The novel learnable physics engines for interpretable elastoplastic models of geomaterials based on the message passing neural network

Accurately predicting the path-dependent plastic behavior of geomaterials is a challenging endeavor because of the intricate evolution of microstructures. In this study, a novel learnable physics engine is proposed to infer the elastoplastic constitutive model based on graph networks. This objective is accomplished by training a neural network model that incorporates interpretable components, for instance, the stored elastic energy function and the yield function. By re - formulating the evolution fields of the physical system into a time - evolving graph network, the suggested method can infer the solutions of constitutive equations. The proposed framework leverages Sobolev training to regulate the derivatives of the elastic energy functions. Additionally, it trains the yield functions as level - set evolution. As a result, this framework is interpretable and, at the same time, shows outstanding prediction accuracy. To verify the robustness and reliability of the proposed method, numerical examples are conducted. The numerical outcomes reveal that the proposed approach can provide efficient and precise long - term forward predictions for the elastoplastic behavior of geomaterials.