Multiscale modeling of martensitic phase transformations

On the numerical determination of heterogeneous mesostructures within shape-memory alloys induced by precipitates

Abstract

The general scope of this contribution is the implementation of a micromechanical constitutive model for martensitic phase transformations based on energy-relaxation into the Multiscale Finite Element Method. Precisely, we study the effect of precipitates on the overall material response of a representative volume element (RVE), where the mesostructure of the material is fully resolved by the Finite Element discretization. The precipitate is modeled as an isotropic linear elastic and circular inclusion within a shape memory alloy (SMA) matrix, where in each Gauß-point of the matrix the aforementioned micromechanical model is applied. Providing macroscopic homogeneous deformations, we study the resulting phase distribution of austenite and martensite as well as the effective material response of the RVE. In particular, the energy minimizing displacement field turns out to be C⁰−smooth and hence, the resulting phase distributions are heterogeneous.