Elastodynamics

The goal of this project is to simulate soft bodies using non linear elastodynamics of hyperelastic materials.

Full Documentation is found in PDF

Target Geometries

Starting with simple bar deformation as test. The endgoal is to import 3D objects like the Stanford Bunny as deformation test subjects.

Target equation

$$ \rho \frac{\partial^2 \mathbf{u}}{\partial t^2} - \frac{\partial \mathbf{c}}{\partial t} + \nabla \mathbf{P} + \mathbf{F} = 0 $$

Where:

• $\rho$ is the material density (mass per unit volume in the reference configuration),
• $\mathbf{u}$ is the displacement field,
• $\frac{\partial^2 \mathbf{u}}{\partial t^2}$ is the acceleration,
• $\mathbf{c}$ is the damping tensor modelling viscoelastic (Maxwell) damping with viscosity $\eta$,
• $\mathbf{P}$ is the stress tensor; for linear elasticity it reduces to the Cauchy stress $\sigma = 2\mu\varepsilon + \lambda \mathrm{tr}(\varepsilon) I$ with strain $\varepsilon$ and Lamé parameters $\mu$, $\lambda$,
• $\mathbf{F}$ is the force term (assumed $0$ for a relaxed initial state).

More infos are in the documentation PDF

Files

Easy to run files are:

• Elastostatics
• Undampened Elastodynamics Test
• Dampened Elastodynamics Test

These need large amounts of RAM:

• Tacoma Narrows Simulation
• Bunny Simulation (min 42GB)

Results

• Wiggle Brick
• Wiggle Brick
• Wiggle Brick
• Tacoma Bridge
• Stanford Bunny
• Stanford Bunny

Contributors

• Christof Stein
• Max Hirtenlehner
• Tobias Gröfler

License

• Code (all .ipynb notebooks) is licensed under the GNU General Public License v3.0 or later.
• Resources (documentation PDF, GIFs, images and README text) are licensed under Creative Commons Attribution 4.0 International (CC BY 4.0).
• Exception: Bunny.stl is the Stanford Bunny from the Stanford 3D Scanning Repository and remains subject to Stanford's terms of use. It is not covered by the licenses above.

The simulations use NGSolve, which is licensed under the LGPL-2.1.