A physics-informed learning framework for evolving anisotropy and asymmetry in plasticity: Metric-support convex-gauge network (MS-CGNet)

Abstract

Hexagonal close-packed (HCP) metals exhibit strong anisotropy, tension–compression asymmetry and strain-dependent evolution behavior, which complicate their constitutive representation. Analytical criteria sometimes remain limitations in capturing evolving complex yield behavior due to their rigid functional forms, whereas unconstrained data-driven models often lack built-in guarantees of convexity, homogeneity and constitutive interpretability. To address this challenge, this study proposes a Metric-Support Convex-Gauge Network (MS-CGNet), a generalized physics-informed framework for describing evolving anisotropic-asymmetric plasticity. This framework represents the yield surface as an accumulated-plastic-strain-parameterized convex-gauge, in which physical consistency is ensured through a convexity-preserving gauge formulation and a reference hardening backbone. Within a unified convex structure, a deviatoric metric branch and a bounded directional support branch are introduced to describe the global anisotropic distortion and local directional polarity, enabling a continuous smooth evolution of anisotropic and asymmetric yielding to be represented. Mechanical tests and viscoplastic self-consistent virtual tests are employed to generate a complex-stress-state yield dataset for network identification. Ablation studies are further performed to quantify the contributions of objective functions and network branches, followed by Bayesian optimization to select the capacities and bounds of the metric and support branches. The calibrated MS-CGNet achieves a mean absolute relative radial error of 0.112% over the complete 18-state dataset. Holdout and unseen-direction evaluations further demonstrate good generalization across strain levels and loading directions, together with favorable accuracy relative to von Mises, Hill48 and Yoon2014. Furthermore, the calibrated MS-CGNet is distilled into a structure-preserving white-box representation through singular value decomposition and closed-form saturation fitting, which is capable of providing explicit evolution functions of complex plasticity with controlled accuracy loss. The proposed framework presents a physics-informed and convex data-driven constitutive modeling framework for evolving anisotropic and asymmetric plasticity, which provides a promising approach to accommodate the complex continuous evolution of anisotropic and asymmetric plasticity over a wide straining range.