Coupled theories FEniCS codes (Research release)

A collection of FEniCS finite element codes for a wide array of coupled-physics theories in solid mechanics.

Constructed by Eric M. Stewart and Lallit Anand.

A selection of example codes are currently provided for:

1. Finite elasticity
2. Finite thermo-elasticity
3. Gel mechanics
4. Gel thermo-mechanics
5. Chemo-mechanically coupled Cahn-Hilliard
6. Electro-elasticity of dielectric elastomers
7. Finite deformation viscoelasticity with inertial effects
8. Electro-viscoelasticity of dielectric elastomers with inertial effects
9. Finite deformation rate-independent isotropic plasticity

Running the codes

We recommend running the FEniCS codes locally and using ParaView to visualize the results. Local installation can be quite tricky and is highly platform-dependent; my FEniCS installation instructions for Mac and Windows machines are available here:

• https://www.ericmstewart.com/fenics

Alternatively, you can run any FEniCS *.py code hosted on a public GitHub repository "in the cloud" (in your web browser, without a local installation) by following the instructions in this Google Colab web notebook:

• https://colab.research.google.com/drive/1ut8XomA4tCFo6Lg3CWTHLROACAdf_Gq_?usp=sharing

Citation

If you use these codes in your own research, cite both of the following:

• E. M. Stewart and L. Anand. Example codes for coupled theories in solid mechanics, 2023. URL https://github.com/SolidMechanicsCoupledTheories/example_codes.

• L. Anand, E.M. Stewart, & S.A. Chester. Introduction to coupled theories in solid mechanics. Oxford University Press, 2026.