{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Homogeneous deformation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Often described as deformation during which lines remain as lines and parallel lines remain parallel. Homogeneous deformation could be described as **affine transformation** of initial coordinates" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\begin{align*}x &= aX+bY+t_X \\\\ y &= cX+dY+t_Y \\end{align*}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "or in matrix form using homogeneous coordinates:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ \\begin{bmatrix} x \\\\ y \\\\ 1 \\end{bmatrix}=\\begin{bmatrix} a & b & t_X \\\\ c & d & t_Y \\\\ 0 & 0 & 1 \\end{bmatrix}\\begin{bmatrix}X \\\\ Y \\\\ 1 \\end{bmatrix}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Properties of homogeneous deformation are not spatially dependent**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Deformation gradient" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Without translation $\\vec{t}$ the homogeneous deformation (rotation and strain) could be described as:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$\\begin{align*}x &= aX+bY \\\\ y &= cX+dY \\end{align*}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ \\begin{bmatrix}x \\\\ y\\end{bmatrix}=\\begin{bmatrix} a & b \\\\ c & d \\end{bmatrix}\\begin{bmatrix}X \\\\ Y\\end{bmatrix}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "or im matrix form" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$x=\\mathbf{F}X$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "where $ \\mathbf{F} $ is so called **deformation gradient**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note, that as we excluded translation, the origin of coordinates do not change during deformation:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ \\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix}=\\mathbf{F}\\begin{bmatrix} 0 \\\\ 0 \\end{bmatrix} $$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Displacement gradient" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Displacement of particle is vector between initial and final postion, i.e:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\\begin{align*}u &= x-X = aX+bY-X = (a-1)X+bY\\\\ v &= y-Y = cX+dY-Y = cX+(d-1)Y\\end{align*}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$ \\begin{bmatrix}u \\\\ v\\end{bmatrix}=\\begin{bmatrix} a-1 & b \\\\ c & d-1 \\end{bmatrix}\\begin{bmatrix}X \\\\ Y\\end{bmatrix}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "or" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "$$u=(\\mathbf{F}-\\mathbf{I})X=\\mathbf{\\nabla u}X$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "where $\\mathbf{\\nabla u}$ is so called **displacement gradient**." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Let's Python it" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Populating the interactive namespace from numpy and matplotlib\n" ] } ], "source": [ "%pylab inline" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lets try to visualize how unit circle deforms during homogeneous deformation:" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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PpqvnuedgwQI4cgTatYMvvgA7nWhcnoQFhhHgE8DuBMdeQFq4vuiz0dLlkycl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\nRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# parametric definition of unit circle\n", "theta = linspace(0, 2*pi, 300)\n", "Xc, Yc = cos(theta), sin(theta)\n", "plot(Xc, Yc, 'g')\n", "\n", "# Apply deformation gradient and plot ellipse\n", "F = array([[2, 0], [0, 0.5]])\n", "xe, ye = dot(F, [Xc, Yc])\n", "plot(xe, ye, 'r')\n", "axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Lets try to visualize how square deforms during homogeneous deformation:" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# coordinates of square\n", "Xs = [1, -1, -1, 1, 1]\n", "Ys = [1, 1, -1, -1, 1]\n", "plot(Xs, Ys, 'g')\n", "\n", "# Apply deformation gradient and plot result\n", "F = array([[2, 0], [0, 0.5]])\n", "xn, yn = dot(F, [Xs, Ys])\n", "plot(xn, yn, 'r')\n", "axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To visualize deformation gradient $\\mathbf{F}$ we have to calculate displacement for points on regular grid and plot it using command `quiver`." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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XL18uqo+JiaGPjw8B0NfXV/TOjsy3jiiwdVi0aJGo/v79+2zZsiUtLCzo7u4u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\njIzMK8r/B94L1alFx9KXAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# create rectangular grid\n", "X, Y = meshgrid(linspace(-2.2, 2.2, 21), linspace(-1.9, 1.9, 17))\n", "\n", "# Apply deformation gradient. As [X, Y] is 3D array, we need\n", "# special function to treat dot product properly. tensordot\n", "# can do it.\n", "x, y = tensordot(F, [X, Y], axes=1)\n", "\n", "# plot displacement vectors on all point\n", "quiver(X, Y, x-X, y-Y, angles='xy')\n", "plot(Xc, Yc, 'g', xe, ye, 'r')\n", "plot(Xs, Ys, 'g', xn, yn, 'r')\n", "axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also calculate displacements directly using displacement gradient $\\mathbf{\\nabla u} = \\mathbf{F} - \\mathbf{I}$:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "image/png": 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XL18uqo+JiaGPjw8B0NfXV/TOjsy3jiiwdVi0aJGo/v79+2zZsiUtLCzo7u4u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\nStqfP38eA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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# calculate displacements\n", "J = F - eye(2)\n", "u, v = tensordot(J, [X, Y], axes=1)\n", "\n", "# plot\n", "quiver(X, Y, u, v, angles='xy')\n", "plot(Xc, Yc, 'g', xe, ye, 'r')\n", "plot(Xs, Ys, 'g', xn, yn, 'r')\n", "axis('equal');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Using functions in Python" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### What are Functions?\n", "Functions are a convenient way to divide your code into useful blocks, allowing us to order our code, make it more readable, reuse it and save some time. Also functions are a key way to define interfaces so programmers can share their code.\n", "\n", "### How do you write functions in Python?\n", "As we have seen already, Python makes use of blocks. A block is a area of code of written in the format of:\n", "```\n", "block_head: \n", " 1st block line \n", " 2nd block line \n", " ...\n", "```\n", "Where a block line is more Python code (even another block), and the block head is of the following format: block_keyword block_name(argument1,argument2, ...) Block keywords you already know are \"if\", \"for\", and \"while\".\n", "\n", "Functions in python are defined using the block keyword \"def\", followed with the function's name as the block's name. For example:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def my_function():\n", " print(\"Hello from my_function!\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Functions may also receive arguments (variables passed from the caller to the function). For example:" ] }, { "cell_type": "code", "execution_count": 7, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def my_function_with_args(username, greeting):\n", " print(\"Hello {}, I wish you {}\".format(username, greeting))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Functions may return a value to the caller, using the keyword- 'return' . For example:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def sum_two_numbers(a, b):\n", " return a + b" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### How do you call functions in Python?\n", "Simply write the function's name followed by (), placing any required arguments within the brackets. For example, lets call the functions written above (in the previous example):" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Hello from my_function!\n", "Hello Johny, I wish you a great day!\n", "7\n" ] } ], "source": [ "# print a simple greeting \n", "my_function()\n", "\n", "#prints - \"Hello Johny, I wish you a great day!\"\n", "my_function_with_args(\"Johny\", \"a great day!\")\n", "\n", "# after this line x will hold the value 7!\n", "x = sum_two_numbers(4, 3)\n", "print(x)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Functions to visualize strain ellipse and displacement field\n", "These functions are provided in `sg2lib.py` library in repository, so later you can import them as `from sg2lib import *`" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from pylab import *\n", "from scipy import linalg as la\n", "\n", "def def_ellipse(F):\n", " # Draw strain ellipse from deformation gradient\n", " theta = linspace(0, 2*pi, 180)\n", " xc, yc = cos(theta), sin(theta)\n", " x,y = dot(F, [xc,yc])\n", " plot(xc, yc, 'r', x, y, 'g')\n", " u, s, v = svd(F)\n", " plot(x, y, 'k', lw=2)\n", " quiver(zeros(2), zeros(2),\n", " hstack((s*u[0],-s*u[0])), hstack((s*u[1],-s*u[1])),\n", " scale=1, units='xy')\n", " axis('equal')\n", "\n", "def dis_ellipse(J):\n", " # Draw strain ellipse from displacement gradient\n", " J = asarray(J)\n", " F = J + eye(2)\n", " def_ellipse(F)\n", "\n", "def dis_field(J):\n", " # Visualize displacement field from\n", " # displacement gradient\n", " X, Y = meshgrid(linspace(-3, 3, 21),\n", " linspace(-2, 2, 17))\n", " u, v = tensordot(J, [X, Y], axes=1)\n", " quiver(X, Y, u, v, angles='xy')\n", " axis('equal')\n", "\n", "def def_field(F):\n", " # Visualize displacement field from\n", " # deformation gradient\n", " F = asarray(F)\n", " J = F - eye(2)\n", " dis_field(J)\n", "\n", "def dis_show(J):\n", " # Draw displacement field and deformation ellipse\n", " # from displacement gradient\n", " dis_field(J)\n", " dis_ellipse(J)\n", " show()\n", "\n", "def def_show(F):\n", " # Draw displacement field and deformation ellipse\n", " # from deformation gradient\n", " def_field(F)\n", " def_ellipse(F)\n", " show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To use defined function we simply define deformation or displacement gradient and call appropriate functions:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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QFhYWwimwSUlJ9PT05KRJk4R45P8E3ZRstRoUFMQ+ffoI8xITE1msWDHhIk6S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\nQYcqCp0D0EEHHXSoovh/xY8bCyjAB+wAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Deformation gradient\n", "F = array([[0.5, 1],\n", " [0 , 2]])\n", "def_field(F)\n", "def_ellipse(F)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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CwoKHDx9WW5+UlERfX1+6ubm94+ETFxenlv758+f08fFh//79aWFhodoX16xZ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du2Ze3atXn58uUi9aUqALxqI0VHR/PEiRNcs2YNJ0yYwJ49e7Ju3bp0dXUtciNpNBreuHGDvr6+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\nJUuWFOnwmN8uSZLo7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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Displacement gradient\n", "J = array([[1, 1],\n", " [0, -0.5]])\n", "dis_field(J)\n", "dis_ellipse(J)" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/html": [ "\n", "\n", "\n" ], "text/plain": [ "" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" } ], "source": [ "from IPython.core.display import HTML\n", "def css_styling():\n", " styles = open(\"./css/sg2.css\", \"r\").read()\n", " return HTML(styles)\n", "css_styling()" ] } ], "metadata": { "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": "3.7.4" } }, "nbformat": 4, "nbformat_minor": 1 }