# An alternative to the Allen-Cahn phase field model for interfaces in solids - numerical efficiency

## TL;DR

This paper introduces an alternative phase field model for solid interfaces that is more numerically efficient than the traditional Allen-Cahn model, especially for low interface energy scenarios.

## Contribution

It formulates a new phase field equation inspired by sharp interface problems and compares its properties and efficiency to the Allen-Cahn model.

## Key findings

- The alternative model is more effective for low interface energy simulations.
- Numerical simulations show improved efficiency with the new model.
- The new model maintains key interface evolution properties.

## Abstract

The derivation of the Allen-Cahn and Cahn-Hilliard equations is based on the Clausius-Duhem inequality. This is not a derivation in the strict sense of the word, since other phase field equations can be fomulated satisfying this inequality. Motivated by the form of sharp interface problems, we formulate such an alternative equation and compare the properties of the models for the evolution of phase interfaces in solids, which consist of the elasticity equations and the Allen-Cahn equation or the alternative equation. We find that numerical simulations of phase interfaces with small interface energy based on the alternative model are more effective then simulations based on the Allen-Cahn model.