Contact phase-field modeling for chemo-mechanical degradation processes. Part I: Theoretical foundations

TL;DR

This paper develops a thermodynamically consistent contact phase-field model based on contact geometry and maximum dissipation, extending traditional PFM to include chemo-mechanical coupling and bidirectional phase changes.

Contribution

It introduces a fundamental contact thermodynamics framework for phase-field modeling, incorporating non-equilibrium thermodynamics and micro-force balance, and extends PFM to chemo-mechanical processes.

Findings

Derived a generalized relaxation equation for PFM from thermodynamics.

Extended PFM to include chemo-mechanical coupling with bidirectional phase change.

Established a viscous Allen-Cahn equation ensuring full dissipation of kinematic variables.

Abstract

As phase-field modeling (PFM) is booming across various disciplines and has been proven fitted for numerically modeling interfacial problems, we aim at taking a step back to revisit its fundamental validity, in the light of non-equilibrium thermodynamics. For that, a general contact thermodynamics (CT) framework is derived from contact geometry, based on the maximum dissipation principle (MaxDP), thus extending Gibbs' seminal geometrical representation of thermostatics. Combining CT and micro-force balance, the gradient flow equation usually derived for PFM from the variational formulation can be written as generalized relaxation equations. The obtained viscous Allen-Cahn equation allows both the PFM kinematic degrees of freedom, the order parameter and its gradient, to be fully dissipative. The model is also extended to a double PFM, in order to include chemo-mechanical coupling, corresponding respectively to endothermic and exothermic processes and thus leading to a phase change bidirectionality. This contact PFM (CPFM) will be applied in the second part of this work to irregular microstructures like geomaterials, valid for porous media in general, with a focus on pressure solution.