Exercise _7.ipynb

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        "<a href=\"https://colab.research.google.com/github/bilgin-kocak/fenics-tutorials-anders-logg/blob/master/Exercise%20_7.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
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      "source": [
        "# Exercise 7: Modeling composite materials\n",
        "\n",
        "![image.png](attachment:image.png)\n",
        "\n",
        "In this exercise, we will compute the effective material stiffness and effective Poisson's ratio of a composite material. The domain $\\Omega$ is a 2D cross-section in the $xy$-plane of a set of cylindrical fibers (going in the $z$-direction) embedded in a surrounding material (matrix). We model the material by dividing the domain $\\Omega$ into two different domains, the matrix (background) domain $\\Omega_0$ and the fiber domain $\\Omega_1$, with different material parameters in the two domains.\n",
        "\n",
        "Just like in Exercise 5a, we will solve the equations of linear elasticity:\n",
        "\\begin{align}\n",
        "-\\mathrm{div}\\,\\sigma(u) = f. \\\\\n",
        "\\end{align}\n",
        "\n",
        "The stress tensor $\\sigma = \\sigma(u)$ is given by\n",
        "$$\n",
        "\\sigma(u) = 2\\mu\\epsilon(u) + \\lambda \\mathrm{tr}\\,\\epsilon(u) I,\n",
        "$$\n",
        "\n",
        "where $\\epsilon(u) = \\frac{1}{2}(\\mathrm{grad}\\,u + (\\mathrm{grad}\\,u)^{\\top})$ is the symmetric gradient and $I$ is the identity matrix. The Lamé parameters are\n",
        "\\begin{align}\n",
        "\\mu &= \\frac{E}{2\\cdot(1 + \\nu)}, \\\\\n",
        "\\lambda &= \\frac{E\\nu}{(1 + \\nu)(1 - 2\\nu)}.\n",
        "\\end{align}\n",
        "\n",
        "Note that this 2D problem is identical to the 3D linear elastic problem in the case of [plane strain](https://en.wikipedia.org/wiki/Infinitesimal_strain_theory#Plane_strain).\n",
        "\n",
        "The parameters $E$ and $\\nu$ will have different values in $\\Omega_0$ and $\\Omega_1$.\n",
        "\n",
        "We will use the following data:\n",
        "\n",
        "* $E_0 = 3\\,\\mathrm{[GPa]}$ (Young's modulus in $\\Omega_0$)\n",
        "* $E_1 = 80\\,\\mathrm{[GPa]}$ (Young's modulus in $\\Omega_1$)\n",
        "* $\\nu_0 = 0.4$ (Poisson's ratio in the matrix)\n",
        "* $\\nu_1 = 0.2$ (Poisson's ratio in the fibers)\n",
        "* Fiber locations given by the file `Ex3-Fibers.txt`\n",
        "* $u_x = 0$ on the left boundary\n",
        "* $u_x = \\delta$ on the right boundary\n",
        "* $u_y = 0$ in the lower left corner\n",
        "\n",
        "We will scale the Young's moduli to `3` and `80` (rather than `3e9` and `80e9`) for numerical stability. Remember that most numerical sofware and number systems perform better when all numbers are close `1`."
      ]
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    {
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      "source": [
        "## Importing FEniCS\n",
        "The first thing we need to do is to import FEniCS."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9I28er3zKSF9",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Installing and Importing Fenics\n",
        "from google.colab import files\n",
        "\n",
        "import platform, sys\n",
        "python_version=platform.python_version()\n",
        "from distutils.version import LooseVersion, StrictVersion\n",
        "\n",
        "if ( LooseVersion(python_version) < LooseVersion(\"3.0.0\")):\n",
        "    print(\"Python3 is needed!\");\n",
        "    print(\"How to fix: Runtime/Change_runtime_type/Python 3\");\n",
        "    sys.exit()\n",
        "try:\n",
        "    from fenics import *; from mshr import *\n",
        "except ImportError as e:\n",
        "    !apt-get install -y -qq software-properties-common python-software-properties module-init-tools\n",
        "    !add-apt-repository -y ppa:fenics-packages/fenics\n",
        "    !apt-get update -qq\n",
        "    !apt install -y --no-install-recommends fenics\n",
        "    from fenics import *; from mshr import *\n",
        "    \n",
        "dolfin_version = dolfin.__version__\n",
        "print ('dolfin version:', dolfin_version)\n",
        "\n",
        "!rm -rf * # clean up all files\n",
        "# Useful commands\n",
        "# Remove an empty folder      : os.rmdir(\"my_results\")\n",
        "# Remove a folder with files  : shutil.rmtree(\"results\")\n",
        "# Make a folder               : os.mkdir(\"my_results\")\n",
        "# Runtime/Change_runtime_type/Python3"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QCelcAgLKSGJ",
        "colab_type": "text"
      },
      "source": [
        "## Initializing notebook plotting\n",
        "When running in a Jupyter notebook, a special line is necessary to show FEniCS plots in the notebook."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ypbdFYt-KSGN",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "%matplotlib inline"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Gj-kXWkLKbc7",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 35
        },
        "outputId": "82b6200d-3f48-41d3-b874-ab1004389aaf"
      },
      "source": [
        "import requests\n",
        "\n",
        "\n",
        "url = 'https://github.com/bilgin-kocak/fenics-tutorials-anders-logg/blob/master/Ex3-Fibers.txt'\n",
        "r = requests.get(url, allow_redirects=True)\n",
        "\n",
        "open('Ex3-Fibers.txt', 'wb').write(r.content)"
      ],
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      "source": [
        "## Loading the fiber coordinates\n",
        "Before creating the mesh, we need to load the fiber coordinates from the text file `Ex3-Fibers.txt`. The file is a so-called CSV file (comma-separated values). Use the `loadtxt()` command from `numpy` to load the data into an array. Each row in the array will give the center coordinates $(x, y)$ and the radius $r$ for a fiber. Store the coordinates and radii in three arrays named `cx`, `cy` and `cr`."
      ]
    },
    {
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        "colab": {},
        "outputId": "4a9a87ea-d2d5-42bc-971a-c8db06433a2c"
      },
      "source": [
        "from numpy import loadtxt\n",
        "fibers = loadtxt('Ex3-Fibers.txt')\n",
        "cx = fibers[:, 0]\n",
        "cy = fibers[:, 1]\n",
        "cr = fibers[:, 2]\n",
        "print(fibers)"
      ],
      "execution_count": null,
      "outputs": [
        {
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            "[[ 6.001447  5.034437  3.25    ]\n",
            " [16.985958  6.019035  2.75    ]\n",
            " [34.966783  6.943401  2.5     ]\n",
            " [80.152196  6.933722  2.75    ]\n",
            " [89.039734  7.061682  2.75    ]\n",
            " [41.995393  7.990612  2.75    ]\n",
            " [47.996703  7.964242  2.75    ]\n",
            " [55.0148    8.048407  2.5     ]\n",
            " [10.996202  9.206415  3.      ]\n",
            " [73.151207  8.983816  3.5     ]\n",
            " [97.        9.        3.25    ]\n",
            " [24.867563  9.985847  3.5     ]\n",
            " [65.043142 10.900814  3.25    ]\n",
            " [84.877569 12.095883  3.25    ]\n",
            " [17.       13.        2.75    ]\n",
            " [37.967763 12.995392  2.5     ]\n",
            " [58.004052 13.024101  3.25    ]\n",
            " [ 5.022265 14.083219  3.      ]\n",
            " [51.903346 14.104241  3.      ]\n",
            " [93.001726 13.995285  2.75    ]\n",
            " [44.999375 15.998124  3.5     ]\n",
            " [22.       17.        2.5     ]\n",
            " [27.020804 17.081191  2.5     ]\n",
            " [34.       18.001358  2.5     ]\n",
            " [66.895852 17.992675  3.75    ]\n",
            " [81.00828  17.987303  3.25    ]\n",
            " [88.037404 18.020709  2.75    ]\n",
            " [74.071478 18.994232  3.25    ]\n",
            " [ 4.060547 19.911699  3.      ]\n",
            " [11.000047 20.011624  3.      ]\n",
            " [38.985207 20.054019  2.5     ]\n",
            " [60.998645 21.170875  3.25    ]\n",
            " [16.977526 21.82964   2.5     ]\n",
            " [28.954269 21.909213  2.5     ]\n",
            " [52.837767 22.236352  3.75    ]\n",
            " [93.891362 22.170897  3.25    ]\n",
            " [23.091417 23.208024  3.      ]\n",
            " [45.979406 23.94998   3.5     ]\n",
            " [37.023772 24.961203  2.5     ]\n",
            " [67.075872 24.98996   3.      ]\n",
            " [12.       26.008509  2.5     ]\n",
            " [82.912044 25.627455  3.25    ]\n",
            " [ 5.019521 26.977296  2.75    ]\n",
            " [31.026897 27.853929  2.75    ]\n",
            " [90.130013 28.060028  2.5     ]\n",
            " [96.991073 28.008927  2.75    ]\n",
            " [24.969958 28.902002  2.25    ]\n",
            " [18.000563 30.063947  3.5     ]\n",
            " [71.031625 29.97974   3.      ]\n",
            " [40.984367 30.93906   2.75    ]\n",
            " [48.04506  30.991331  3.25    ]\n",
            " [55.98531  31.031404  3.5     ]\n",
            " [77.031382 31.246962  3.25    ]\n",
            " [ 7.021017 32.043263  2.75    ]\n",
            " [62.831152 32.024158  3.5     ]\n",
            " [11.9878   33.004332  2.25    ]\n",
            " [85.845377 32.913521  3.      ]\n",
            " [31.102929 33.881011  2.25    ]\n",
            " [35.988631 34.132912  2.5     ]\n",
            " [24.171864 34.783791  2.75    ]\n",
            " [93.002082 34.95635   2.5     ]\n",
            " [52.026994 36.964916  3.25    ]\n",
            " [70.955548 36.946973  3.      ]\n",
            " [79.       38.        3.      ]\n",
            " [12.162965 38.953769  2.75    ]\n",
            " [37.901962 39.810523  3.      ]\n",
            " [65.025794 39.990254  3.5     ]\n",
            " [85.056883 39.935233  3.      ]\n",
            " [31.       41.000539  3.25    ]\n",
            " [58.061624 40.966373  3.      ]\n",
            " [ 5.942153 41.905384  2.5     ]\n",
            " [92.000377 41.994346  3.      ]\n",
            " [47.006905 43.069789  3.5     ]\n",
            " [73.964043 43.027521  3.5     ]\n",
            " [16.648776 44.260481  3.25    ]\n",
            " [25.999026 43.998273  2.75    ]\n",
            " [11.045024 46.102816  3.      ]\n",
            " [40.923676 45.932644  3.25    ]\n",
            " [61.903074 46.97634   2.75    ]\n",
            " [87.012785 46.867348  3.      ]\n",
            " [80.037505 47.832876  2.75    ]\n",
            " [96.938631 48.099143  3.      ]\n",
            " [20.938315 49.070067  2.75    ]\n",
            " [50.9866   50.017596  3.5     ]\n",
            " [73.961454 50.012285  2.75    ]\n",
            " [28.00298  50.900041  2.75    ]\n",
            " [35.963138 50.956643  2.5     ]\n",
            " [66.948611 51.067199  2.75    ]\n",
            " [16.080618 51.973569  3.      ]\n",
            " [44.018262 52.990006  3.5     ]\n",
            " [85.1076   54.002349  3.75    ]\n",
            " [31.987563 55.793505  3.5     ]\n",
            " [78.016645 56.085891  3.      ]\n",
            " [ 5.       57.        3.      ]\n",
            " [11.997171 56.974998  3.      ]\n",
            " [24.953215 56.869901  2.75    ]\n",
            " [58.100808 56.866469  2.75    ]\n",
            " [64.999992 57.001011  3.      ]\n",
            " [38.961719 58.061506  3.      ]\n",
            " [91.963625 58.066491  3.5     ]\n",
            " [18.983795 59.009278  2.75    ]\n",
            " [45.99296  60.024119  3.25    ]\n",
            " [71.029728 59.969389  3.75    ]\n",
            " [85.990559 62.018337  4.      ]\n",
            " [28.021007 63.011074  2.5     ]\n",
            " [56.09679  63.025303  3.      ]\n",
            " [ 7.95141  63.886483  3.      ]\n",
            " [34.914762 63.958977  3.5     ]\n",
            " [64.096974 64.187456  2.75    ]\n",
            " [14.918549 65.027259  2.75    ]\n",
            " [21.976194 65.128133  2.5     ]\n",
            " [97.034615 64.970199  3.      ]\n",
            " [41.952531 66.966545  3.75    ]\n",
            " [69.043468 67.926047  3.      ]\n",
            " [77.255222 67.900922  3.75    ]\n",
            " [27.03144  69.013206  3.25    ]\n",
            " [49.911027 69.120477  3.75    ]\n",
            " [57.012872 69.938199  3.      ]\n",
            " [93.926653 69.854006  2.75    ]\n",
            " [ 9.99637  71.01578   2.75    ]\n",
            " [63.100036 71.129634  2.75    ]\n",
            " [17.943365 72.111423  3.5     ]\n",
            " [83.018995 72.970664  3.25    ]\n",
            " [39.030719 73.996941  3.5     ]\n",
            " [ 4.849714 75.047196  3.      ]\n",
            " [31.158114 74.954348  3.5     ]\n",
            " [68.836227 74.899225  3.25    ]\n",
            " [88.994    74.98254   2.5     ]\n",
            " [24.189685 76.103251  3.5     ]\n",
            " [13.056731 76.961076  2.5     ]\n",
            " [55.08452  77.081163  3.      ]\n",
            " [62.054879 77.148566  2.75    ]\n",
            " [75.022732 78.007053  3.5     ]\n",
            " [83.974436 80.078786  3.5     ]\n",
            " [94.039403 79.932814  3.5     ]\n",
            " [ 8.977976 81.893637  3.      ]\n",
            " [19.017817 81.947556  3.5     ]\n",
            " [38.987195 81.953651  3.5     ]\n",
            " [67.93765  81.959977  3.      ]\n",
            " [31.999541 82.842979  3.75    ]\n",
            " [51.022254 82.87006   3.25    ]\n",
            " [59.984762 82.965649  2.5     ]\n",
            " [88.997521 84.988791  2.75    ]\n",
            " [45.055016 86.007372  2.5     ]\n",
            " [73.998398 85.966193  3.75    ]\n",
            " [80.980177 86.068869  3.25    ]\n",
            " [14.103409 86.827508  3.5     ]\n",
            " [95.000807 87.002208  3.      ]\n",
            " [55.94549  87.975311  3.25    ]\n",
            " [65.10924  87.923568  3.      ]\n",
            " [25.056506 89.056211  3.25    ]\n",
            " [ 7.065259 89.88162   2.75    ]\n",
            " [33.922964 89.939224  3.5     ]\n",
            " [19.122522 91.791096  3.      ]\n",
            " [49.504433 92.252353  2.5     ]\n",
            " [43.01786  93.006088  3.25    ]\n",
            " [84.836673 93.185085  2.5     ]\n",
            " [12.090824 93.893441  2.75    ]\n",
            " [70.966043 94.115764  4.      ]\n",
            " [93.020777 94.188936  2.75    ]\n",
            " [56.980757 94.941024  3.25    ]\n",
            " [26.989617 95.814182  3.5     ]\n",
            " [37.015918 95.986634  3.      ]\n",
            " [63.969811 96.118701  3.      ]]\n"
          ],
          "name": "stdout"
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      "source": [
        "## Creating the mesh\n",
        "\n",
        "In order for the fibers not to overlap, compute the number `feps` as `0.01` times the average fiber radius and then make sure that the distance between any two fibers is at least `feps`. Also use `feps` to expand the size of the enclosing domain so as not to touch the fibers.\n",
        "\n",
        "Use FEniCS `mshr` to create the mesh. Figure out the dimensions of the fiber sample by computing $x_{\\mathrm{min}} = \\min(x - r)$ and similarly $x_{\\mathrm{max}}$, $y_{\\mathrm{min}}$ and $y_{\\mathrm{max}}$. Create a rectangle using these coordinates and mark each fiber as a subdomain (`1`, `2`, `3`, ...) using the `set_subdomain()` command. See the section on [generating meshes with subdomains](https://fenicsproject.org/pub/tutorial/sphinx1/._ftut1005.html#generating-meshes-with-subdomains) in the [FEniCS Tutorial](https://fenicsproject.org/tutorial/) for details.\n",
        "\n",
        "Use a resolution of $m = 64$ for the mesh generation. Note that it may take some time to generate the mesh so you might want to start with $m = 16$.\n",
        "\n",
        "Also note that we will use the original scaling of the fiber coordinates. The actual dimension of the fiber sample is ca $16\\,\\mu\\mathrm{m}$, but since the scaling of the domain is not relevant to the computation of the effective material stiffness and Poisson's ratio, we will keep the original scaling."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "koA2BlS0KSGc",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "from mshr import *\n",
        "from numpy import mean\n",
        "\n",
        "# Compute feps as 0.01 times the average fiber radius\n",
        "feps = 0.01*mean(cr)\n",
        "\n",
        "# Make sure that the distance between all fiber pairs is at least feps\n",
        "for i in range(len(cr)):\n",
        "    for j in range(i + 1, len(cr)):\n",
        "        d = sqrt((cx[i] - cx[j])**2 + (cy[i] - cy[j])**2)\n",
        "        if d - feps < cr[i] + cr[j]:\n",
        "            cr[i] = d - feps - cr[j]\n",
        "\n",
        "# Compute xmin, xmax, ymin, ymax\n",
        "xmin = min(cx - cr) - feps\n",
        "xmax = max(cx + cr) + feps\n",
        "ymin = min(cy - cr) - feps\n",
        "ymax = max(cy + cr) + feps\n",
        "\n",
        "# Define the background domain\n",
        "domain = Rectangle(Point(xmin, ymin), Point(xmax, ymax))\n",
        "\n",
        "# Mark the fibers\n",
        "for i, (x, y, r) in enumerate(fibers):\n",
        "    circle = Circle(Point(x, y), r)\n",
        "    domain.set_subdomain(i + 1, circle)\n",
        "\n",
        "# Generate the mesh\n",
        "m = 64\n",
        "mesh = generate_mesh(domain, m)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "R5Hkf_5yKSGj",
        "colab_type": "text"
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      "source": [
        "## Creating domain markers\n",
        "Use a `MeshFunction` to create markers for the subdomains of the mesh. Since we only need two subdomains (the default value `0` for the matrix and `1` for the fibers) we modify the markers to either `0` or `1`. Use the domain markers to define an integration measure `dx` connected to the markers.\n",
        "\n",
        "Use the integration measure to compute the volume fraction of fibers in the domain as the integral of `1*dx(1)` divided by the integral of `1*dx` (which is identical to `1*(dx(0) + dx(1))`. The integrals can be computed using the `assemble()` function in FEniCS."
      ]
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        "outputId": "fecad00b-d092-4806-f376-4f1d4ff92f79"
      },
      "source": [
        "# Create MeshFunction for domain markers\n",
        "domain_markers = MeshFunction('size_t', mesh, 2, mesh.domains())\n",
        "\n",
        "# Mark all fiber domains as 1\n",
        "for i in range(domain_markers.size()):\n",
        "    if domain_markers[i] > 0:\n",
        "        domain_markers[i] = 1\n",
        "        \n",
        "# Plot and save the markers to file for inspection\n",
        "plot(domain_markers)\n",
        "File('exercise7/domain_markers.pvd') << domain_markers\n",
        "\n",
        "# Create integration measure dx connected to the markers\n",
        "dx = Measure('dx', domain=mesh, subdomain_data=domain_markers)\n",
        "\n",
        "# Compute the volume fraction\n",
        "Vf = assemble(1*dx(1)) / assemble(1*dx)\n",
        "print('Vf =', Vf)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Calling FFC just-in-time (JIT) compiler, this may take some time.\n",
            "Calling FFC just-in-time (JIT) compiler, this may take some time.\n",
            "Vf = 0.4591017014027414\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yVoONhwxKSGs",
        "colab_type": "text"
      },
      "source": [
        "## Setting problem parameters\n",
        "We will use the following problem parameters."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nMWs8-9WKSGu",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "E0 = 3        # Young's modulus in domain 0 (matrix)\n",
        "E1 = 80       # Young's modulus in domain 1 (fibers)\n",
        "nu0 = 0.4     # Poisson's ratio in domain 0 (matrix)\n",
        "nu1 = 0.2     # Poisson's ratio in domain 1 (fibers)\n",
        "strain = 0.01 # Strain (relative displacement)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "J8P3P3jwKSGx",
        "colab_type": "text"
      },
      "source": [
        "## Defining the finite element function space\n",
        "When we have loaded the mesh, we can define the finite element function space. We will use a piecewise quadratic $P_2$ function space. Since the displacement is vector-valued, we will need to create a `VectorFunctionSpace`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0H48bt3sKSGy",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "V = VectorFunctionSpace(mesh, 'P', 2)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "hDAOhdCaKSG2",
        "colab_type": "text"
      },
      "source": [
        "## Defining the boundary conditions\n",
        "The three boundary conditions can be defined by using the `DirichletBC` class in combination with either FEniCS `SubDomain` classes or by directly specifying expressions for the boundary conditions, for example `'near(x[0], %.16g) % xmin'`. Note that for the point-wise boundary condition at the lower left corner one needs to specify the additional argument `'pointwise'`.\n",
        "\n",
        "Use `V.sub(0)` and `V.sub(1)` to set boundary conditions separately for the $u_x$ and $u_y$ displacement components."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JnGPnb2XKSG4",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "bc0 = DirichletBC(V.sub(0), 0, 'near(x[0], %.16g)' % xmin)\n",
        "bc1 = DirichletBC(V.sub(1), 0, 'near(x[0], %.16g) && near(x[1], %.16g)' % (xmin, ymin), 'pointwise')\n",
        "bc2 = DirichletBC(V.sub(0), strain*(xmax - xmin), 'near(x[0], %.16g)' % xmax)\n",
        "bcs = [bc0, bc1, bc2]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UzMiCl-DKSG8",
        "colab_type": "text"
      },
      "source": [
        "## Defining the variational problem\n",
        "The finite element variational problem for the linear elasticy problem reads: Find $u \\in V$ such that\n",
        "$$\n",
        "\\int_{\\Omega_0} \\sigma_0(u) : \\varepsilon(v) \\,\\mathrm{d}x +\n",
        "\\int_{\\Omega_1} \\sigma_1(u) : \\varepsilon(v) \\,\\mathrm{d}x\n",
        "=\n",
        "\\int_{\\Omega} f \\cdot v \\,\\mathrm{d}x\n",
        "$$\n",
        "for all $v \\in V$.\n",
        "\n",
        "This can be expressed in FEniCS by defining the *bilinear form* $a$ and the *linear form* $L$:\n",
        "\n",
        "\\begin{align}\n",
        "  a(u, v) &= \\int_{\\Omega_0} \\sigma_0(u) : \\varepsilon(v) \\,\\mathrm{d}x + \\int_{\\Omega_1} \\sigma_1(u) : \\varepsilon(v) \\,\\mathrm{d}x, \\\\\n",
        "  L(v) &= \\int_{\\Omega} f \\cdot v \\,\\mathrm{d}x,\n",
        "\\end{align}\n",
        "\n",
        "where $\\sigma_0(u)$ and $\\sigma_1(u)$ are two different expressions for the stress tensor depending on the different material parameters for the two domains $\\Omega_0$ and $\\Omega_1$. These domains are the matrix domain (marked as `0`) and the fiber domain (marked as `1`).\n",
        "\n",
        "The two integration domains can be expressed in FEniCS as `dx(0)` and `dx(1)`."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nb6r7RU8KSG8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def epsilon(u):\n",
        "    return sym(grad(u))\n",
        "\n",
        "def sigma(u, E, nu):\n",
        "    mu = E / (2.0*(1.0 + nu))\n",
        "    lmbda = E*nu / ((1.0 + nu)*(1.0 - 2.0*nu))\n",
        "    return 2.0*mu*epsilon(u) + lmbda*tr(epsilon(u))*Identity(2)\n",
        "\n",
        "u = TrialFunction(V)\n",
        "v = TestFunction(V)\n",
        "f = Constant((0, 0))\n",
        "a = inner(sigma(u, E0, nu0), grad(v))*dx(0) + inner(sigma(u, E1, nu1), grad(v))*dx(1)\n",
        "L = dot(f, v)*dx"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "yVDekgplKSHB",
        "colab_type": "text"
      },
      "source": [
        "## Solving the variational problem\n",
        "The variational problem can now be solved by calling the FEniCS `solve` command. Use the `plot` command to visualize the solution. Use a new variable `u_h` to store the solution (rather than overwriting the trial function `u`) since we will make use of both `u` and `u_h` below..."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "kJAHdQeeKSHB",
        "colab_type": "code",
        "colab": {},
        "outputId": "fb5e9dd7-8709-4df6-b6fd-43c71956ef44"
      },
      "source": [
        "u_h = Function(V)\n",
        "solve(a == L, u_h, bcs)\n",
        "plot(u_h)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Calling FFC just-in-time (JIT) compiler, this may take some time.\n",
            "Calling FFC just-in-time (JIT) compiler, this may take some time.\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.quiver.Quiver at 0x7fd1a7a8ce10>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 11
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "z8AVYWqqKSHG",
        "colab_type": "text"
      },
      "source": [
        "## Computing the reaction force\n",
        "To compute the effective material stiffness, we note that if $-\\nabla\\cdot u = f$ in a domain $\\Omega$, then it follows from integration by parts that\n",
        "$$\n",
        "\\int_{\\Omega} \\sigma(u):\\varepsilon(v) \\,\\mathrm{d}x \n",
        "= \\int_{\\partial\\Omega} g \\cdot v \\,\\mathrm{d}s\n",
        "+ \\int_{\\Omega} f \\cdot v \\,\\mathrm{d}x,\n",
        "$$\n",
        "where $g = \\sigma\\cdot n$ is the *boundary traction*. Note that this holds for any (differentiable) function $v$.\n",
        "\n",
        "To compute the reaction force $F$ on the left boundary $\\Gamma_{\\mathrm{L}}$, we note that if $f = 0$ and $\\psi$ is a function that is equal to $(1, 0)$ on $\\Gamma_{\\mathrm{L}}$ and zero on the remaining boundary, then\n",
        "$$\n",
        "F = \\int_{\\Gamma_{\\mathrm{L}}} (\\sigma\\cdot n) \\cdot (-1,0) \\,\\mathrm{d}s\n",
        "= -\\int_{\\partial\\Omega} g \\cdot \\psi \\,\\mathrm{d}s\n",
        "= -\\int_{\\Omega} \\sigma(u):\\varepsilon(\\psi) \\,\\mathrm{d}x.\n",
        "$$\n",
        "In other words, the reaction force on the boundary can be computed by an integral of the stress over the domain weighted by the strain of the function $\\psi$.\n",
        "\n",
        "Alternatively, the reaction force may be computed by noting that if $\\mathcal{I}$ is the set of indices for the nodes\n",
        "on the left boundary $\\Gamma_{\\mathrm{L}}$ related to the $x$-component of the finite element solution, then the function $\\psi$ can be expressed as\n",
        "$$\n",
        "\\psi(x) = \\sum_{i\\in\\mathcal{I}} \\phi_i(x).\n",
        "$$\n",
        "It follows that\n",
        "$$\n",
        "F\n",
        "= -\\int_{\\Omega} \\sigma(u):\\varepsilon(\\psi) \\,\\mathrm{d}x\n",
        "= -\\int_{\\Omega} \\sigma\\left(\\sum_{j=1}^N U_j \\phi_j\\right):\\varepsilon\\left(\\sum_{i\\in\\mathcal{I}}\\phi_i\\right) \\,\\mathrm{d}x\n",
        "= -\\sum_{i\\in\\mathcal{I}} \\sum_{j=1}^N U_j \\int_{\\Omega} \\sigma(\\phi_j):\\varepsilon(\\phi_i) \\,\\mathrm{d}x\n",
        "= -\\sum_{i\\in\\mathcal{I}} (AU)_i,\n",
        "$$\n",
        "where $A$ is the stiffness matrix and $U$ is the vector of degrees of freedom for the computed solution. We may thus compute the reaction force by applying the stiffness matrix (before application of boundary conditions!) to the solution vector $U$ and then sum over the rows corresponding to the normal component degrees of freedom on the left boundary.\n",
        "\n",
        "Note that both alternatives should yield the same result for the reaction force (to within machine precision).\n",
        "\n",
        "The function $\\psi$ may be constructed in FEniCS by creating a vector-valued function in the function space $V$ and setting the value on the left boundary to $(1, 0)$ using a `DirichletBC` applied to the vector $\\Psi$ of degrees of freedom for the function $\\psi$. Summing over the degrees of freedom on the boundary may be expressed by taking the inner product of the vector $AU$ with the degrees of freedom $\\Psi$ of the function $\\psi$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xLYzGw2MKSHJ",
        "colab_type": "code",
        "colab": {},
        "outputId": "17859bdd-32f1-481f-8f94-0a93fc00930e"
      },
      "source": [
        "# Create the finite element function psi\n",
        "psi = Function(V)\n",
        "bc = DirichletBC(V.sub(0), Constant(1), 'near(x[0], %.16g)' % xmin)\n",
        "PSI = psi.vector()\n",
        "bc.apply(PSI)\n",
        "psi_x, psi_y = psi.split()\n",
        "plot(psi_x)\n",
        "File('exercise7/psi_x.pvd') << psi_x\n",
        "\n",
        "# Alternative 1: Evaluate the form on the function psi\n",
        "F2 = -assemble(inner(sigma(u_h, E0, nu0), grad(psi))*dx(0) + inner(sigma(u_h, E1, nu1), grad(psi))*dx(1))\n",
        "print(\"F1 =\", F2)\n",
        "\n",
        "# Alternative 2: Apply the stiffness matrix\n",
        "A = assemble(a)\n",
        "U = u_h.vector()\n",
        "y = U.copy()\n",
        "A.mult(U, y)\n",
        "F1 = -y.inner(PSI)\n",
        "print(\"F2 =\", F1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Calling FFC just-in-time (JIT) compiler, this may take some time.\n",
            "F1 = 9.119101736994807\n",
            "F2 = 9.119101736994773\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "RyYr8htsKSHP",
        "colab_type": "text"
      },
      "source": [
        "## Computing the strains\n",
        "To compute the total strains, we note that\n",
        "$$\n",
        "\\frac{1}{\\Omega} \\int_{\\Omega} \\varepsilon_{xx} \\,\\mathrm{d}x\\mathrm{d}y\n",
        "=\n",
        "\\frac{1}{y_{\\mathrm{max}} - y_{\\mathrm{min}}} \n",
        "\\int_{y_{\\mathrm{min}}}^{y_{\\mathrm{max}}} \\frac{u_x(x_{\\mathrm{max}}, y) - u_x(x_{\\mathrm{min}}, y)}{x_{\\mathrm{max}} - x_{\\mathrm{min}}} \\,\\mathrm{d}y.\n",
        "$$\n",
        "In other words, the average of $\\varepsilon_{yy}$ over the domain is equal to the average relative $x$-displacement. Similarly, the average of $\\varepsilon_{xx}$ over the domain is equal to the average relative $y$-displacement."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "heIjM3SuKSHQ",
        "colab_type": "code",
        "colab": {},
        "outputId": "87e00074-0b16-466d-e90e-d865accc07dc"
      },
      "source": [
        "area = assemble(Constant(1)*dx) \n",
        "epsilon_xx = assemble(epsilon(u_h)[0,0]*dx) / area\n",
        "epsilon_yy = assemble(epsilon(u_h)[1,1]*dx) / area\n",
        "\n",
        "print('area =', area, ' should be equal to', (xmax - xmin)*(ymax - ymin))\n",
        "print('epsilon_xx =', epsilon_xx, ' should be equal to', strain)\n",
        "print('epsilon_yy =', epsilon_yy)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Calling FFC just-in-time (JIT) compiler, this may take some time.\n",
            "Calling FFC just-in-time (JIT) compiler, this may take some time.\n",
            "Calling FFC just-in-time (JIT) compiler, this may take some time.\n",
            "area = 9685.866837637512  should be equal to 9685.866837637597\n",
            "epsilon_xx = 0.010000000000000111  should be equal to 0.01\n",
            "epsilon_yy = -0.0054988158492224465\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "fqmCoj9gKSHT",
        "colab_type": "text"
      },
      "source": [
        "## Computing the effective material stiffness and Poisson's ratio\n",
        "To compute the effective material stiffness $E$, we divide the reaction force by the area (length) of the left boundary to get the stress and then divide again by the strain.\n",
        "\n",
        "We similarly compute the effective Poisson's ratio as $\\nu = -\\varepsilon_{yy}/\\varepsilon_{xx}$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "vVUmN4OUKSHU",
        "colab_type": "code",
        "colab": {},
        "outputId": "b5cefada-9b23-40c5-a369-04463beb4a56"
      },
      "source": [
        "F = F1\n",
        "S = F / (ymax - ymin)\n",
        "E = S / epsilon_xx\n",
        "nu = - epsilon_yy / epsilon_xx\n",
        "\n",
        "print('E =', E, \"GPa\")\n",
        "print('nu =', nu)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "E = 9.344256625779627 GPa\n",
            "nu = 0.5498815849222385\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "o9bEhsV1KSHa",
        "colab_type": "text"
      },
      "source": [
        "### Postprocessing\n",
        "To postprocess the solution using an external postprocessor, for example Paraview, save the solution to VTK format (file suffix `.pvd`)."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZXvBHkIoKSHb",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "File('exercise7/solution.pvd') << u_h"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "hsYW8FMtKSHe",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}