Automatic generation of interpretable hyperelastic material models by symbolic regression

TL;DR

This paper introduces a symbolic regression method to automatically generate simple, interpretable hyperelastic material models that fit experimental data well, enabling physical understanding and direct implementation.

Contribution

It presents a novel symbolic regression approach for creating interpretable hyperelastic models, validated on benchmark and real experimental data.

Findings

Successfully recovers predefined models in benchmark tests

Achieves good fit with experimental data for rubber and thermoplastic elastomers

Provides physically interpretable algebraic strain energy functions

Abstract

In this paper, we present a new procedure to automatically generate interpretable hyperelastic material models. This approach is based on symbolic regression which represents an evolutionary algorithm searching for a mathematical model in the form of an algebraic expression. This results in a relatively simple model with good agreement to experimental data. By expressing the strain energy function in terms of its invariants or other parameters, it is possible to interpret the resulting algebraic formulation in a physical context. In addition, a direct implementation of the obtained algebraic equation is possible. For the validation of the proposed approach, benchmark tests on the basis of the generalized Mooney-Rivlin model are presented. In all these tests, the chosen ansatz can find the predefined models. Additionally, this method is applied for the multi-axial loading data set of vulcanized rubber. Finally, a data set for a temperature-dependent thermoplastic polyester elastomer is evaluated. In latter cases, good agreement with the experimental data is obtained.