Unsupervised discovery of constitutive laws

We propose a new approach for data-driven automated discovery of constitutive laws. The approach is

  • unsupervised, i.e., it requires no stress data but only displacement and global force data, which are realistically available through mechanical testing and digital image correlation (DIC) techniques;

  • interpretable, i.e., the models are embodied by parsimonious mathematical expressions discovered through sparse regression of a large catalogue of candidate functions;

  • one-shot, i.e., discovery only needs one experiment - but can use more if available;

  • physics-informed and combines decades of modeling experience and knowledge to discover models that physically consistent.

Our method serves as a departure from supervised constitutive modeling using, e.g, neural networks and data-driven model-free approaches which show poor data-efficiency and generalization beyond training data.

Ref: M. Flaschel*, S. Kumar*, L. De Lorenzis, Unsupervised discovery of interpretable hyperelastic constitutive laws, Computer Methods in Applied Mechanics and Engineering, 381 (2021), 113852

* equal contribution

TU Delft, Mekelweg 2, Delft 2628 CD, Netherlands