A constitutive level-set model for ferromagnetic shape-memory alloys
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O R I G I NA L A RT I C L E
Antonios I. Arvanitakis
A constitutive level-set model for ferromagnetic shape-memory alloys
Received: 20 August 2019 / Accepted: 11 March 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020
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. Keywords Constitutive model · Magnetic shape-memory alloys · Level-set function · Twin boundary motion · Magnetic shape-memory effect · Magnetization hysteresis · Pseudoelasticity 1 Introduction Ferromagnetic shape-memory alloys (FSMAs), also called magnetic shape-memory alloys (MSMAs), are a special and newly discovered class of smart materials capable of producing deformations in response to magnetic fields. Typically, FSMAs are alloys of nickel, manganese and gallium. Ullakko and co-workers [36] were the first to observe the response of FSMA materials under external field with magnetically induced strain up to 0.2%. Nowadays, the current research provides manufacturing techniques for alloy treatment that produce materials that exhibit magnetic field-induced deformations up to 10–20% [31,33,37]. Besides large magnetically induced strain, FSMAs exhibit short response times that make them superior candidates for the design of innovative actuators and other devices of major technological importance in relevant fields, such as robotics, medical science and mechatronics [34]. FSMAs consist of two phases: the high-temperature phase called austenite and the low-temperature phase called martensite. However, a single martensitic crystal may assume a different orientation direction or as it is called, a vari
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