Unsupervised discovery of interpretable hyperelastic constitutive laws

We propose a new approach for data-driven automated discovery of isotropic hyperelastic constitutive laws. The is unsupervised, i.e., it requires no stress data but only displacement and global force data, which are realistically available through mechanical testing digital image correlation techniques; delivers interpretable models, models that embodied by parsimonious mathematical expressions discovered sparse regression large catalogue candidate functions; one-shot, needs one experiment — can use more if available. problem unsupervised solved enforcing equilibrium constraints in the bulk at loaded boundary domain. Sparsity solution achieved ℓp regularization combined with thresholding, calls non-linear optimization scheme. ensuing fully algorithm leverages physics-based automatic determination penalty parameter term. Using numerically generated including artificial noise, we demonstrate ability to accurately discover five different complexity. also show that, “true” feature missing function library, proposed able surrogate such way actual response still predicted.