A continuum theory for mineral solid solutions undergoing chemo-mechanical processes

TL;DR

This paper develops a thermodynamically consistent continuum framework to model chemo-mechanical interactions in metamorphic mineral solid solutions, integrating phase-field methods with geoscience parameters for simulating complex mineral behaviors.

Contribution

It introduces a novel coupled chemo-mechanical model for mineral solid solutions using continuum mechanics, thermodynamics, and phase-field theory, applicable to 2D and 3D geoscience simulations.

Findings

Demonstrates chemo-mechanical coupling effects in mineral evolution.

Validates the framework through numerical simulations of spinodal decomposition and reactions.

Provides a comprehensive tool for modeling complex geoscience processes.

Abstract

Recent studies on metamorphic petrology as well as microstructural observations suggest the influence of mechanical effects upon chemically active metamorphic minerals. Thus, the understanding of such a coupling is crucial to describe the dynamics of geomaterials. In this effort, we derive a thermodynamically-consistent framework to characterize the evolution of chemically active minerals. We model the metamorphic mineral assemblages as a solid-species solution where the species mass transport and chemical reaction drive the stress generation process. The theoretical foundations of the framework rely on modern continuum mechanics, thermodynamics far from equilibrium, and the phase-field model. We treat the mineral solid solution as a continuum body, and following the Larch\'e and Cahn network model, we define displacement and strain fields. Consequently, we obtain a set of coupled chemo-mechanical equations. We use the aforementioned framework to study single minerals as solid solutions during metamorphism. Furthermore, we emphasise the use of the phase-field framework as a promising tool to model complex multi-physics processes in geoscience. Without loss of generality, we use common physical and chemical parameters found in the geoscience literature to portrait a comprehensive view of the underlying physics. Thereby, we carry out 2D and 3D numerical simulations using material parameters for metamorphic minerals to showcase and verify the chemo-mechanical interactions of mineral solid solutions that undergo spinodal decomposition, chemical reactions, and deformation.