Eur. Phys. J. B (2013) 86: 171
https://doi.org/10.1140/epjb/e2013-30941-6

Regular Article

Rearrangement of martensitic variants in Ni₂MnGa studied with the phase-field method^*

¹ Karlsruhe University of Applied Sciences, Institute of Materials and Processes (IMP), Moltkestraße 30, 76133 Karlsruhe, Germany
² Karlsruhe Institute of Technology (KIT), Institute of Applied Materials - Reliability of Components and Systems (IAM-ZBS), Engelbert-Arnold-Straße 4, 76131 Karlsruhe, Germany

^a e-mail: christian.mennerich@hs-karlsruhe.de

Received: 12 October 2012
Received in final form: 9 January 2013
Published online: 22 April 2013

Abstract

A phase-field model is introduced to simulate the magnetic shape memory effect, i.e. the solid-state rearrangement of the boundaries of a martensitic microstructure using an external magnetic field, in the shape memory material Ni₂MnGa. The model is derived from an existing phase-field model that has proven well in several applications in materials science, based on the interpolation of free energies. The micromagnetic and elastic energy contributions entering the constitutive free energy functional are given, and the coupled kinetic equations of motion for the phase fields that describe the microstructure geometry, the spontaneous magnetization and the elastic displacement field are derived from the principle of minimization of free energy. The concept of representative volume elements is applied for the microstructure simulations carried out to analyze the material behavior, and the relevant boundary conditions are discussed. Stress vs. strain and strain vs. applied magnetic field curves are shown for Ni₂MnGa.