On a unified approach to the description of phase transitions and strain localization (Q1912021)

In this very dense paper, the authors introduce the concept of stress fluctuation at a discontinuity surface in order to resolve the contradictions usually met at phase transition fronts. This concerns, on the one hand, the relationship between the onset of strain localization and that of phase transition, and, on the other hand, the problem of traction continuity at the front. The strain localization is formulated in terms of a kinetic theory of time-dependent surface-damage behavior and fracture. The classical description is recovered when the fluctuating stress is absent. It is shown in parallel that phase transitions require a non-zero fluctuating stress, so that the noted contradiction appears only in the classical approximation. Equilibrium phase transitions are also considered by taking into account both energy of internal stresses and a threshold-type thermodynamical dissipative force (configurational force). This applies to the case of the deformation of pseudo-elastic materials where a dependence of this ``force'' on the volume fraction of martensite can be determined. The writing style of the paper is somewhat confusing as the authors apparently tried to put too much in a single paper.