TY - JOUR

T1 - Variational formulation of Cahn–Hilliard-type diffusion coupled with crystal plasticity

AU - Gaddikere Nagaraja, Swaroop

AU - Flachberger, Wolfgang

AU - Antretter, Thomas

N1 - Publisher Copyright: © 2023 The Authors

PY - 2023/8

Y1 - 2023/8

N2 - This article presents a relatively general framework for the description of the Cahn–Hilliard-type diffusion in solids undergoing infinitesimal elastic and plastic deformations. The coupled chemo-mechanical problem, characterised by phenomena such as phase segregation, microstructure coarsening and swelling, is treated using the variational framework which is governed by continuous-time, discrete-time and discrete-space–time incremental variational principles. It is shown that the governing equations of the coupled problem can be derived as Euler equations of minimisation and saddle point principles. A point of departure from the existing works is the coupling of crystal plasticity to the problem of diffusion and optimising the potential with respect to the plastic variables such that they are solved locally at the integration points. This is done using a return map algorithm which results in a reduced global problem. The variational framework results in a system of symmetric non-linear algebraic equations that are solved by Newton–Raphson-type iterative methods. This is a novel and attractive feature with respect to numerical implementation, as models resulting from the proposed variational framework are computationally less expensive in comparison with non-symmetric formulations. The numerical simulations presented at the end predict the applicability of models resulting from the proposed variational framework for multiple scenarios.

AB - This article presents a relatively general framework for the description of the Cahn–Hilliard-type diffusion in solids undergoing infinitesimal elastic and plastic deformations. The coupled chemo-mechanical problem, characterised by phenomena such as phase segregation, microstructure coarsening and swelling, is treated using the variational framework which is governed by continuous-time, discrete-time and discrete-space–time incremental variational principles. It is shown that the governing equations of the coupled problem can be derived as Euler equations of minimisation and saddle point principles. A point of departure from the existing works is the coupling of crystal plasticity to the problem of diffusion and optimising the potential with respect to the plastic variables such that they are solved locally at the integration points. This is done using a return map algorithm which results in a reduced global problem. The variational framework results in a system of symmetric non-linear algebraic equations that are solved by Newton–Raphson-type iterative methods. This is a novel and attractive feature with respect to numerical implementation, as models resulting from the proposed variational framework are computationally less expensive in comparison with non-symmetric formulations. The numerical simulations presented at the end predict the applicability of models resulting from the proposed variational framework for multiple scenarios.

KW - Cahn–Hilliard diffusion

KW - Chemo-mechanical coupling

KW - Monolithic solution scheme

KW - Phase-field model

KW - Variational formulation

KW - Variational Formulation

KW - Cahn-Hilliard-Type Diffusion

KW - Crystal Plasticity

UR - http://www.scopus.com/inward/record.url?scp=85162000717&partnerID=8YFLogxK

U2 - 10.1016/j.ijplas.2023.103652

DO - 10.1016/j.ijplas.2023.103652

M3 - Article

AN - SCOPUS:85162000717

VL - 167.2023

JO - International journal of plasticity

JF - International journal of plasticity

SN - 0749-6419

IS - August

M1 - 103652

ER -