Bayesian-EUCLID: discovering hyperelastic material laws with uncertainties

TL;DR

Bayesian-EUCLID introduces an unsupervised Bayesian framework for discovering interpretable hyperelastic material laws with quantified uncertainties using full-field displacement data, without relying on stress measurements.

Contribution

It extends EUCLID by incorporating Bayesian methods with sparsity priors to identify physically consistent constitutive laws and quantify uncertainties.

Findings

Successfully recovers various hyperelastic models like Neo-Hookean and Ogden.

Efficiently handles both epistemic and aleatoric uncertainties.

Demonstrates applicability in elastostatics and elastodynamics.

Abstract

Within the scope of our recent approach for Efficient Unsupervised Constitutive Law Identification and Discovery (EUCLID), we propose an unsupervised Bayesian learning framework for discovery of parsimonious and interpretable constitutive laws with quantifiable uncertainties. As in deterministic EUCLID, we do not resort to stress data, but only to realistically measurable full-field displacement and global reaction force data; as opposed to calibration of an a priori assumed model, we start with a constitutive model ansatz based on a large catalog of candidate functional features; we leverage domain knowledge by including features based on existing, both physics-based and phenomenological, constitutive models. In the new Bayesian-EUCLID approach, we use a hierarchical Bayesian model with sparsity-promoting priors and Monte Carlo sampling to efficiently solve the parsimonious model selection task and discover physically consistent constitutive equations in the form of multivariate multi-modal probabilistic distributions. We demonstrate the ability to accurately and efficiently recover isotropic and anisotropic hyperelastic models like the Neo-Hookean, Isihara, Gent-Thomas, Arruda-Boyce, Ogden, and Holzapfel models in both elastostatics and elastodynamics. The discovered constitutive models are reliable under both epistemic uncertainties - i.e. uncertainties on the true features of the constitutive catalog - and aleatoric uncertainties - which arise from the noise in the displacement field data, and are automatically estimated by the hierarchical Bayesian model.