Rediscovering Hyperelasticity by Deep Symbolic Regression

International Journal for Numerical Methods in Engineering, vol. 127

Abstract

ABSTRACT Accurate hyperelastic material modeling of elastomers under multi‐axial loading still remains a research challenge. This work employs deep symbolic regression as an interpretable machine learning approach to discover novel strain energy functions directly from experimental results, with a specific focus on the classical Treloar and Kawabata data sets for vulcanized rubber. The proposed approach circumvents traditional human model selection biases by exploring possible functional forms of strain energy functions expressed in terms of both the first and second principal invariants of the right Cauchy‐Green tensor. The resulting models exhibit high predictive accuracy for various deformation modes, including uniaxial and equibiaxial tension, pure shear, and general biaxial loading. This underscores the potential of deep symbolic regression in advancing hyperelastic material modeling and highlights the importance of both invariants in capturing the complex behaviors of rubber‐like materials.

Authors 2

1. Rasul Abdusalamov corresponding Aachen Department of Continuum Mechanics

   RWTH Aachen University

   Affiliation as printed

   Department of Continuum Mechanics RWTH Aachen University Aachen Germany

2. M. Itskov Aachen Department of Continuum Mechanics

   RWTH Aachen University · Keele University

   Affiliation as printed

   Department of Continuum Mechanics RWTH Aachen University Aachen Germany

   School of Computer Science & Mathematics Keele University Staffordshire UK