Micromorphic approach to phase-field modeling of multivariant martensitic transformation with rate-independent dissipation effects

Abstract

A micromorphic formulation of the phase-field model of martensitic transformation is developed within the incremental energy minimization framework. In contrast to the conventional phase-field formulation, the order parameters are viewed as local variables and the corresponding evolution equations are solved at the material-point level, i.e. at the Gauss points in the finite-element setting. From a computational standpoint, such a treatment is advantageous for complex evolution laws that may lead to computational difficulties if treated globally, as in the conventional phase-field formulation. In the micromorphic formulation, each order parameter is coupled to its micromorphic counterpart governed by a global Helmholtz-type PDE. This coupling ensures that the interfacial energy and related size effects are correctly captured by the model. In this work, the micromorphic approach is applied to a finite-strain multivariant phase-field model that incorporates rate-independent dissipation. The augmented Lagrangian technique is then used to transform the resulting non-smooth incremental minimization problem to a smooth and unconstrained saddle-point problem. Microstructure evolution under nano-indentation is studied to illustrate the approach.