Supplementary material from "Coupled strain-gradient plasticity and incoherent martensitic phase boundary kinetics in isotropic solids: Theory and analytical results"

A thermodynamically consistent and physically motivated original small strain theory of coupled strain-gradient plasticity and kinetics of incoherent austenite (A)-martensite (M) phase boundary (PB) is developed for isotropic solids considering yielding of the PBs for the first time. Extending the Mises rate-independent theory for bulk and PBs, the hardenings are considered to depend on the incompatibility tensors, given by double curl of the plastic strain tensor and a tensor related to the jump in curl of the plastic strain tensor across the PBs, respectively, under isotropic symmetry. Thus, the internal length scales are introduced. The coupled PB kinetic law and flow rules for the phases and PBs are derived and used to study the response of a semi-infinite two-phase thin slab with a planar PB under thermomechanical load. However, the existing studies in the literature neglect yielding and kinetic law for the PBs, which is far from the reality. The system of equations is solved semi-analytically during the A → M transformation, which is the first attempt of this kind, and the results would be the benchmark solution for computational studies on this topic. The effect of the length scales and different loadings on the slab response is studied.