English

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

Numerical Analysis 2025-09-22 v2 Numerical Analysis

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.

Keywords

Cite

@article{arxiv.2304.02406,
  title  = {Multi-phase-field elasticity model based on partial rank-one energy relaxation on pairwise interfaces},
  author = {Mohammad Sarhil and Oleg Shchyglo and Hesham Salama and Dominik Brands and Ingo Steinbach and Jörg Schröder},
  journal= {arXiv preprint arXiv:2304.02406},
  year   = {2025}
}
R2 v1 2026-06-28T09:50:46.764Z