7Sp9w2acHR0BAQsAcOQ0qdsu9zE2PU4F9kva/KKilGhltWq4fzD4fU8falC6FZXWXmVzlEw1PmtD07MTMasDIWABAPInbTL39NHkicc5u/9UxnaOIw8Zp9LY1M9Hk9mA1ox5I1pyJFmrvSNgAQDyJGtzVmISrIYdNlsvof8wR/bKGU9asBBhroarrJfK7zqHaDsIWACAI07pJq5i4+cn631eqcT/soSttBymrBLrTZvlhargOPfGx4aa3IWzwRFTucdg5VyL0ATOkn5qk34etGcELBy21r0TGsDRKvgB1ZQuwsCezGrJG0OflquaUHk1DMPyB6ynCDagZTybPvie+wqPJgQstCaiF4CsWlY5pPYbBrsObbC70G/hUlYpUWK9dOXdPOj/1E1IN35TVrCXsJFX5eyuDE4oSqY6OhCwAABHSmMN3qphpgb/MO//dWq4UY1OeZVxO2Fyt5XkUPcmLkpokh+Rrk1NdoHLZLnU4Y9zNyyO0xEQsBAi/joByKrRyiGYuvwbCdMyVvYXivhNWZm3EHrNV0q0sokxWIkTN8QXJ9vJ3dSGLf9o43cRBvJWcIIGP2l5A7Ca2kiXa7UctHN8IiJsjd4pDQBNHt4eDF4iwRYf1ZCu0l/VMNGoN8LdKmW1slqsVsZrwXKUVWKSg+azl8YVJSImmZT85QitX5SmTNNgReVqjWL0VUdHwAIA5E/GBO4pAlM22OR2lv5B/3td4k/qTO9KvJglIlqsE1gtJ/NMwdTj+gOwrJLAvKM22FIl6duZ0zQom/jTsM5OznBF6uo4CFgIC3+XAIQkZchTjoHjSqykR6SUQe5K/AkatFhHeU1ZxusidJRt2ipefqjyw5Z/sYaf2ea+srlO39h6zw2r6DAMq93jQxGHhzkaALRYY+OrMtcXDDRoZUzg3nBTYbIdK3FsMkgpsQ33Dx4qXZnk/YNez6C3bf2OQpuSriRbO1ZquXPzDmBUe0dEwEIotHgrXihtG8aoej8b7osGgAZZFslRolS2JqtgR2HqbhXoNAxM7pm2EKE3DEspqwORS4vVIk7aZFW2oe3IWmVEGautKGMTg9H9ce4pg7dy5K0sDxt5LsssWQSvdoyAhcOQUg9aUTrZKJ+o8qyySovW6XWEodYAjjLeF7DklqgmNn5n6wHMPkdDyu01Nm0a94i2StmIGEe5jtiIciPK1WIdpUREB6Ke17FnRBnRrihjlTeJVbCL0CYPzdI/6O+xwf3W/xHoBMyevCyD3zsKAhZCYZXjKMdREUcSVVryT6BiAoAsdPonUZZGLJVtI61bMLmRbA5LzDLqaKvERsRqZR2xjrgFYiLKFATGwnsZy4iVZFegscpabaxKxixlrWqIVt7V0joHszRBZf+NU4Zh5UpU1gptWO1ZJN8FQLsVqAGV4yitxNHiNcfrRqcBBIBDSWkVyjLHVcae4GHK+pNgOdpoZR1ltDIR5eUqV4uJpGYfa60Ra8Vasa71WrCUK2KSg9y9DevPuBUchtVorspSF2Zfo5CGq46GgIUWCaYrrZVWEokox/F2NLSNJ4dDeDsMuQtAI1RgolGRRHO4iGSu9BzsKExdMyf5058EK3ELYSSRsVwvZgWu6Q1gt1asm2zBckUnWrC85iurrPWmaUhboycpI2Z5kzL4zzZ25yA6KLoIER5rbc+yaGVxXbkTLZP6MlPcPdq3254hXT4bXrz1xAg3HALIQatctySnh6fUnWnTuNvE6KtETtPaePOLOso4ykTEa8Ryi3WsWLlFSoqVE1FOQylE6qx70DpRU1BnC+tsxFoVt9oVnVjp2SaDU+JP8vtkzpsKU7oClddG5jM5pitN30c3YbtEwMJh88aHWmt7lkd7lhyocKJlEi0zBd2jvbvvHdz18xGdtvaPuIYbCQF4/EFXKsdnkMr+MGWhmsxjAn+8tJYYs+A1X4mNKOOI20nFisUtVrazdooC3ThKVNS6ddbWWeegLagzBXHrxK12rXaNdq32GrHS1uVpGIYVGPCeMh4rV83XlGFYaM8IWAiD0urYHvWVJQfLE+kqUhbt033vkK6fn9pp6/GRmCvGEZVrSQoAR4lmtGPrHLNkBdJVWtKygXSVWIJQxNHWUdZRJqJNRJlOOlasYp216aRUgTj+HYFKqTqJH7T2gNFfm8KDpiBuddxo12rXKtcoK+IanWiBSt4kmDbrVdos7Q3FTxtfZXPOQcr30I6EgIXDpEQpdWyPaM+SAz2cunKJllunLNqr276qrl+cUbK5t3PQiG3qLdkAOphG/u3neiptCUKdllsaRpn7ksOikl10yiqxWltHGUcbRzX0DJaoaImKFytVqJxgzKmzsTpjDhhVJ06dFLrixK2Oi45b7d1C2DAJlv9HUn6qjD0pcnQGph5DvOpQCFg4XLp7abxrUayzEyuReInYTm6XkljPTvv7Fn5V6Rz0vlI6orQovzrTufoFABwlsrdO5WjmzhjPnm12Bi/mpM7RoKwjJqKMVrZYxTup+iLtFilTqLRNDm8Xkbh1o9bUWakXp84UGKu8dGWscq32phu1ydFX1r98YLIGlZG0Gn6PYGoyTW2jSs9aZK92iLsIcZiy/7PXypt4RiJKRZSKeGMhACCN314VXPU5o3HLpjVrSWrPoKTs8WfASo7E8m4nNEpZLUaJaFFaGqYYtclVDa1IzOq41XHrxK2T6B8Uba0YqxNzNCSDXNbGqsxJRyVHmEznT3jFsjkdBQ0JCI1K/p83gbKjbESpAqWKxAmmK5qvAGTIlqiUsjlmbWh4UTBsqYamLJVYGMf6G05ibRzrKPEWndAZF3VFWdEx63g9g8Zq15trtGH0lUqsMm0zxrOnTd3uPWsyn/L2WPEaxJj+quPiow6hseL9hbJaG28xCod0BSDtg6b5bdkpGSTrlO7p7Vh+F2Ji9natrFJGeysSJsqkJLBslxWJWRW3OibaFcebvT0uyoo3wj11jgZpCFWS1mSV0YIVuM3QBvejw+PTDi2SNiDA+2aZWGfMaiWOMlpsQXI4hFeXMdQdQAqdrU5ofBhW4GGWBq3kZKXiN2J5E2J5MUtMcpnn4B1+RkRi1sYl2TMoyrVOXLT17h9M5CqVnKMh17Sigce5VsjJvhsdEwELrSitkmEYFnB0SrRcN+G2wSyrEDY8lW3S9rTJGhL9gyLJ8KbEapXIVR4dfLGIiLgS7NtT1iojYm1ipWfvFkLTMEtocJLTZLRKmVy04Wdm0soypTuDrjooAhZaXeZABwBHs5yN2f5+lWyMCvxf4LDs28lxTyKJge2ilfjRyhuJ1fhnnhXlWuWKksR4rMRChMmfiYOylyrr1Az+/zWrW9DvuCR6tWcELABAPqRHlEZmzErfYTMzVuBnIKf5U8McOqoYUfFEkNLGahFxrfJWfQ5cOGWW0SzNVIHx7zl/G3+60vSR78amTO9OvGrfCFhoLdprq6f5CoDkXhVHZ3bZZX25BFd69tkc6cpb6TnxUmVFxEnpJcw4T3LDiBaRxMRXNjG8PWUSLP/o1FzlT8WV3NPQm6hSd6ZemBHvHRYBC+HL0X4PAEmNjbVKfSp381WwHSuYtFQg+3jp6lA9g1YSk4B6E1+JN0eDEWUaYlZyTojUWUaz9/0lhmH5tw3atKdyvQQdCQELRwgTNADI2Y7VcIC/ofw5pxo7LHNnyjj3lLYrb8M51O3MtpGRWv4so2lXDuStjCmvEidt/KLoePjMAwC0LekRJdvCz8Emq/T5GkTET1eNj4fKcmkVLEPiXkJ/ltG0ItqUaJVyL2HGb5Ll/kEf0412RAQsAMCRl3UGrMbalrwxTVmzlP98xuSeCVqslsbGjFsRI4n7B0XEJNaOzhHrGlkep3FNacdKP4Sh7u0VAQsAkFdZpxttROrhNveQLXWIoVINgk1I/jQN3v7gNO7+mVS2IKeS02LlHELvP0wZlUXzVcdEwEIrYoQ7gHQ6x+dOrvoi2/70SJLRiOStZJjcbkaC8e8ilGwdd6lTYaVsZx965Z8lc8EckzEfPDoWAhYAoC0JJqpGGrea3ccoIqKbnGn8KUazrJOTOCJ4dK6zNPFqWS7f0leirSBgAQDyLTMZqZQIZYP7D7UdPFmu2xCz8hqubO5xXhndkzmOyrq/KYOpiFUdCAELANBmJOZXyPpUsgkp2xrPKRuBV6Q+bN6AcZMraeWa+yplHlLxZ49nsMTRiYCFkFCFAGiixAwLrfMBlFhDIrgsc5OGYQXjlL88TsZKzwG5Rl9lauJQe5qvOhYCFgCgvWn+N7om9hWmzdSQk1WSOr9oxgHJ67ZomWd0AAQsAEDb0KzYlHuK0cTzrdGsHsqg9awD2BnV3uEQsAAAbVgTc1LKOjkpYaXpdw56TPKTMfdo96zD75PXt6kPsyJNHQUIWACA9imvQz8b6R9srFsw+wB5egY7IAIWAOBIaEmfXaIfUDW8OPMkYcQsL/Zktl0ZUckJsVIW42nGSZMypnenFauDI2ABAI64JqQtm3qMVYfKUnls0CIsIQMBCwCQX0okELlCHZ2um3cX36G08N7AHPsz1+LxDieudQgELABARxJOPMlcsjkfpUA7RsACAORJI41VzWnHanzKqtZFkEIOBCwAQHtzqETVlKnb02QuRGhyXCbcXkd0VAQsHCaWyAHQRjUxZrl5bIYyTNDQYRGwAABHLyNWAivkAGEhYKFFEsMj+PsDoJ1RIkopnXupadqUEIpIvgvQQsdcXprvIsBXL/KFiMh+kf0iW0RE6qRkiQxakt9yAW1DQbmT7yLkl1ZaxJssVGnRSmklSkSLaCvaiFailDgi2lhHi6OMo0W71lHWUVYr44jVyiixoqwVY8S4IiLGirVirNi4tTFrI6Iiro6YgogpjLhFEeM4IhEddyJRp3C/drUjVkfqtd2rC421ImLFikhU3H3G7jcF+2zxAbeo3i1wXUdcFXFtkWsk7jpxKYwb47omrsVVOq5UXClXtCvi/TTiuKKsl96s1qIcq0S0FqWNcqwYq10rxoprlDHehngb1ooRsSJGWaPFm9HUWrHKGmEYRvv959NeAxYAtBddBhbluwhtk99UFG/ei4xIrKmHW4l8LZGvpeRzKWtW4bRIFzFdJNqsV4kSibTso9WbR5VugY6D/5YAAAAhI2ABAACEjIAFAAAQMgIWAABAyAhYAAAAISNgAQAAhIyABQAAEDICFgAAQMgIWAAAACEjYAEAAISMgAUAABAyAhYAAEDICFgAAAAhI2ABAACEjIAFAAAQMgIWAABAyAhYAAAAISNgAQAAhIyABQAAEDICFgAAQMgIWAAAACEjYAEAAISMgAUAABAyAhYAAEDICFgAAAAhI2ABAACEjIAFAAAQMgIWAABAyAhYAAAAISNgAQAAhIyABQAAEDICFgAAQMgIWAAAACEjYAEAAISMgAUAABAyAhYAAEDICFgAAAAhI2ABAACEjIAFAAAQMgIWAABAyAhYAAAAISNgAQAAhIyABQAAEDICFgAAQMgIWAAAACEjYAEAAISMgAUAABAyAhYAAEDICFgAAAAhI2ABAACEjIAFAAAQMgIWAABAyAhYAAAAISNgAQAAhIyABQAAEDICFgAAQMgIWAAAACEjYAEAAISMgAUAABAyAhYAAEDICFgAAAAhI2ABAACEjIAFAAAQMgIWAABAyAhYAAAAISNgAQAAhIyABQAAEDICFgAAQMgIWAAAACEjYAEA0HZdf/313bt3b8pOtCmRfBcAyL/rr79+/vz5u3fvHjx4cI8ePRYvXpzvEgE4ehUUFNx0002u63bu3LmiomLdunUictVVV3Xp0qWoqKhz584LFiwQke985zvRaLSwsPDpp592HCf4kunTp+f7lwABCwCAtuSyyy77y1/+8pe//KW4uHjWrFlewCopKdm8eXN1dbVSavr06evXr1+yZMmqVavGjh17yimn9O/fP/iSfP8GEKGLEBARa63WWkQcx8l3WQAc7fr167dy5UoRqaur89KVx9u21u7YsaOgoGDLli0isn379vLy8lwvQR4RsADZs2dP7969RaRPnz75LguAo922bdsGDBggIsXFxYMGDfL3n3HGGd5Gr169YrGYMUZErLVKqVwvQR7RRQhIdXX1zTfffMYZZ3Tp0mX58uX5Lg6Ao9rrr78+ceLEc889t6SkZNWqVf7+nj17TpgwoXPnzn/4wx9GjhzZlJcgj9TAgQMHDhyY72IAQGNqampqamqor3DU8u/FyXdBcGhefUULFgAAbd28efP279+f71KgGQhY7cN5553XpUuX7du3r1692t8uLS31d7bB4q1evfqiiy7avXu3Uqpz587btm2LRCL9+vU7ePDgokWL2kghi4uLvbJ1797d26ipqfGKvWLFiiNfyLRylpaWXn755c8//7yIpL2ZNTU1eSleI4U888wzM9/MPBYSedHGKytPsJBjx45VSm3durVPnz7xeHzt2rWDBg1qC6UNFnLMmDFpZWs7b2mwnEOGDPEqecdx2tSbKSLB6vTI/M1kkHv7UFBQ8Mc//rFnz57B7eDONli88vJy79lOnTotXLjwhBNO+PDDDw8ePPjuu++2nUL6ZfM3/GLnS7Cce/fu3bFjh4hkvpl5LKHkKGTmm5nfQiIv2nhl5QmW5/3336+uru7Xr18kEnEcp6Kioo2UNliMzLK1kUKmldOv5NvamymBmkqO1N9MAlZ7Yq3N3A7uzK+04n3jG9/wBoxHo9ErrrjiwIEDIlJYWFhfX5+3ImYU0i+bv+EXO7/S/rNmfTPzLq2QmW9mvgqGvGvjlZXHK8+uXbvGjRv3zjvvrF279u233/ZvJW4jpfWKkatsbaSQEiiJV8m3zTczTWu/jQSs9sFxnAsuuODzzz8fPHiwv+1v5Lt02YtXW1t79tln9+jRY/ny5fF4vLq6+pRTTvnwww/bVCH9svkbfrHbQjn9nZlvZr6K58layMw3M48lRL608crKEyzkpEmT9u3b16tXr/79+59//vnbtm1rI6UNFjKzbG2kkGnl9Cv5tvZmBh2xv5ncRQigHeAuQgDthVdf0YIFAAAQMu4ibK/qXi8WpUVrpZVorZQSrUVrUUp5G1qJUqK0aKW0Fu8ApYL7bWJbiVaitRUlWrwDrFaiRLS2SkQrq5Qo8fcnfqrktharlFUiShL7tdiGw1J3Jh6KaGVFrBZJ2ZnYCL4quEeUWB3YzvjZsJG4nJXAya0Ej7He2YIPky+0okQkuVP7z1qVPFLpxLb3xoiy3puqEn+8d8sGfopWVmurlNVitUr8Uco6yiglWhlHWcd7VrtaiVZGi3WUdZRxlNFKHGW0Mo5YRxmtbPKhSRwjiSMdZbQYRxlHTMQ7MvHQjfjbyjjiOspExOiGw1xHbCRxKuuIdcRoZSNiHRFHiSPiKOWIOKIcpRzRjtJalCNaK/3tW5hCGukOVVklqyavsgo8K4EKymot4tVUiZ02uZ2sJRp2Jv5NKq82E6uVV7klazP/Wb8Sy6yjVLBSsn51l6yCMiufRJ2ZuzZLHiYiGfVV4kibtrOF9ZUS0Rn1lbLivc1iE/WV9+Zp0coktr13RTdUTTql+jJ+rZWowbT16iidqKO8ZxNVU6CasrqhUvIqFqO1SVZKyVpLghVasu5KVE2Jh/5TwZ+RZB2VqOjEOt7DfFdZtGABAACEjIAFAAAQMgIWAABAyAhYAAAAISNgAQAAhIyABQAAEDICFgAAQMiYB6u9Kr68Lt9FyM2KuPkuQ3tmRMxhnUDz3QltR1uvrOzh/nuDV2XFWvhqJeKIOKGWqE2gFgYAAAgZAQsAACBkBCwAAICQEbAAAABCRsACAAAIGQELAAAgZAQsAACAkBGwAAAAQkbAAgAACBkBCwAAIGQELAAAgJARsAAAAEJGwAIAAAgZAQsAACBkqqKioqKiIt/FAIDG1NbW1tbWUl8BaPu8+ur/A1X4QISi9+8KAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622F37610>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.21 --\n",
      "Iteration:   0, Error: 2.1993e-04\n",
      "Iteration:   1, Error: 1.1540e-05\n",
      "Iteration:   2, Error: 1.9346e-06\n",
      "Iteration:   3, Error: 3.4096e-07\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622ABDDC0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.23 --\n",
      "Iteration:   0, Error: 1.7663e-04\n",
      "Iteration:   1, Error: 7.8292e-06\n",
      "Iteration:   2, Error: 1.0810e-06\n",
      "Iteration:   3, Error: 1.5698e-07\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622123A30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.24 --\n",
      "Iteration:   0, Error: 1.4436e-04\n",
      "Iteration:   1, Error: 5.3929e-06\n",
      "Iteration:   2, Error: 6.1581e-07\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622098700>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.26 --\n",
      "Iteration:   0, Error: 1.1961e-04\n",
      "Iteration:   1, Error: 3.7868e-06\n",
      "Iteration:   2, Error: 3.5947e-07\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F062213B9D0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.28 --\n",
      "Iteration:   0, Error: 1.0027e-04\n",
      "Iteration:   1, Error: 2.6940e-06\n",
      "Iteration:   2, Error: 2.1381e-07\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622123070>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-- Solving for t = 0.29 --\n",
      "Iteration:   0, Error: 8.4945e-05\n",
      "Iteration:   1, Error: 1.9469e-06\n",
      "Iteration:   2, Error: 1.2991e-07\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<PIL.Image.Image image mode=RGB size=800x300 at 0x7F0622123CA0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "load0 = float(eps_c)*L # reference value for the loading (imposed displacement)\n",
    "loads = load0*np.linspace(0,1.5,20)\n",
    "\n",
    "energies = np.zeros((len(loads),4))\n",
    "iterations = np.zeros((len(loads),2))\n",
    "\n",
    "alt_min_parameters = {\"atol\": 1.e-6,\"max_iter\": 100}\n",
    "\n",
    "with alpha.vector.localForm() as alpha_local:\n",
    "    alpha_local.set(0)\n",
    "\n",
    "for i_t, t in enumerate(loads):\n",
    "    with nonzero_u.vector.localForm() as bc_local:\n",
    "        bc_local.set(t) \n",
    "        \n",
    "    # update the lower bound\n",
    "    alpha.vector.copy(alpha_lb.vector)    \n",
    "    print(f\"-- Solving for t = {t:3.2f} --\")\n",
    "    alternate_minimization(state,parameters=alt_min_parameters,monitor=postprocessing)\n",
    "    plot_damage_state(state)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "id": "gySiyQlrer24"
   },
   "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"
    }
   ],
   "source": [
    "p1, = plt.plot(energies[:,0], energies[:,1],'b*',linewidth=2)\n",
    "p2, = plt.plot(energies[:,0], energies[:,2],'r^',linewidth=2)\n",
    "p3, = plt.plot(energies[:,0], energies[:,3],'ko',linewidth=2)\n",
    "plt.legend([p1, p2, p3], [\"Elastic\",\"Dissipated\",\"Total\"])\n",
    "plt.xlabel('Displacement')\n",
    "plt.ylabel('Energies')\n",
    "\n",
    "plt.axvline(x=eps_c*L, color='grey',linestyle='--', linewidth=2)\n",
    "plt.axhline(y=H, color='grey', linestyle='--', linewidth=2)\n",
    "\n",
    "plt.savefig(f\"output/energies.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "2UCtv-Yker2_"
   },
   "source": [
    "## Verification\n",
    "\n",
    "The plots above indicates that the crack appear at the elastic limit calculated analytically (see the gridlines) and that the dissipated energy coincide with the length of the crack times $G_c$. Let's check the latter explicity"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "id": "mrptael7er3A"
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The dissipated energy on a crack is 0.319\n",
      "The expeceted value is 0.300000\n"
     ]
    }
   ],
   "source": [
    "print(f\"The dissipated energy on a crack is {dolfinx.fem.assemble_scalar(dissipated_energy):.3f}\")\n",
    "print(f\"The expeceted value is {H:f}\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "id": "C-jo1UDHer3B"
   },
   "source": [
    "Let us look at the damage profile"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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y53Cpy7/rogpdIi2YNfSRwBbn3DbnXDkwF5hcZ5kfAc855w4AOOf2hDamSHD27t1LUVER6enptSfLirTevXuTmZlJSUkJu3fv9iSDJKZgDqHrDOwKuF0MjKqzTB8AM1sKJAMznXPv1H0hM5sOTAfIzs4mLy+vCZGhtLS0yc+NVRpzcJYvXw7AeeedxyeffBKGVMHp0aMHa9eu5ZVXXmHkyJFBP0+fc2II15hDdUx0CpADjAe6AB+b2SDn3MHAhZxzs4HZACNGjHDjx49v0pvl5eXR1OfGKo05OB9++CEAEydO9PTnNX78eNauXUt1dXWjcuhzTgzhGnMwUy5fAV0DbnepuS9QMbDQOVfhnCsCNuMreJGI+vTTTwEYNaruH5GRpXl08UIwhf4ZkGNmPc0sDZgKLKyzzJv41s4xsw74pmC2hS6mSMOqq6trN4h6Xej+i1L794kXiYQGC905VwnMAN4FNgLznHPrzewRM5tUs9i7wD4z2wAsAe51zu0LV2iR09m8eTOHDh2iU6dOdOnSxdMs/fv3Jy0tjS1btnDo0CFPs0jiCGo/dOfcIudcH+dcb+fcYzX3PeicW1jzvXPO3e2c6++cG+ScmxvO0CKnEy3TLQBpaWm1F7zQtItEio4UlbgRTYUO/ziwyX+gk0i4qdAlbkTL/LmfCl0iTYUuceH48eOsWbMGM/PskP+6VOgSaSp0iQsFBQVUVlYyYMAAMjMzvY4DwMCBA0lLS2Pz5s0cPnzY6ziSAFToEheibf4cfBtGBw0aBGjDqESGCl3iQjQWOmh/dIksFbrEhRUrVgDRV+iaR5dIUqFLzCspKWHHjh1kZGR4dobF+qjQJZJU6BLz/GvnI0eOJDk52eM0Jxs0aBCpqals2rSJI0eOeB1H4pwKXWKe/5S5Y8aM8TjJqVq0aMHAgQNxzukaoxJ2KnSJedFc6KBpF4kcFbrEtIqKCvLz8wEYPXq0x2lOz1/o2tNFwk2FLjFtzZo1lJWVkZOTQ/v27b2Oc1r+QvefmkAkXFToEtOifboFYMiQIbRo0YJNmzZx4MABr+NIHFOhS0zz7+ESzYWelpZWe4CR1tIlnFToEtNiYQ0d/jG/7z+iVSQcVOgSs3bv3k1RURHp6elRd0BRXf5C9/9FIRIOKnSJWYEHFKWkpHic5swCC90553EaiVcqdIlZsTLdAtC1a1c6duzIgQMH+PLLL72OI3FKhS4xK5YK3cw07SJhp0KXmHTixInaPUai9YCiuvxnglShS7io0CUmff7555SVldGvXz86dOjgdZygaA1dwk2FLjHpk08+AeDCCy/0OEnwRowYQVJSEoWFhRw9etTrOBKHVOgSk2Kx0NPT0xk8eDBVVVU6UZeEhQpdYk51dTVLly4FYqvQQdMuEl4qdIk569ev58CBA3Tt2pXu3bt7HadRVOgSTip0iTmxON3i5y/0ZcuW6QAjCTkVusScWC70Pn36cM4557B79262bNnidRyJMyp0iSnOudpCHzdunMdpGs/ManP7xyESKip0iSk7duzgq6++4qyzzqJ///5ex2kS/18WKnQJNRW6xJTAtfOkpNj89fUX+scff+xxEok3Qf2LMLMrzGyTmW0xs/vOsNzVZubMbEToIor8QyzPn/sNHTqUjIwMtm3bxtdff+11HIkjDRa6mSUDzwFXAv2B68zslL91zSwT+H+AzuAvYRMPhZ6SksIFF1wAaNpFQiuYNfSRwBbn3DbnXDkwF5h8muUeBX4NlIUwn0itkpISvvjiC9LT02svvByrNI8u4RDMVQE6A7sCbhcDowIXMLPhQFfn3Ntmdm99L2Rm04HpANnZ2eTl5TU6MEBpaWmTnxurNGb44IMPABg4cGDtkaKxKiMjA4DFixefNEZ9zokhbGN2zp3xC7gG+O+A2zcCzwbcTgLygB41t/OAEQ29bm5urmuqJUuWNPm5sUpjdu7WW291gHviiSe8CRRCx44dc6mpqc7M3IEDB2rv1+ecGJozZiDf1dOrwUy5fAV0DbjdpeY+v0xgIJBnZtuB0cBCbRiVUPvoo48AuPTSSz1O0nytWrXi/PPPxzkX839tSPQIptA/A3LMrKeZpQFTgYX+B51zh5xzHZxzPZxzPYAVwCTnXH5YEktCKioqoqioiHbt2jF06FCv44SE5tEl1BosdOdcJTADeBfYCMxzzq03s0fMbFK4A4oALFmyBIDx48eTnJzscZrQ0P7oEmpBXSrdObcIWFTnvgfrWXZ882OJnCyeplv8xo4dS1JSEvn5+Rw9epT09HSvI0mMi81D7SShOOfistDbtWvHsGHDqKioYNmyZV7HkTigQpeot2nTJkpKSsjKyorZ87fUZ/z48QAJt9uehIcKXaJe4Nq5mXmcJrQuueQSQIUuoaFCl6gXj9Mtfv6TjK1cuZLS0lKv40iMU6FLVKuqqqrdw8W/NhtP2rZtS25uLpWVlZpHl2ZToUtUKygoYP/+/XTv3p3evXt7HScs/PPo/v+4RJpKhS5R7f333wdgwoQJcTd/7qcNoxIqKnSJaoGFHq/GjRtHcnIyn332GcePH/c6jsQwFbpErbKyMpYuXYqZcdlll3kdJ2zatGlDbm4uVVVVrF271us4EsNU6BK1CgsLKS8vJzc3l/bt23sdJ6z8G3xXr17tbRCJaSp0iVr5+b7zu8XzdIuffx69oKDA2yAS01ToErVWrVoFJEahjxs3jtTUVDZv3sy+ffu8jiMxSoUuUembb75h27ZttG7duvb6m/EsIyODiy++mOrqat555x2v40iMUqFLVPJfbu6iiy6iRYsWHqeJjO985zsAvP322x4nkVilQpeolAi7K9blL/TFixdTWVnpcRqJRSp0iTrV1dUJWeg5OTl06dKFgwcPsnz5cq/jSAxSoUvUWbVqFSUlJXTo0IGBAwd6HSeiRo8eDWjaRZpGhS5R58033wR8e37E6+H+9VGhS3Oo0CXqBBZ6ohk8eDCZmZmsW7eOHTt2eB1HYowKXaLK5s2b2bBhA23btmXIkCFex4m41NTU2u0GWkuXxlKhS1T5y1/+AsA//dM/kZIS1DXM4452X5SmUqFLVPFPt3z3u9/1NoiHrrrqKgA+/PBDjh496nEaiSUqdIka33zzDcuXL6dFixZ8+9vf9jqOZ84991xGjRrFiRMneO+997yOIzFEhS5R469//SvOOSZMmEBGRobXcTw1efJk4B9/sYgEQ4UuUcNfXv/yL//iaY5o4P8ZvPXWWzpqVIKmQpeocPjwYT744APMjH/+53/2Oo7n+vbtS58+fdi/fz9/+9vfvI4jMUKFLlHhrbfeory8nAsvvJCsrCyv43jOzGqnXfx7/og0RIUuUWH+/PkATJkyxeMk0cM/7fLmm2/inPM2jMQEFbp47siRIyxevBgz43vf+57XcaLGqFGjyMrKYvv27brWqARFhS6ee/vttzlx4gRjx46lU6dOXseJGsnJyUyaNAnQ3i4SnKAK3cyuMLNNZrbFzO47zeN3m9kGMys0sw/NrHvoo0q88k+3XHPNNR4niT6B0y4iDWmw0M0sGXgOuBLoD1xnZv3rLFYAjHDODQYWAE+EOqjEp9LSUhYtWgTA1Vdf7XGa6HPZZZeRkZFBQUEBW7Zs8TqORLlg1tBHAlucc9ucc+XAXGBy4ALOuSXOuWM1N1cAXUIbU+LVokWLKCsrY8yYMXTpol+bulq2bFl7GoQ//elPHqeRaBfM2Y86A7sCbhcDo86w/K3A4tM9YGbTgekA2dnZ5OXlBZeyjtLS0iY/N1bF65iff/55AIYNG3bK+OJ1zGdyujH7L/Lxhz/8IS7PEa/POYScc2f8Aq4B/jvg9o3As/UsewO+NfQWDb1ubm6ua6olS5Y0+bmxKh7HfOTIEde6dWsHuB07dpzyeDyOuSGnG3NFRYU755xzHOBWrVoV+VBhps+5cYB8V0+vBjPl8hXQNeB2l5r7TmJmlwMPAJOccyea/D+MJIz/+Z//4dixY1xwwQV069bN6zhRKyUlhWuvvRaA119/3eM0Es2CKfTPgBwz62lmacBUYGHgAmY2DHgBX5nvCX1MiUcvv/wyALfccou3QWLA9ddfD/jm0auqqjxOI9GqwUJ3zlUCM4B3gY3APOfcejN7xMwm1Sz2JJABzDez1Wa2sJ6XEwGgqKiIvLw8WrVqpaNDgzB69Gh69uzJ119/zccff+x1HIlSQe2H7pxb5Jzr45zr7Zx7rOa+B51zC2u+v9w5l+2cG1rzNenMryiJ7o9//CMA3/ve92jbtq3HaaKfmdWupb/22msep5FopSNFJeKqq6t55ZVXAPjhD3/obZgY4i/0BQsWcPz4cY/TSDRSoUvEffLJJxQVFdG1a1cuueQSr+PEjP79+zNixAgOHTrEggULvI4jUUiFLhHn3xh60003kZyc7G2YGPPjH/8YgFmzZnmcRKKRCl0i6siRI7Xnbrn55ps9ThN7pk6dSmZmJsuWLdMZGOUUKnSJqJdffpmjR49y0UUXkZOT43WcmJORkcGNN94IwAsvvOBxGok2KnSJmOrqap555hkA7rrrLo/TxC7/tMucOXM4evSox2kkmqjQJWLeffddvvzyS7p161Z7eTVpvMGDBzNmzBgOHz7M3LlzvY4jUUSFLhHzu9/9DoA77riDlJRgzgsn9bntttsAbRyVk6nQJSI2bdrEO++8Q6tWrZg2bZrXcWLelClTOOuss8jPz+fTTz/1Oo5ECRW6RIR/7vyGG27g7LPP9jhN7GvVqhU/+tGPAHj66ae9DSNRQ4UuYXfw4MHafc/vvPNOb8PEkRkzZpCcnMz8+fPZtWtXw0+QuKdCl7D7/e9/z9GjR7n00ksZNGiQ13HiRteuXbnmmmuoqqri2Wef9TqORAEVuoTV8ePHa6cE7rvvlOuLSzP97Gc/A2D27NnahVFU6BJeL7/8Mnv27GH48OFcfvnlXseJO6NGjWLMmDEcPHiw9oRnkrhU6BI2lZWVPPnkkwDcf//9cXctzGjhX0t/+umnqa6u9jiNeEmFLmEzf/58ioqKyMnJqb1yvYTed7/7Xbp3786XX36ptfQEp0KXsHDO8Z//+Z8A/PznP9dZFcMoJSWFxx57DID/+I//4MiRIx4nEq+o0CUsXnvtNQoLC+nYsWPtyaQkfK6//npGjx7NN998w69+9Suv44hHVOgScvv37+fuu+8G4LHHHqNFixYeJ4p/ZsZvf/tbAH7zm9+wdetWjxOJF1ToEnL3338/e/fu5aKLLtIl5iJo5MiR3HTTTZSXl3Pvvfd6HUc8oEKXkFq2bBmzZ88mNTWVWbNmac+WCHv88cdJT0/nz3/+M4sXL/Y6jkSYCl1CpqKiovYsgD//+c/p16+fx4kST6dOnZg5cybgOyOjNpAmFhW6hMyjjz7K2rVr6dWrFw888IDXcRLWT3/6U4YPH87OnTv5xS9+4XUciSAVuoTEihUreOyxxzAzXnrpJVq1auV1pISVkpLCiy++SHJyMs888wzLly/3OpJEiApdmq20tJQbbriB6upq/u3f/o2LL77Y60gJb+jQodx7770455g2bRplZWVeR5IIUKFLs91zzz1s3bqVwYMH8+ijj3odR2o8+OCD5OTksGHDBm699Vacc15HkjBToUuzvPjii8yePZu0tDReffVV7XMeRVq1asWCBQvIyMjg9ddf55FHHvE6koSZCl2abN68eSddNUfnOo8+gwcPZu7cuSQlJTFz5kxef/11ryNJGKnQpUkWLVrED37wA5xzPPLII9x+++1eR5J6fOc736k9J/0tt9zCvHnzvA0kYaNCl0abM2cOV199NZWVldxzzz3aNS4G3HnnnfzsZz+jvLyca6+9lpkzZ+pUu3FIhS5BO3z4MDfeeCM33XQTZWVl3HbbbTz55JM6GjRGPPXUU/zXf/0XSUlJPPzww0ydOpWDBw96HUtCKKhCN7MrzGyTmW0xs1OuI2ZmLczsjZrHPzWzHiFPKp5xzvGXv/yF4cOH8+qrr9K6dWtefPFFnn/+eZV5DDEzfvrTn/LWW2/Rpk0b5s+fT//+/VmwYIH2gIkTKQ0tYGbJwHPABKAY+MzMFjrnNgQsditwwDl3nplNBX4NXBuOwIcOHeLgwYPs3bs3HC8ftcI9Zv8/aOcczjnKy8spLy9n69atzJw5kxUrVgAwZMgQ5s6dS9++fcOWRcLryiuv5NNPP+Vf//VfWb58OVOmTGHixImMHTuWrl270qlTJ84++2zatWtHmzZtSEoK7x/yifjvOWzXf/X/A67vCxgDvBtw+37g/jrLvAuMqfk+Bfg7YGd63dzcXNcUV111lQP0FeGvc845xz399NOurKysSZ9bUyxZsiRi7xUtIjnmqqoq9/zzz7s2bdp4/vuVaF+XXHJJkz83IN/V06sNrqEDnYFdAbeLgVH1LeOcqzSzQ0B7fMVey8ymA9MBsrOzycvLC+LtT1ZWVkabNm0S7k9951zYx+x/fTMjJSWF1NRUWrZsyUUXXcSUKVNo3bp1RA8jLy0tbdLvSCyL9Jj79evHSy+9xNKlS9mzZw979uxh3759lJaWUlpayrFjx8I+HROJ3+1ok5qaGp7Pub6md/9Y+74G+O+A2zcCz9ZZZh3QJeD2VqDDmV63qWvozmnNLVFozIlBY24czrCGHszk2FdA14DbXWruO+0yZpYCtAX2NfH/GBERaYJgCv0zIMfMeppZGjAVWFhnmYXAzTXfXwN8VPM/iYiIREiDc+jONyc+A9+Gz2TgJefcejN7BN+q/0LgRWCOmW0B9uMrfRERiaBgNorinFsELKpz34MB35cBU0IbTUREGkNHioqIxAkVuohInFChi4jECRW6iEicMK/2LjSzvcCOJj69A3WOQk0AGnNi0JgTQ3PG3N05d87pHvCs0JvDzPKdcyO8zhFJGnNi0JgTQ7jGrCkXEZE4oUIXEYkTsVros70O4AGNOTFozIkhLGOOyTl0ERE5VayuoYuISB0qdBGROBHVhZ6IF6cOYsx3m9kGMys0sw/NrLsXOUOpoTEHLHe1mTkzi/ld3IIZs5l9v+azXm9mr0c6Y6gF8bvdzcyWmFlBze/3VV7kDBUze8nM9pjZunoeNzP7Xc3Po9DMhjf7Teu78oXXX/hO1bsV6AWkAWuA/nWW+Qkwq+b7qcAbXueOwJgvAVrXfH97Ioy5ZrlM4GNgBTDC69wR+JxzgALgrJrbWV7njsCYZwO313zfH9jude5mjvkiYDiwrp7HrwIWAwaMBj5t7ntG8xr6SGCLc26bc64cmAtMrrPMZOCVmu8XAJdZbF+csMExO+eWOOeO1dxcge8KUrEsmM8Z4FHg10BZJMOFSTBj/hHwnHPuAIBzbk+EM4ZaMGN2QJua79sCX0cwX8g55z7Gd32I+kwG/uh8VgDtzKxjc94zmgv9dBen7lzfMs65SsB/cepYFcyYA92K73/4WNbgmGv+FO3qnHs7ksHCKJjPuQ/Qx8yWmtkKM7siYunCI5gxzwRuMLNifNdfuDMy0TzT2H/vDQrqAhcSfczsBmAEcLHXWcLJzJKA3wA/9DhKpKXgm3YZj++vsI/NbJBz7qCXocLsOuBl59xTZjYG31XQBjrnqr0OFiuieQ09ES9OHcyYMbPLgQeASc65ExHKFi4NjTkTGAjkmdl2fHONC2N8w2gwn3MxsNA5V+GcKwI24yv4WBXMmG8F5gE455YDLfGdxCpeBfXvvTGiudAT8eLUDY7ZzIYBL+Ar81ifV4UGxuycO+Sc6+Cc6+Gc64Fvu8Ek51y+N3FDIpjf7TfxrZ1jZh3wTcFsi2DGUAtmzDuBywDMrB++Qt8b0ZSRtRC4qWZvl9HAIedcSbNe0estwQ1sJb4K35rJVuCBmvsewfcPGnwf+HxgC7AS6OV15giM+QNgN7C65muh15nDPeY6y+YR43u5BPk5G76ppg3AWmCq15kjMOb+wFJ8e8CsBiZ6nbmZ4/0TUAJU4PuL61bgNuC2gM/4uZqfx9pQ/F7r0H8RkTgRzVMuIiLSCCp0EZE4oUIXEYkTKnQRkTihQhcRiRMqdBGROKFCFxGJEyp0kRpmdn7Nealbmll6zXnIB3qdSyRYOrBIJICZ/RLfEcitgGLn3OMeRxIJmgpdJEDNeUY+w3fe9Qucc1UeRxIJmqZcRE7WHsjAd5bHlh5nEWkUraGLBDCzhfiuptMT6Oicm+FxJJGg6QIXIjXM7Cagwjn3upklA8vM7FLn3EdeZxMJhtbQRUTihObQRUTihApdRCROqNBFROKECl1EJE6o0EVE4oQKXUQkTqjQRUTixP8H11k+JsKd9PcAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from utils import evaluate_on_points\n",
    "tol = 0.001 # Avoid hitting the outside of the domain\n",
    "y = np.linspace(0 + tol, L - tol, 101)\n",
    "points = np.zeros((3, 101))\n",
    "points[0] = y\n",
    "points[1] = H/2\n",
    "\n",
    "\n",
    "fig = plt.figure()\n",
    "points_on_proc, alpha_val = evaluate_on_points(alpha, points)\n",
    "plt.plot(points_on_proc[:,0], alpha_val, \"k\", linewidth=2, label=\"Damage\")\n",
    "plt.grid(True)\n",
    "plt.xlabel(\"x\")\n",
    "plt.legend()\n",
    "\n",
    "# If run in parallel as a python file, we save a plot per processor\n",
    "plt.savefig(f\"output/damage_line_rank{MPI.COMM_WORLD.rank:d}.png\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises\n",
    "\n",
    "- Replace the mesh with an unstructured mesh generated with gmsh\n",
    "- Refactor `alternate_minimization` as an external function or class to put in a seperate `.py` file to import in the notebook\n",
    "- Run simulations for\n",
    "    1. A slab with an hole in the center\n",
    "    2. A slab with a V-notch"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "VarFrac.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}