ML-Approach for Modeling Viscoelastic and Physically Nonlinear Materials Based on Symbolic Regression

This paper explores the application of symbolic regression, a technique rooted in genetic programming, to model the nonlinear hyperelastic and viscoelastic deformation behaviors of materials. The research focuses on two theoretical models (Neo-Hookean and Mooney-Rivlin) for hyperelastic material identification and generalized linear viscoelastic model. The models in their combinations are discovered in the context of soft bio tissue deformation. Synthetic datasets are generated based on these models, and symbolic regression is employed to obtain mathematical expressions representing the material behavior. The study presents the results of an implementation of the symbolic regression procedure based on those datasets in the form of analytical expressions and graph-tree structures. The iterative dependencies of the convergency of the symbolic regression for the analyzed cases are carried out. The results showcase the capability of the symbolic regression approach in capturing the time-dependent and complex nature of viscoelastic deformation. However, the problem of identification of the models that represent periodic time-varying that is set in a parametric way is figured out. It is shown the iterative dependencies of the convergency of the symbolic regression for the analyzed cases.