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
SN - 0749-6419
VL - 167.2023
JO - International journal of plasticity
JF - International journal of plasticity
IS - August
M1 - 103652
ER -