A Modeling Framework for Coupling Plasticity with Species Diffusion (Communications in Computational Physics, 2022)
This paper presents a modeling framework—mathematical model and computational framework—to study the response of a plastic material due to the presenceand transport of a chemical species in the host material. Such a modeling frameworkis important to a wide variety of problems ranging from Li-ion batteries, moisturediffusion in cementitious materials, hydrogen diffusion in metals, to consolidation ofsoils under severe loading-unloading regimes. The mathematical model incorporatesexperimental 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 viceversa) and two-way couplings between deformation and transport subproblems. Theresulting coupled equations are not amenable to analytical solutions; so, we present arobust computational framework for obtaining numerical solutions. Given that popular numerical formulations do not produce nonnegative solutions, the computationalframework uses an optimized-based nonnegative formulation that respects physicalconstraints (e.g., nonnegative concentrations). For completeness, we also show theeffect and propagation of the negative concentrations, often produced by contemporary transport solvers, into the overall predictions of deformation and concentrationfields. Notably, anisotropy of the diffusion process exacerbates these unphysical violations. Using representative numerical examples, we discuss how the concentrationfield 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 variousperformance metrics such as optimization iterations and time-to-solution.
Keywords: Species diffusion; plasticity; non-negative solutions; damage mechanics; degradation/healing; coupled problem.