{ "cells": [ { "cell_type": "markdown", "id": "14d1ef5a", "metadata": {}, "source": [ "# 3 · Elastic Energy Intuition\n", "\n", "The deformation gradient $F$ says *how* a triangle is deformed. An **elastic\n", "energy** $\\psi(F)$ turns that into a single number: *how much* it costs.\n", "\n", "We will **write each energy out ourselves** — one line of math each —\n", "so nothing is hidden, then compare three classics:\n", "\n", "* **Linear elasticity**\n", "* **ARAP** (as-rigid-as-possible)\n", "* **Neo-Hookean** (classical)\n", "\n", "A good energy is **zero for rigid motions** (translation, rotation) and grows\n", "with genuine deformation (scale, shear). We'll see linear elasticity fail the\n", "rotation test, and Neo-Hookean blow up as a triangle is crushed flat." ] }, { "cell_type": "code", "execution_count": 1, "id": "17a40ece", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:22:21.444616Z", "iopub.status.busy": "2026-06-09T05:22:21.444455Z", "iopub.status.idle": "2026-06-09T05:22:21.947134Z", "shell.execute_reply": "2026-06-09T05:22:21.946853Z" } }, "outputs": [], "source": [ "%matplotlib inline\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import simkit\n", "import utils" ] }, { "cell_type": "markdown", "id": "e91d61e5", "metadata": {}, "source": [ "## The three energies, written out\n", "\n", "All three are functions of $F$ alone, with material constants $\\mu$ (shear)\n", "and $\\lambda$ (bulk). Let $I$ be the identity and $\\dim = 2$ here.\n", "\n", "**Linear elasticity** — small-strain tensor $\\varepsilon = \\tfrac12(F + F^\\top) - I$:\n", "\n", "$$\n", "\\psi = \\mu\\,\\lVert\\varepsilon\\rVert_F^2 + \\tfrac{\\lambda}{2}\\,\\mathrm{tr}(\\varepsilon)^2.\n", "$$\n", "\n", "**ARAP** — $R$ is the rotation from the polar decomposition of $F$; it\n", "measures the distance from the *nearest pure rotation*:\n", "\n", "$$\n", "\\psi = \\mu\\,\\lVert F - R\\rVert_F^2.\n", "$$\n", "\n", "**Neo-Hookean** — with $I_C = \\lVert F\\rVert_F^2$ and $J = \\det F$ (the\n", "area ratio). The $-\\mu\\ln J$ term is the key one: it $\\to +\\infty$ as\n", "$J \\to 0$, forbidding the material from being crushed to zero area:\n", "\n", "$$\n", "\\psi = \\tfrac{\\mu}{2}(I_C - 2)\\; -\\; \\mu\\ln J\\; +\\; \\tfrac{\\lambda}{2}(\\ln J)^2.\n", "$$" ] }, { "cell_type": "code", "execution_count": 2, "id": "fa6987cc", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:22:21.948384Z", "iopub.status.busy": "2026-06-09T05:22:21.948304Z", "iopub.status.idle": "2026-06-09T05:22:21.950780Z", "shell.execute_reply": "2026-06-09T05:22:21.950600Z" } }, "outputs": [], "source": [ "def linear_energy(F, mu=1.0, lam=1.0):\n", " eps = 0.5 * (F + F.T) - np.eye(2) # small-strain tensor\n", " E_shear = mu * np.sum(eps**2) # deviatoric (shape) term\n", " E_volume = 0.5 * lam * np.trace(eps)**2 # volumetric term\n", " E_total = E_shear + E_volume\n", " return E_total\n", "\n", "def arap_energy(F, mu=1.0, lam=1.0):\n", " R = simkit.polar_svd(F[None])[0][0] # nearest rotation to F\n", " E_shape = mu * np.sum((F - R)**2) # distance to that rotation\n", " return E_shape # single term; ARAP ignores lam\n", "\n", "def neo_hookean_energy(F, mu=1.0, lam=1.0):\n", " I_C = np.sum(F**2)\n", " J = np.linalg.det(F)\n", " E_shear = 0.5 * mu * (I_C - 2) # resists shearing/stretching\n", " E_barrier = -mu * np.log(J) # forbids inversion (J -> 0)\n", " E_volume = 0.5 * lam * np.log(J)**2 # resists volume change\n", " E_total = E_shear + E_barrier + E_volume\n", " return E_total\n", "\n", "ENERGIES = {\"Linear\": linear_energy, \"ARAP\": arap_energy, \"Neo-Hookean\": neo_hookean_energy}\n", "\n", "# rest triangle and the deformation maps we'll sweep\n", "X = np.array([[-0.5, 0.0], [0.5, 0.0], [0.0, np.sqrt(3) / 2]])\n", "T = np.array([[0, 1, 2]])\n", "def translate(X, t): return X + np.asarray(t, float)\n", "def rotate(X, th):\n", " c, s = np.cos(th), np.sin(th); return X @ np.array([[c, -s], [s, c]]).T\n", "def scale(X, s): return X * np.array([s, s])\n", "def shear(X, k): return X @ np.array([[1.0, k], [0.0, 1.0]]).T" ] }, { "cell_type": "markdown", "id": "eaefd705", "metadata": {}, "source": [ "## Translation costs no energy\n", "\n", "Sliding the triangle leaves every energy flat at zero. (We fix the y-axis so the\n", "flat line doesn't look like noise.)" ] }, { "cell_type": "code", "execution_count": 3, "id": "ac4512eb", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:22:21.951674Z", "iopub.status.busy": "2026-06-09T05:22:21.951626Z", "iopub.status.idle": "2026-06-09T05:22:22.839484Z", "shell.execute_reply": "2026-06-09T05:22:22.839253Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 3, "metadata": {}, "output_type": "execute_result" } ], "source": [ "d = np.linspace(0, 3, 40)\n", "states = [translate(X, [dx, 0.0]) for dx in d]\n", "series = {name: np.zeros_like(d) for name in ENERGIES}\n", "for i, U in enumerate(states):\n", " F = simkit.deformation_gradient(X, T, U)[0]\n", " for name, fn in ENERGIES.items():\n", " series[name][i] = fn(F)\n", "\n", "utils.line_plot(d, series, xlabel=\"translation distance\", ylabel=\"elastic energy\",\n", " title=\"Translation costs no energy\", ylim=(-0.5, 2.0))\n", "plt.show()\n", "\n", "fig, anim = utils.animate_scene_energy(states, d, series, rest=X,\n", " xlabel=\"translation distance\", lims=((-1.2, 4.0), (-1.2, 1.6)),\n", " scene_title=\"triangle sliding\", title=\"energy vs translation\", fps=20,\n", " energy_ylim=(-0.5, 2.0)) # fixed y-axis (matches the static plot) -> flat line\n", "utils.show_video(fig, anim, \"media/03_translation.mp4\", fps=20)" ] }, { "cell_type": "markdown", "id": "f231e656", "metadata": {}, "source": [ "## Scale: every energy grows (the intuitive case)\n", "\n", "Uniform scaling genuinely deforms the material, so all three energies rise as we\n", "move away from $s = 1$." ] }, { "cell_type": "code", "execution_count": 4, "id": "7143e227", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:22:22.840613Z", "iopub.status.busy": "2026-06-09T05:22:22.840537Z", "iopub.status.idle": "2026-06-09T05:22:23.876110Z", "shell.execute_reply": "2026-06-09T05:22:23.875830Z" } }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 4, "metadata": {}, "output_type": "execute_result" } ], "source": [ "s = np.linspace(0.5, 1.8, 50)\n", "states = [scale(X, si) for si in s]\n", "series = {name: np.zeros_like(s) for name in ENERGIES}\n", "for i, U in enumerate(states):\n", " F = simkit.deformation_gradient(X, T, U)[0]\n", " for name, fn in ENERGIES.items():\n", " series[name][i] = fn(F)\n", "\n", "utils.line_plot(s, series, xlabel=\"scale factor s\", ylabel=\"elastic energy\",\n", " title=\"Energy vs uniform scale\")\n", "plt.show()\n", "fig, anim = utils.animate_scene_energy(states, s, series, rest=X, xlabel=\"scale factor s\",\n", " scene_title=\"triangle scaling\", title=\"energy vs scale\", fps=20)\n", "utils.show_video(fig, anim, \"media/03_scale.mp4\", fps=20)" ] }, { "cell_type": "markdown", "id": "24fb608f", "metadata": {}, "source": [ "## Shear: every energy grows too" ] }, { "cell_type": "code", "execution_count": 5, "id": "2ee40907", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:22:23.877161Z", "iopub.status.busy": "2026-06-09T05:22:23.877093Z", "iopub.status.idle": "2026-06-09T05:22:25.054204Z", "shell.execute_reply": "2026-06-09T05:22:25.053977Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 5, "metadata": {}, "output_type": "execute_result" } ], "source": [ "k = np.linspace(0.0, 1.6, 50)\n", "states = [shear(X, ki) for ki in k]\n", "series = {name: np.zeros_like(k) for name in ENERGIES}\n", "for i, U in enumerate(states):\n", " F = simkit.deformation_gradient(X, T, U)[0]\n", " for name, fn in ENERGIES.items():\n", " series[name][i] = fn(F)\n", "\n", "utils.line_plot(k, series, xlabel=\"shear k\", ylabel=\"elastic energy\",\n", " title=\"Energy vs shear\")\n", "plt.show()\n", "fig, anim = utils.animate_scene_energy(states, k, series, rest=X, xlabel=\"shear k\",\n", " scene_title=\"triangle shearing\", title=\"energy vs shear\", fps=20)\n", "utils.show_video(fig, anim, \"media/03_shear.mp4\", fps=20)" ] }, { "cell_type": "markdown", "id": "8dfb7771", "metadata": {}, "source": [ "## Rotation: linear elasticity is *not* rotation-invariant\n", "\n", "Now the surprise. Spin the triangle through a full turn. **ARAP** and\n", "**Neo-Hookean** stay at zero — rotation is free. **Linear elasticity**\n", "rises and falls: its small-strain tensor $\\varepsilon$ mistakes rotation for\n", "stretch. This is why linear elasticity is only valid for *tiny* deformations." ] }, { "cell_type": "code", "execution_count": 6, "id": "ba930b0d", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:22:25.055229Z", "iopub.status.busy": "2026-06-09T05:22:25.055168Z", "iopub.status.idle": "2026-06-09T05:22:26.349408Z", "shell.execute_reply": "2026-06-09T05:22:26.349130Z" } }, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" } ], "source": [ "ang = np.linspace(0, 2 * np.pi, 60)\n", "states = [rotate(X, a) for a in ang]\n", "series = {name: np.zeros_like(ang) for name in ENERGIES}\n", "for i, U in enumerate(states):\n", " F = simkit.deformation_gradient(X, T, U)[0]\n", " for name, fn in ENERGIES.items():\n", " series[name][i] = fn(F)\n", "\n", "utils.line_plot(ang, series, xlabel=\"rotation angle (rad)\", ylabel=\"elastic energy\",\n", " title=\"Only linear elasticity penalizes rotation\")\n", "plt.show()\n", "fig, anim = utils.animate_scene_energy(states, ang, series, rest=X,\n", " xlabel=\"rotation angle (rad)\", scene_title=\"triangle rotating\",\n", " title=\"energy vs rotation angle\", fps=20)\n", "utils.show_video(fig, anim, \"media/03_rotation.mp4\", fps=20)" ] }, { "cell_type": "markdown", "id": "71fb90e2", "metadata": {}, "source": [ "## Crushing the triangle flat: Neo-Hookean $\\to \\infty$\n", "\n", "Drive the apex down toward the base so the area $J = \\det F \\to 0$.\n", "\n", "**Why didn't it explode before?** The Neo-Hookean blow-up is real but only\n", "*logarithmic*: $\\psi \\approx \\tfrac{\\lambda}{2}(\\ln J)^2 - \\mu\\ln J$. Since\n", "$\\ln J$ grows slowly, you have to (a) drive $J$ *extremely* close to zero\n", "**and** (b) use a stiff, nearly-incompressible material (large $\\lambda$) for the\n", "number to actually rocket. So here we collapse hard — $y = y_0\\,10^{-9t}$,\n", "i.e. $J$ down to $\\sim 10^{-9}$ — with $\\lambda = 50$. Now\n", "**Neo-Hookean reaches $\\sim 10^4$** and is climbing to $+\\infty$, while\n", "**ARAP** sits at a finite plateau (it has no volume term) and **linear** stays\n", "modest. We plot on a log axis." ] }, { "cell_type": "code", "execution_count": 7, "id": "19744091", "metadata": { "execution": { "iopub.execute_input": "2026-06-09T05:22:26.350551Z", "iopub.status.busy": "2026-06-09T05:22:26.350469Z", "iopub.status.idle": "2026-06-09T05:22:28.186789Z", "shell.execute_reply": "2026-06-09T05:22:28.186571Z" } }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "det F at full collapse: 1.00e-09 Neo-Hookean energy: 10757\n" ] }, { "data": { "image/png": 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" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/html": [ "" ], "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" } ], "source": [ "t = np.linspace(0, 1, 50)\n", "y0 = X[2, 1]\n", "def collapse_apex(frac):\n", " U = X.copy(); U[2, 1] = y0 * 10.0**(-9.0 * frac); return U # hard log collapse -> J ~ 1e-9\n", "states = [collapse_apex(f) for f in t]\n", "series = {name: np.zeros_like(t) for name in ENERGIES}\n", "for i, U in enumerate(states):\n", " F = simkit.deformation_gradient(X, T, U)[0]\n", " for name, fn in ENERGIES.items():\n", " series[name][i] = fn(F, mu=1.0, lam=50.0) # nearly-incompressible: lam >> mu\n", "\n", "Jend = np.linalg.det(simkit.deformation_gradient(X, T, states[-1])[0])\n", "print(f\"det F at full collapse: {Jend:.2e} Neo-Hookean energy: {series['Neo-Hookean'][-1]:.0f}\")\n", "\n", "utils.line_plot(t, series, xlabel=\"collapse parameter\", ylabel=\"elastic energy\",\n", " logy=True, title=\"Neo-Hookean rockets to infinity as area -> 0\")\n", "plt.show()\n", "fig, anim = utils.animate_scene_energy(states, t, series, rest=X,\n", " xlabel=\"collapse parameter\", scene_title=\"apex crushed onto the base\",\n", " title=\"energy vs collapse\", logy=True, fps=18)\n", "utils.show_video(fig, anim, \"media/03_collapse.mp4\", fps=18)" ] }, { "cell_type": "markdown", "id": "1b70a786", "metadata": {}, "source": [ "### Takeaways\n", "* We wrote each energy in one line: linear (strain tensor), ARAP (distance to a\n", " rotation), Neo-Hookean (with the $-\\mu\\ln J$ inversion barrier).\n", "* Good energies are zero for rigid motion and grow with scale/shear.\n", "* **Linear** breaks rotation-invariance; **Neo-Hookean** diverges at collapse;\n", " **ARAP** saturates.\n", "\n", "Next: minimize an energy (plus constraints) to actually *pose* a shape." ] } ], "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": "3.13.9" } }, "nbformat": 4, "nbformat_minor": 5 }