A Modeling Framework for Coupling Plasticity with Species Diffusion

Mohammad S. Joshaghani

doi:10.4208/cicp.OA-2021-0198

A Modeling Framework for Coupling Plasticity with Species Diffusion

2022-01-01

0

OA

AI

M

Mohammad S. Joshaghani

K

K. B. Nakshatrala *

DOI：10.4208/cicp.OA-2021-0198

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This paper presents a modeling framework???mathematical model and com-putational 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) ma-terial 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 popu-lar 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 also show the effect and propagation of the negative concentrations, often produced by contempo-rary transport solvers, into the overall predictions of deformation and concentration fields. Notably, anisotropy of the diffusion process exacerbates these unphysical vio-lations. Using representative numerical examples, we discuss how the concentration field affects plastic deformations of a degrading solid. Based on these numerical ex-amples, 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.

Keyword:

Species diffusion

plasticity

non-negative solutions

damage mechanics

degrada-tion

healing

coupled problem

A Modeling Framework for Coupling Plasticity with Species Diffusion

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