Integrating physics-informed symbolic regression with finite element models for damage law discovery

Abstract

Numerical simulation of fracture behavior in materials is a complex and challenging task. Accurate modeling of nonlinear mechanical behavior in systems affected by degradation and fracture relies on implementing suitable damage models within finite element methods (FEMs). This study explores the integration of physics-informed symbolic regression (SR) with FEM to derive an analytical damage law directly from experimental wedge splitting test data. Using genetic programming operations, a population of candidate damage equations evolves over hundreds of generations to identify the best fit to the measured load–displacement (F-D) data. Our findings demonstrate that the SR method yields a damage model that balances both accuracy and interpretability. Additionally, we discuss the efficiency and challenges associated with integrating SR with FEM, highlighting its potential for practical engineering applications.