Machine learning methods for solid mechanics

Development of constitutive models with physics-conforming neural networks

Advanced manufacturing technologies such as 3D printing or bio-fabrication allow engineers to design new types of metamaterials and composites with functional properties. These architected materials often behave in highly nonlinear (large deformations and instabilities), anisotropic (direction-dependent), inelastic (dissipation and damage), and multi-physical (e.g., coupled mechanical and electro-magnetic effects) way, which makes material modeling for design and simulation very challenging. To this end, we are developing novel approaches for constitutive modeling, which are based on machine learning methods such as artificial neural networks. However, such constitutive models must comply to certain thermodynamic and continuum mechanical requirements, i.e., the neural networks must be formulated in a physics-conforming way.

In this project, the IREP student will contribute to the development of such constitutive models with physics-conforming neural networks. Depending on the student’s interest, the scope of the project may include aspects such as the generation of calibration data through multiscale simulations of metamaterials, the development and training of new types of machine learning based model formulations, the extension of models from purely elastic behavior to inelasticity or multi-physics, or the verification of models in finite element and multiscale simulations.

This Project is supervised by Prof. Dr. Oliver Weeger.

Knowledge in machine learning, continuum mechanics, and the finite element method is of advantage.

  • D. Klein, M. Fernández, R.J. Martin, P. Neff, O. Weeger: “Polyconvex anisotropic hyperelasticity with neural networks”, Journal of the Mechanics and Physics of Solids, 159, p. 104703 (2022).

Further literature and initial training will be provided before the starting date.

Additional Information

Capactiy 1-2 IREP Students
Project Available for Spring, Summer and Fall 2024
Credits 18 ECTS
Available via Remote Yes