# Multi-component chemo-mechanics based on transport relations for the chemical potential

## TL;DR

This paper develops a chemo-mechanical model for multi-component materials, introducing a semi-analytical inversion of chemical potential to improve numerical stability and applying it to spinodal decomposition with elastic and plastic effects.

## Contribution

A novel semi-analytical inversion method for chemical potential in multi-component chemo-mechanical models, enhancing numerical stability and enabling detailed spinodal decomposition simulations.

## Key findings

- Improved numerical conditioning of transport equations.
- Successful demonstration of convergence to Cahn-Hilliard solutions.
- Insights into elastic and plastic effects on spinodal morphologies.

## Abstract

A chemo-mechanical model for a finite-strain elasto-viscoplastic material containing multiple chemical components is formulated and an efficient numerical implementation is developed to solve the resulting transport relations. The numerical solution relies on inverting the constitutive model for the chemical potential. In this work, a semi-analytical inversion for a general family of multi-component regular-solution chemical free energy models is derived. This is based on splitting the chemical free energy into a convex contribution, treated implicitly, and a non-convex contribution, treated explicitly. This results in a reformulation of the system transport equations in terms of the chemical potential rather than the composition as the independent field variable. The numerical conditioning of the reformulated system, discretised by finite elements, is shown to be significantly improved, and convergence to the Cahn-Hilliard solution is demonstrated for the case of binary spinodal decomposition. Chemo-mechanically coupled binary and ternary spinodal decomposition systems are then investigated to illustrate the effect of anisotropic elastic deformation and plastic relaxation of the resulting spinodal morphologies in more complex material systems.