A modeling framework for coupling plasticity with species diffusion

TL;DR

This paper introduces a coupled modeling and computational framework to simulate how chemical species transport influences plastic deformation in materials, ensuring physically realistic solutions through an optimized nonnegative formulation.

Contribution

The paper develops a novel computational framework that accurately models coupled transport and plasticity, incorporating physical constraints and handling anisotropic diffusion effects.

Findings

The framework effectively predicts deformation due to chemical degradation.

It maintains nonnegative concentration solutions in simulations.

Anisotropic diffusion increases unphysical violations in traditional models.

Abstract

This paper presents a modeling framework---mathematical model and computational framework---to study the response of a plastic material due to the presence and transport of a chemical species in the host material. Such a modeling framework is important to a wide variety of problems ranging from Li-ion batteries, moisture diffusion in cementitious materials, hydrogen diffusion in metals, to consolidation of soils under severe loading-unloading regimes. The mathematical model incorporates experimental observations reported in the literature on how (elastic and plastic) material properties change because of the presence and transport of a chemical species. Also, the model accounts for one-way (transport affects the deformation but not vice versa) and two-way couplings between deformation and transport subproblems. The resulting coupled equations are not amenable to analytical solutions; so, we present a robust computational framework for obtaining numerical solutions. Given that popular numerical formulations do not produce nonnegative solutions, the computational framework uses an optimized-based nonnegative formulation that respects physical constraints (e.g., nonnegative concentrations). For completeness, we will also show the effect and propagation of the negative concentrations, often produced by contemporary transport solvers, into the overall predictions of deformation and concentration fields. Notably, anisotropy of the diffusion process exacerbates these unphysical violations. Using representative numerical examples, we will discuss how the concentration field affects plastic deformations of a degrading solid. Based on these numerical examples, we also discuss how plastic zones spread because of material degradation. To illustrate how the proposed computational framework performs, we report various performance metrics such as optimization iterations and time-to-solution.