TY - JOUR
T1 - A Modeling Framework for Coupling Plasticity with Species Diffusion
AU - Joshaghani , M. S.
AU - Nakshatrala , K. B.
JO - Communications in Computational Physics
VL - 1
SP - 83
EP - 125
PY - 2022
DA - 2022/07
SN - 32
DO - http://doi.org/10.4208/cicp.OA-2021-0198
UR - https://global-sci.org/intro/article_detail/cicp/20789.html
KW - Species diffusion, plasticity, non-negative solutions, damage mechanics, degradation/healing, coupled problem.
AB - <p style="text-align: justify;">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 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 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.</p>