Metal plasticity and nonlocal damage modeling: A thermodynamically consistent GSM approach with computational implications

This paper presents a comprehensive analysis of generalized standard materials (GSMs), with a particular focus on their application to metal plasticity and nonlocal damage models. Building on the foundational work of Halphen and Nguyen, the GSM framework is explored in the contexts of both small strain von Mises plasticity and advanced models for ductile fracture, such as the GLD framework, which incorporates cavity shape effects and nonlocal interactions. The study addresses key challenges, including the numerical stability and convergence of finite element implementations, with simulations of compact tension (CT) specimen fracture tests for two different steels demonstrating the accuracy and predictive capability of the GLD model. In addition, the paper delves into nonlocal damage models, presenting two key theoretical results: the attenuation of high-frequency components, where Gaussian kernels act as low-pass filters, and the connection of nonlocal formulations to a diffusion-like equation. A modified evolution equation with logarithmic terms is proposed to address excessive smoothing, and a sensitivity analysis of the length scale parameter l provides practical guidelines for optimizing nonlocal formulations for realistic damage simulation while maintaining numerical stability.