Discovery of Yield Functions in Plasticity via Physics-Informed Convex Neural Networks

Abstract

This study presents a physics-informed framework for discovering elasto-plastic yield functions directly from full-field displacement measurements and reaction force data, without relying on stress observations or predefined parametric forms. The yield function is modeled using a convex neural network explicitly designed to satisfy convexity and positive homogeneity of degree one, consistent with rate-independent plasticity theory. The network is embedded within a finite element discretization and trained by minimizing the residuals of the force balance equations across multiple loading scenarios. An explicit stress integration scheme is employed to enable gradient-based optimization while preserving physical consistency. The method is validated on three benchmark yield models—von Mises, Hill 1948, and Yld2000-2d—and is shown to accurately reconstruct both isotropic and anisotropic yield surfaces from a limited set of synthetic tests. To enable deployment in standard implicit solvers, the trained neural yield function is post-processed by fitting it to a smooth polynomial surrogate, which is successfully incorporated into return-mapping–based finite element simulations. These results demonstrate that the proposed approach provides a robust and generalizable pathway for data driven identification of elasto-plastic constitutive behavior.