README.md

PythonFem

Linear Finite Element Method (FEM) for simulating hyperelastic cubes, all codes are based on pure Python.

Overview

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

Requirements

imageio==2.28.1
matplotlib==3.5.3
numpy==1.21.5
seaborn==0.12.2

Usage

Single

python main_single_2d.py

Args

# 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'
    
# 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

Symplectic Euler Methods

Implict Euler Methods

Multiple

python main_multiple_2d.py

Args

'--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]'
    
# 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

Symplectic Euler Methods

Linear Elasticity

St. Venant-Kirchhoff

Corotated linear elasticity

Neohookean elasticity

Implict Euler Methods

St. Venant-Kirchhoff

Neohookean elasticity

Reference

FEM Simulation of 3D Deformable Solids: A practitioner's guide to theory, discretization and model reduction