
Experimental Validation of the EUCLID Framework for Automated Discovery of Hyperelastic Material Models
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Data-driven methods are gaining traction in computational solid mechanics for modeling complex material behavior. One prominent approach, EUCLID (Efficient Unsupervised Constitutive Law Identification and Discovery), has been developed for automated discovery of constitutive laws [1]. EUCLID identifies a material model from a large library of nonlinear candidates using mechanical testing data, typically consisting of global forces and displacement fields. A key advantage of EUCLID over the standard approach of manually choosing a model and identifying its unknown parameters is that EUCLID discovers interpretable models through sparse regression, extracting parsimonious mathematical expressions from a broad catalogue of potential models. The discovery process is formulated as a joint optimization, ensuring that the weak form of linear momentum balance is satisfied both within the bulk material and on the boundaries through reaction force balance. Sparsity-promoting regularization further ensures that the resulting models are concise and interpretable. Another key advantage of EUCLID is that it operates in an unsupervised manner, meaning that stress data are not required for the discovery process. While EUCLID has demonstrated its capabilities in discovering material behavior on data generated via finite element simulations [1-4], it has not yet been comprehensively validated using experimental full-field displacement measurements acquired through techniques like digital image correlation (DIC) and global reaction forces. This work seeks to address that gap by experimentally validating EUCLID’s performance to discover hyperelastic constitutive laws on natural rubber specimens with varying geometrical complexities. Mechanical tests, including tension tests and shear tests, were performed on standard specimens as well as on specimens containing circular and elliptical holes. We first evaluate the classical approach, where a single fixed model is used instead of a library of candidates, and to highlight the advantages of incorporating full-field displacement data over traditional global force-displacement curves in constitutive law identification. Traditionally, identifying constitutive laws for incompressible hyperelastic materials requires multiple tests, such as uniaxial, and pure shear. However, using full-field measurements offers an alternative: a single test on a specimen with complex geometry, designed to widely span the plane of strain invariants.