Generalizing the Gurson Model Using Symbolic Regression and Transfer Learning to Relax Inherent Assumptions

Abstract

Abstract To generate material models with fewer limiting assumptions while maintaining closed-form, interpretable solutions, we propose using genetic programming based symbolic regression (GPSR), a machine learning (ML) approach that describes data using free-form symbolic expressions. To maximize interpretability, we start from an analytical, derived material model, the Gurson model for porous ductile metals, and systematically relax inherent assumptions made in its derivation to understand each assumption’s contribution to the GPSR model forms. We incorporate transfer learning methods into the GPSR training process to increase GPSR efficiency and generate models that abide by known mechanics of the system. The results show that regularizing the GPSR fitness function is critical for generating physically valid models and illustrate how GPSR allows a high level of interpretability compared with other ML approaches. The method of systematic assumption relaxation allows the generation of models that address limiting assumptions found in the Gurson model, and the symbolic forms allow conjecture of decreased material strength due to void interaction and non-symmetric void shapes.