Print Email Facebook Twitter Automated discovery of generalized standard material models with EUCLID Title Automated discovery of generalized standard material models with EUCLID Author Flaschel, Moritz (ETH Zürich) Kumar, Siddhant (TU Delft Team Sid Kumar) De Lorenzis, Laura (ETH Zürich) Date 2023 Abstract We extend the scope of our recently developed approach for unsupervised automated discovery of material laws (denoted as EUCLID) to the general case of a material belonging to an unknown class of constitutive behavior. To this end, we leverage the theory of generalized standard materials, which encompasses a plethora of important constitutive classes including elasticity, viscosity, plasticity and arbitrary combinations thereof. We show that, based only on full-field kinematic measurements and net reaction forces, EUCLID is able to automatically discover the two scalar thermodynamic potentials, namely, the Helmholtz free energy and the dissipation potential, which completely define the behavior of generalized standard materials. The a priori enforced constraint of convexity on these potentials guarantees by construction stability and thermodynamic consistency of the discovered model; balance of linear momentum acts as a fundamental constraint to replace the availability of stress–strain labeled pairs; sparsity promoting regularization enables the automatic selection of a small subset from a possibly large number of candidate model features and thus leads to a parsimonious, i.e., simple and interpretable, model. Importantly, since model features go hand in hand with the correspondingly active internal variables, sparse regression automatically induces a parsimonious selection of the few internal variables needed for an accurate but simple description of the material behavior. A fully automatic procedure leads to the selection of the hyperparameter controlling the weight of the sparsity promoting regularization term, in order to strike a user-defined balance between model accuracy and simplicity. By testing the method on synthetic data including artificial noise, we demonstrate that EUCLID is able to automatically discover the true hidden material model from a large catalogue of constitutive classes, including elasticity, viscoelasticity, elastoplasticity, viscoplasticity, isotropic and kinematic hardening. Subject Constitutive modelsGeneralized standard materialsInterpretable modelsInverse problemsSparse regressionUnsupervised learning To reference this document use: http://resolver.tudelft.nl/uuid:9c847254-2500-4291-a628-d102e18aaf2e DOI https://doi.org/10.1016/j.cma.2022.115867 ISSN 0045-7825 Source Computer Methods in Applied Mechanics and Engineering, 405 Part of collection Institutional Repository Document type journal article Rights © 2023 Moritz Flaschel, Siddhant Kumar, Laura De Lorenzis Files PDF 1_s2.0_S0045782522008234_main.pdf 1.86 MB Close viewer /islandora/object/uuid:9c847254-2500-4291-a628-d102e18aaf2e/datastream/OBJ/view