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

Abstract To model mechanically driven phase transformations using the phase-field theory, suitable models are needed to describe the mechanical fields associated with the 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 both 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 all the jump conditions between all the locally active phase-fields along the associated 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 that compare the developed model against the equal-strain and equal-stress limiting cases.