TY - JOUR

T1 - A variational framework for Cahn–Hilliard-type diffusion coupled with Allen–Cahn-type multi-phase transformations in elastic and dissipative solids

AU - Gaddikere Nagaraja, Swaroop

AU - Antretter, Thomas

N1 - Publisher Copyright: © 2024 The Authors

PY - 2024/9/24

Y1 - 2024/9/24

N2 - This article presents a variational framework for coupled chemo-mechanical solids undergoing irreversible micro-structural changes at infinitesimal strains. The coupled problem is characterised by phenomena such as phase transitions, micro-structure coarsening and swelling. It is an extension of our previous work on variational inelasticity for a conserved chemo-mechanical setting to a unified conserved and non-conserved setting which include multi-phase transformations. The variational framework, again governed by continuous-time, discrete-time and discrete-space–time incremental variational principles, is outlined for coupled diffusion-phase transformation phenomena in elastic and dissipative solids. For the sake of simplicity, focus is restricted to isothermal conditions. It is shown that the governing macro- and micro-balance equations of the coupled problem appear as Euler equations of these minimisation and saddle point principles. In contrast to our previous work, extended variational principles (with the gradient of the chemical potential and phase fractions) are constructed that account for diffusion-phase transformation coupling. This is achieved by Legendre transformations. Note that the local–global solution strategy is still preserved and the resulting system of symmetric non-linear algebraic equations are solved by Newton–Raphson-type iterative methods. The applicability of the proposed framework is demonstrated by numerical simulations that qualitatively characterise lower bainitic micro-structure.

AB - This article presents a variational framework for coupled chemo-mechanical solids undergoing irreversible micro-structural changes at infinitesimal strains. The coupled problem is characterised by phenomena such as phase transitions, micro-structure coarsening and swelling. It is an extension of our previous work on variational inelasticity for a conserved chemo-mechanical setting to a unified conserved and non-conserved setting which include multi-phase transformations. The variational framework, again governed by continuous-time, discrete-time and discrete-space–time incremental variational principles, is outlined for coupled diffusion-phase transformation phenomena in elastic and dissipative solids. For the sake of simplicity, focus is restricted to isothermal conditions. It is shown that the governing macro- and micro-balance equations of the coupled problem appear as Euler equations of these minimisation and saddle point principles. In contrast to our previous work, extended variational principles (with the gradient of the chemical potential and phase fractions) are constructed that account for diffusion-phase transformation coupling. This is achieved by Legendre transformations. Note that the local–global solution strategy is still preserved and the resulting system of symmetric non-linear algebraic equations are solved by Newton–Raphson-type iterative methods. The applicability of the proposed framework is demonstrated by numerical simulations that qualitatively characterise lower bainitic micro-structure.

KW - Allen–Cahn multi phase-transformation

KW - Cahn–Hilliard diffusion

KW - Crystal plasticity

KW - Monolithic solution scheme

KW - Variational formulation

UR - http://www.scopus.com/inward/record.url?scp=85204622351&partnerID=8YFLogxK

U2 - 10.1016/j.ijplas.2024.104131

DO - 10.1016/j.ijplas.2024.104131

M3 - Article

AN - SCOPUS:85204622351

VL - 182.2024

JO - International journal of plasticity

JF - International journal of plasticity

SN - 0749-6419

IS - November

M1 - 104131

ER -