Automated discovery of material models - Laura De Lorenzis

Sammanfattning (engelska)

Automated discovery of material models - Laura De Lorenzis
Computational Mechanics Lab, ETH Zürich, Tannenstrasse 3, 8092 Zürich, Switzerland
Joint work with Moritz Flaschel, Siddhant Kumar, Enzo Marino et al.

We propose a new approach for data-driven automated discovery of constitutive laws in continuum solid mechanics, which we denote as EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery). At the core of EUCLID are two main ideas: i. while conventional material model identification departs from an a priori chosen functional form and seeks the best values of the unknown parameters based on data, here we start from an arbitrarily large model space, which may possibly embed physics-based requirements, and perform simultaneously and automatically model selection and parameter identification. The combination of these two tasks is what we refer to as discovery, and the basic mathematical tool enabling discovery is sparse regression; ii. unlike in many recent data-driven approaches for solid mechanics, we do not rely on the availability of stress data, which are very difficult or impossible to obtain. Instead, we only require displacement and global force data, which can be realistically obtained from mechanical testing and digital image or volume correlation techniques. Another important advantage over competing approaches is that EUCLID delivers interpretable models, i.e., models that are embodied by parsimonious mathematical expressions. The talk explains the basic approach, illustrates its application to different categories of material behavior, and concludes with its most general formulation in which not only the specific material model within a pre-assumed category but also the category itself is automatically discovered. Recent applications to human brain tissues and metamaterials are also highlighted.