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