Unsupervised discovery of interpretable hyperelastic constitutive laws

We propose a new approach for data-driven automated discovery of isotropic hyperelastic constitutive laws. The approach is unsupervised, i.e., it requires no stress data but only displacement and global force data, which are realistically available through mechanical testing and digital image correl...

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Bibliographic Details
Published in:Computer methods in applied mechanics and engineering 2021-08, Vol.381, p.113852, Article 113852
Main Authors: Flaschel, Moritz, Kumar, Siddhant, De Lorenzis, Laura
Format: Article
Language:English
Subjects:
Algorithms
Automation
Constitutive models
Digital imaging
Hyperelasticity
Interpretable models
Inverse problems
Mechanical tests
Optimization
Regularization
Sparse regression
Unsupervised learning
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Summary:We propose a new approach for data-driven automated discovery of isotropic hyperelastic constitutive laws. The approach is unsupervised, i.e., it requires no stress data but only displacement and global force data, which are realistically available through mechanical testing and digital image correlation techniques; it delivers interpretable models, i.e., models that are embodied by parsimonious mathematical expressions discovered through sparse regression of a large catalogue of candidate functions; it is one-shot, i.e., discovery only needs one experiment — but can use more if available. The problem of unsupervised discovery is solved by enforcing equilibrium constraints in the bulk and at the loaded boundary of the domain. Sparsity of the solution is achieved by ℓp regularization combined with thresholding, which calls for a non-linear optimization scheme. The ensuing fully automated algorithm leverages physics-based constraints for the automatic determination of the penalty parameter in the regularization term. Using numerically generated data including artificial noise, we demonstrate the ability of the approach to accurately discover five hyperelastic models of different complexity. We also show that, if a “true” feature is missing in the function library, the proposed approach is able to surrogate it in such a way that the actual response is still accurately predicted. •We propose a new approach for data-driven automated discovery of constitutive laws.•The approach is unsupervised, i.e. it needs only displacement and global force data.•The approach is interpretable, i.e. it discovers parsimonious laws through sparse regression.•The approach is one-shot, i.e. it only needs one experimental dataset.•Sparse regression is empowered by domain knowledge.
ISSN:0045-7825
1879-2138
DOI:10.1016/j.cma.2021.113852