Multi-phase-field elasticity model based on partial rank-one energy relaxation on pairwise interfaces

TL;DR

This paper introduces a new multi-phase-field elasticity model that accurately satisfies interface conditions in phase transformations by using partial rank-one relaxation of elastic energy on pairwise interfaces.

Contribution

The novel model ensures static equilibrium and compatibility conditions across all phase-field interfaces, addressing limitations of previous models.

Findings

Model satisfies jump conditions between all locally-active phase-fields.

Numerical examples demonstrate the model's effectiveness against existing limiting cases.

The approach improves the accuracy of phase transformation simulations.

Abstract

To model mechanically-driven phase transformations using the phase-field theory, suitable models are needed for describing the mechanical fields related to individual phase-fields in the interfacial regions. They play a crucial role in obtaining the mechanical driving forces of phase-field evolution. Quantitative modeling requires satisfying the interfacial static equilibrium and kinematic compatibility conditions. To the best of our knowledge, no existing multi-phase-field elasticity model has been able to satisfy the jump conditions between all the locally-active phase-fields associated to their pairwise normals, except in the dual-phase-field regions. In this work, we introduce a novel multi-phase-field elasticity model based on the partial rank-one relaxation of the elastic energy density defined on the pairwise interfaces as a function of pairwise strains. These ad hoc pairwise definitions enable us to satisfy the static equilibrium and kinematic compatibility conditions between all the locally-active phase-fields. Different numerical examples are presented, which compare the developed model against the equal-strain and equal-stress limiting cases.