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Update ex01_specimen_amplitudes.ipynb
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‎docs/notebooks/ex01_specimen_amplitudes.ipynb

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@@ -34,7 +34,9 @@
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"import termtables as tt\n",
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"from pypardiso import spsolve\n",
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"\n",
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"import fiberreinforcedrubber as frr"
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"import fiberreinforcedrubber as frr\n",
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"\n",
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"frr.__version__"
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]
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},
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{
@@ -190,10 +192,268 @@
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" color=\"lightgrey\",\n",
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" line_width=4,\n",
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")\n",
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"plotter.camera.tight()\n",
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"# plotter.add_axes(label_size=(0.06, 0.06), viewport=(-0.1, -0.1, 0.2, 0.2))\n",
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"# plotter.camera.zoom(0.8)\n",
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"plotter.show(\"test_specimen_mesh_rubber.png\", scale=2, jupyter_backend=\"static)"
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"plotter.show(jupyter_backend=\"static\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "670ebca4-0b05-4f49-bc8d-d7ca94bce291",
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"metadata": {},
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"source": [
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"View the fiber mesh"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "740d2142-5096-42cc-bf4f-8c022e513ac4",
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"metadata": {},
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"outputs": [],
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"source": [
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"view = fem.ViewMesh(fem.mesh.concatenate([fibers_1, fibers_2]))\n",
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"plotter = view.plot(\n",
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" notebook=True,\n",
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" theme=\"document\",\n",
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" add_axes=False,\n",
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" color=\"black\",\n",
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" line_width=4,\n",
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")\n",
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"plotter.show(jupyter_backend=\"static\")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "4de0761b-1584-4f30-a44d-ab917885d153",
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"metadata": {},
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"source": [
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"Create a numeric region and a displacement field"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "e664a84b-d735-453d-81ec-163e6391eb2f",
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"metadata": {},
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"outputs": [],
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"source": [
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"region = fem.RegionQuad(mesh)\n",
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"field = fem.FieldContainer([fem.Field(region, dim=2)])"
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]
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},
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{
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"cell_type": "markdown",
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"id": "37925fc3-01de-4167-a71c-2190d00e3f21",
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"metadata": {},
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"source": [
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"Setup boundary conditions"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "23e14ba6-d67b-4ed5-b711-222f9d8cd04a",
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"metadata": {},
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"outputs": [],
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"source": [
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"bounds, loadcase = fem.dof.shear(field)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "a69ceeea-5075-41e0-9ae3-2f57af29c813",
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"metadata": {},
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"source": [
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"Constitutive material behavior for rubber and cord"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "ca660c8b-1575-43a3-a968-3e08edcd1acb",
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"metadata": {},
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"outputs": [],
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"source": [
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"neohooke, fibermat1, fibermat2, vector1, vector2 = frr.fiber_reinforced_rubber(\n",
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" C10=C10,\n",
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" fiber_angle=fiber_angle,\n",
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" fiber_modulus=fiber_modulus,\n",
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" fiber_area=fiber_area,\n",
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" thickness=thickness,\n",
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" strain_exponent=strain_exponent,\n",
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" axis=fiber_axis,\n",
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" fiber_distance=fiber_distance,\n",
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")"
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]
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},
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{
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"cell_type": "markdown",
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"id": "fe4f68c0-8845-4426-8a00-2b8d43f1acc4",
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"metadata": {},
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"source": [
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"Solid bodies"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "32f27770-e91e-4e88-b72c-3caf3242dbaa",
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"metadata": {},
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"outputs": [],
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"source": [
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"rubber = fem.SolidBody(neohooke, field)\n",
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"fiber1 = fem.SolidBody(fibermat1, field)\n",
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"fiber2 = fem.SolidBody(fibermat2, field)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "7c61f1c5-2907-4298-baf4-b1c8ccd1e6f1",
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"metadata": {},
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"source": [
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"Tension and shear at V = 3 mm (Fy = 3 kN)"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "99534f23-7d1d-4618-a9fe-c680a53be7d0",
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"metadata": {},
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"outputs": [],
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"source": [
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"fiber_forces = [[], []]\n",
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"\n",
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"\n",
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"def evaluate_fiber_forces(i, j, substep):\n",
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" field = substep.x\n",
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"\n",
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" # get fiber normal forces per undeformed (fiber) area\n",
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" force1 = frr.fiber_force(fiber1, thickness, fiber_area, vector1)\n",
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" force2 = frr.fiber_force(fiber2, thickness, fiber_area, vector2)\n",
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"\n",
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" # interpolate fiber forces to the line-meshes of the fiber families\n",
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" r_1 = frr.interpolate(mesh, force1, fibers_1, mask_points_1)\n",
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" r_2 = frr.interpolate(mesh, force2, fibers_2, mask_points_2)\n",
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"\n",
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" fiber_forces[0].append(r_1)\n",
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" fiber_forces[1].append(r_2)\n",
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"\n",
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"\n",
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"step = fem.Step(\n",
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" items=[rubber, fiber1, fiber2],\n",
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" boundaries=bounds,\n",
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" ramp={\n",
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" bounds[\"compression_top\"]: fem.math.linsteps([3, 3], num=2),\n",
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" bounds[\"move\"]: lateral_max * fem.math.linsteps([-1, 1], num=2),\n",
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" },\n",
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")\n",
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"job = fem.Job(steps=[step], callback=evaluate_fiber_forces)\n",
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"job.evaluate(solver=spsolve, tol=1e-2)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "4e5f97fb-d1e8-4a0f-a255-41e740949500",
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"metadata": {},
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"source": [
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"Interpolate displacements to the line-meshes of the fiber families"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "29bcfb45-c182-4839-b0ec-3afa8663ba73",
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"metadata": {},
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"outputs": [],
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"source": [
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"u_1 = frr.interpolate(mesh, field[0].values, fibers_1, mask_points_1)\n",
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"u_2 = frr.interpolate(mesh, field[0].values, fibers_2, mask_points_2)"
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]
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},
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{
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"cell_type": "markdown",
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"id": "28589f7c-ee4b-4754-92f9-6b9a56f4996a",
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"metadata": {},
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"source": [
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"Deformed line mesh for the fibers"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "f1ce9d7c-98b0-43c4-9deb-616495afb20c",
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"metadata": {},
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"outputs": [],
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"source": [
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"fibers_1.points += u_1\n",
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"fibers_2.points += u_2"
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]
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},
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{
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"cell_type": "markdown",
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"id": "08c9c252-368f-4c7f-9aad-ed5b900d205e",
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"metadata": {},
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"source": [
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"## Postprocessing\n",
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"Deformed Views"
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]
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},
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{
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"cell_type": "markdown",
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"id": "e25fe2c5-99a9-41b3-998b-b4d9593d10be",
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"metadata": {},
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"source": [
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"View on fiber families"
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]
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},
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{
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"cell_type": "code",
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"execution_count": null,
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"id": "0fbd325a-20af-42cf-a02b-043072e0d2a9",
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"metadata": {},
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"outputs": [],
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"source": [
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"fiberfamilies = [\n",
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" (fiber_forces[0], fibers_1, fibers_2, [400, 900]),\n",
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" (fiber_forces[1], fibers_2, fibers_1, [400, 900]),\n",
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"]\n",
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"for i, (fiberforce, fiberfamily1, fiberfamily2, clim) in enumerate(fiberfamilies):\n",
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" view = fem.ViewSolid(field)\n",
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" plotter = view.plot(\n",
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" notebook=True,\n",
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" theme=\"document\",\n",
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" show_edges=False,\n",
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" add_axes=False,\n",
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" )\n",
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" plotter.add_axes(label_size=(0.06, 0.06))\n",
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"\n",
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" forcerange = np.abs(fiberforce[-1] - fiberforce[-3])\n",
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"\n",
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" fiberview1 = fem.ViewMesh(\n",
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" fiberfamily1,\n",
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" point_data={\n",
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" \"Normal Force (Range) per Undeformed Area (Fibre) in MPa\": forcerange\n",
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" },\n",
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" )\n",
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" fiberview2 = fem.ViewMesh(\n",
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" fiberfamily2,\n",
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" )\n",
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" plotter = fiberview2.plot(\n",
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" plotter=plotter,\n",
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" line_width=3,\n",
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" add_axes=False,\n",
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" )\n",
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" fiberplotter = fiberview1.plot(\n",
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" \"Normal Force (Range) per Undeformed Area (Fibre) in MPa\",\n",
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" label=\"Normal Force (Range) per Undeformed Area (Fibre) in MPa\",\n",
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" plotter=plotter,\n",
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" component=None,\n",
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" clim=clim,\n",
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" below_color=\"darkgrey\",\n",
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" above_color=\"lightgrey\",\n",
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" line_width=3,\n",
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" add_axes=False,\n",
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" )\n",
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" fiberplotter.show(jupyter_backend=\"static\")"
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]
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}
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],

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