Hyperelastic material modelling using symbolic regression

PAMM, vol. 22

Abstract

Abstract Recently, data‐driven approaches in the field of material modeling have gained significant attention. A major advantage of these approaches is the direct integration of experimental results into the models. Nevertheless, artificial neural networks (ANNs) are especially challenging to interpret from a physical point of view, since internal processes of ANNs are difficult to understand. In this work a new automatic method for the generation of constitutive models for hyperelastic materials is introduced. The presented method is based on symbolic regression, which is a genetic algorithm. Thereby, a mathematical model in the form of an algebraic expression is found that fits the given data as accurately as possible and has a compact representation. The strain energy density function is determined directly as a function of the strain invariants. The proposed ansatz is embedded into a continuum mechanical framework combining the benefits of known physical relations with the unbiased optimization approach of symbolic regression. Benchmark tests for the generalized Mooney‐Rivlin model for uniaxial, equibiaxial and pure shear tests are presented. Finally, the presented procedure is tested on a temperature‐dependent dataset of a thermoplastic polyester elastomer. A good agreement between obtained material models and experimental data is demonstrated.

Authors 3

1. Rasul Abdusalamov corresponding Aachen Department of Continuum Mechanics

   RWTH Aachen University

   Affiliation as printed

   Department of Continuum Mechanics RWTH Aachen University Aachen Germany

   Department of Continuum Mechanics, RWTH Aachen University, Aachen, Germany

   Rasul Abdusalamov

   Telephone: +49 241 80 96444

2. Markus Hillgärtner Aachen Department of Continuum Mechanics

   RWTH Aachen University

   Affiliation as printed

   Department of Continuum Mechanics RWTH Aachen University Aachen Germany

   Department of Continuum Mechanics, RWTH Aachen University, Aachen, Germany

3. Mikhail Itskov Aachen Department of Continuum Mechanics

   RWTH Aachen University

   Affiliation as printed

   Department of Continuum Mechanics RWTH Aachen University Aachen Germany

   Department of Continuum Mechanics, RWTH Aachen University, Aachen, Germany