Beyond empirical models: Discovering constitutive laws in solids with graph-based equation discovery

Constitutive models are fundamental to solid mechanics and materials science, underpinning the quantitative description of material behaviors. Traditional phenomenological models are often built on expert intuition and empirical fitting, which limits their generalizability. In this work, we propose a graph-based equation discovery framework for automated discovery of constitutive laws directly from multicase experimental data. This framework expresses equations as directed graphs, where nodes represent operators and variables, edges denote computational relations, and edge features encode parametric dependencies. This enables the generation and optimization of free-form symbolic expressions with undetermined material-specific parameters. Through the framework, we have found constitutive models for strain-rate effects in alloy steel materials, deformation behavior of lithium metal, and hyperelastic behavior of filled rubbers. The discovered models exhibit compact analytical structures and achieve higher accuracy than empirical models. The proposed framework provides a generalizable and interpretable approach for data-driven scientific modeling, particularly in contexts where traditional empirical models are inadequate for representing complex physical phenomena.