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| # PythonFem | ||
| Linear Finite Element Method for simulating hyperelastic cubes | ||
| <img src="./gifs/Multiple_2D_Neohookean_implicit_False_bend_8.gif" div align=middle width = "49%" /><img src="./gifs/Multiple_2D_Neohookean_implicit_False_fall_8.gif" div align=middle width = "49%" /> | ||
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| Linear Finite Element Method (FEM) for simulating hyperelastic cubes, all codes are based on pure Python. | ||
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| ## Overview | ||
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| | Constitutive Models | Time Integration | Multiple cubes | | ||
| | :------------- | :----------: | :----------: | | ||
| | Linear Elasticity | Symplectic Euler | Yes | | ||
| | St. Venant-Kirchhoff | Symplectic/Implict Euler | Yes | | ||
| | Corotated linear elasticity | Symplectic Euler | Yes | | ||
| | Neohookean elasticity | Symplectic/Implict Euler | Yes | | ||
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| ## Requirements | ||
| ```python | ||
| imageio==2.28.1 | ||
| matplotlib==3.5.3 | ||
| numpy==1.21.5 | ||
| seaborn==0.12.2 | ||
| ``` | ||
| ## Usage | ||
| ### Single Terahedron | ||
| ```shell | ||
| python main_single_2d.py | ||
| ``` | ||
| Args | ||
| ```shell | ||
| # Parameters of Afine transformation | ||
| '--theta', type=float, default=-25.0, help='Counterclockwise rotation angle' | ||
| '--tx', type=float, default=3.0, help='Movement along the x-axis' | ||
| '--ty', type=float, default=3.0, help='Movement along the y-axis' | ||
| '--sx', type=float, default=2, help='Stretching along the x-axis' | ||
| '--sy', type=float, default=2, help='Stretching along the y-axis' | ||
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| # Parameters of FEM | ||
| '--model', type=int, default=3, help='Constitutive model, 0:Linear, 1:STVK, 2:Co-rotated, 3: Neohookean' | ||
| '--Y', type=int, default=100, help='Youngs modulus' | ||
| '--V', type=float, default=0.1, help='Poisson ratio, [-1, 0.5]' | ||
| '--dt', type=float, default=0.01, help='Time horizon' | ||
| '--max_iter', type=int, default=200, help='Iteration' | ||
| '--mass', type=float, default=1.0, help='Mass of the point' | ||
| '--gravity', type=bool, default=True, help='Add gravity' | ||
| '--fix', type=bool, default=True, help='Fix a point on the wall' | ||
| '--implict', action='store_true', help='Implict Euler Method, for STVK and Neohookean' | ||
| ``` | ||
| ####Visual Results | ||
| **<center>Symplectic Euler Methods</center>** | ||
| <img src="./gifs/single_2D_Linear_implicit_False.gif" div align=middle width = "49%" /><img src="./gifs/single_2D_STVK_implicit_False.gif" div align=middle width = "49%" /> | ||
| <img src="./gifs/single_2D_Co-rotated_implicit_False.gif" div align=middle width = "49%" /><img src="./gifs/single_2D_Neohookean_implicit_False.gif" div align=middle width = "49%" /> | ||
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| **<center>Implict Euler Methods</center>** | ||
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| <img src="./gifs/single_2D_STVK_implicit_True.gif" div align=middle width = "49%" /><img src="./gifs/single_2D_Neohookean_implicit_True.gif" div align=middle width = "49%" /> | ||
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| ### Multiple Terahedrons | ||
| ```shell | ||
| python main_multiple_2d.py | ||
| ``` | ||
| Args | ||
| ```shell | ||
| '--voxelx', type=int, default=8, help='Number of voxels (x-axis)' | ||
| '--voxely', type=int, default=3, help='Number of voxels (y-axis)' | ||
| '--em', type=list, default=[2,3,6,7,10,11,14,15], help='Empty voxels:[],[2,3,6,7,10,11,14,15],[2,3,6,7]' | ||
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| # Parameters of FEM | ||
| '--mode', type=str, default="bend", help='Mode: bend/fall' | ||
| '--model', type=int, default=0, help='Constitutive model, 0:Linear, 1:STVK, 2:Co-rotated, 3: Neohookean' | ||
| '--Y', type=int, default=10000, help='Youngs modulus' | ||
| '--V', type=float, default=0.1, help='Poisson ratio [-1, 0.5]' | ||
| '--dt', type=float, default=0.001, help='Time horizon' | ||
| '--max_iter', type=int, default=200, help='Iteration' | ||
| '--mass', type=float, default=1.0, help='Mass of the point' | ||
| '--implict', action='store_true', help='Implict Euler Method, for STVK and Neohookean' | ||
| ``` | ||
| ####Visual Results | ||
| <center>Symplectic Euler Methods</center> | ||
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| **<center>Linear Elasticity</center>** | ||
| <img src="./gifs/Multiple_2D_Linear_implicit_False_bend_8.gif" div align=middle width = "49%" /><img src="./gifs/Multiple_2D_Linear_implicit_False_fall_8.gif" div align=middle width = "49%" /> | ||
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| **<center>St. Venant-Kirchhoff </center>** | ||
| <img src="./gifs/Multiple_2D_STVK_implicit_False_bend_8.gif" div align=middle width = "49%" /><img src="./gifs/Multiple_2D_STVK_implicit_False_fall_8.gif" div align=middle width = "49%" /> | ||
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| **<center>Corotated linear elasticity</center>** | ||
| <img src="./gifs/Multiple_2D_Co-rotated_implicit_False_bend_8.gif" div align=middle width = "49%" /><img src="./gifs/Multiple_2D_Co-rotated_implicit_False_fall_8.gif" div align=middle width = "49%" /> | ||
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| **<center>Neohookean elasticity</center>** | ||
| <img src="./gifs/Multiple_2D_Neohookean_implicit_False_bend_8.gif" div align=middle width = "49%" /><img src="./gifs/Multiple_2D_Neohookean_implicit_False_fall_8.gif" div align=middle width = "49%" /> | ||
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| ## Reference | ||
| [FEM Simulation of 3D Deformable Solids: A practitioner's guide to theory, discretization and model reduction](http://viterbi-web.usc.edu/~jbarbic/femdefo/) | ||
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| All codes are based on pure Python |
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