A constitutive level-set model for ferromagnetic shape-memory alloys

Abstract

This work proposes a phenomenological level-set model for ferromagnetic shape-memory alloys (FSMAs), developed under consistent thermodynamic analysis. A set of adequate internal and external variables is chosen so as to describe the rate-independent magneto-mechanical response of a FSMA single crystal. Almost every phenomenological model in bibliography adopts martensitic volume fractions as internal variables. The novelty of this work is the introduction of a continuous level-set function as an internal variable of state, which accounts implicitly for the dissipative twin boundary motion in the evolution of inelastic reorientation of martensitic variants. Following the usual internal variable formalism within the framework of standard magnetomechanics, the evolution equations for the level-set function are derived for the forward and reverse variant reorientation processes. The model is implemented in a two-dimensional special case, where the reduced equations are numerically solved capturing the important effects of stress-induced and magnetic field-induced martensitic variant reorientation, such as magnetization hysteresis, pseudoelastic/partial pseudoelastic behavior and magnetic shape-memory effect. The proposed constitutive model is capable of explaining the constitutive response caused by the reorientation of martensitic variants in FSMAs and may be further improved so as to be implemented in even more complicated situations, such as dynamic and rate-dependent analysis.