Material model discovery with FEMU
Please login to view abstract download link
Our group has developed a computational framework based on sparse regression, denoted as EUCLID (Efficient Unsupervised Constitutive Law Identification & Discovery) [1,2], to perform automated discovery of material laws out of a library of candidate functions. The loss function in the inverse problem has been formulated based on unbalanced internal and boundary forces computed from full-field displacement and global force data, similar to identification strategies such as the equilibrium gap and the virtual fields methods. The computation of the loss function thus involves the numerical differentiation of the experimental displacement data to obtain the strains, an operation that is notoriously sensitive to noise. In the present work, we aim at combining the discovery process of EUCLID based on sparse regression with a loss function based on the displacement field, in the spirit of the so-called finite element model updating (FEMU) technique. Exploiting the experimentally measured displacement data directly (without differentiation) provides a more noise-robust discovery algorithm; however, the new inverse problem becomes non-convex, requiring robust optimisation techniques. We illustrate the solution to the non-convex, non-linear inverse problem and highlight the potential of this new approach. REFERENCES [1] Flaschel M, Kumar S, De Lorenzis L. Unsupervised discovery of interpretable hyperelastic constitutive laws. Comput Methods Appl Mech Eng 2021;381:113852. https://doi.org/10.1016/j.cma.2021.113852. [2] Flaschel M, Kumar S, De Lorenzis L. Automated discovery of generalized standard material models with EUCLID. Comput Methods Appl Mech Eng 2023;405:115867. https://doi.org/10.1016/j.cma.2022.115867.
