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

Constitutive models are fundamental to solid mechanics and materials science, underpinning the quantitative description and prediction of material responses under diverse loading conditions. Traditional phenomenological models, which are derived through empirical fitting, often lack generalizability and rely heavily on expert intuition and predefined functional forms. In this work, we propose a graph - based equation discovery framework for the automated discovery of constitutive laws directly from multisourc e 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 proposed framework, we have discovered new constitutive models for strain - rate effects in alloy steel materials and the deformation behavior of lithium metal. Com pared with conventional empirical models, these new models exhibit compact analytical structures and achieve higher accuracy. The proposed graph - based equation discovery framework provides a generalizable and interpretable approach for data - driven scientific mode l ling, particularly in contexts where traditional empirical formulations are inadequate for representing complex physical phenomena. Keywords: Constitutive model, graph, equation discovery, solid mechanics, data - driven modelling . Introduction Constitutive laws serve as fundamental elements in solid mechanics, establishing the relationship between kinematic measures and static quantities to characterize material - specific behavior. Unlike conservation principles and kinematic relations, which are derived from first principles and regarded as axiomatic foundations, constitutive models encapsulate empirical descriptions of material responses to external stimuli . Accordingly, they are typically established through phenomenological approaches, guided by systematic experimentation and theoretical generalization, to characterize nonlinear behaviors across varying conditions ( 1) . The accuracy and generality of constitutive models are critical for the reliability of mechanical analysis, directly influencing both theoretical developments and practical applications in computational mechanics and materials engineering.