Laura De Lorenzis KEYNOTE seminar “EUCLID: Efficient Unsupervised Constitutive Law Identification and Discovery”

Laura DeLorenzis_ Feb_17_2022.pdf (pdf 178 kB)

We propose a new approach for data-driven automated discovery of constitutive laws in continuum mechanics. The approach is unsupervised, i.e., it requires no stress data but only displacement and global force data, which can be realistically obtained from mechanical testing and digital image or volume correlation techniques; it can deliver either interpretable models, i.e., models that are embodied by parsimonious mathematical expressions, or black-box models encoded in artificial neural networks; it is one-shot, i.e., discovery only needs one experiment in principle - but can use more if available. The machine learning tools which enable discovery are sparse regression, leading to the automatic selection of a few relevant entries from a potentially very large model space, as well as Bayesian regression, which allows for the discovery of several constitutive laws along with their probabilities. After discussing the basics of the methodology, the talk illustrates its first applications to hyperelasticity and plasticity, using both artificial and experimental data, and highlights the ongoing work on further applications.