Magnetic shape-memory alloys: thermomechanical modelling and analysis

• Published in: Continuum mechanics and thermodynamics Vol. 26; no. 6; pp. 783 - 810
• Main Authors: Roubíček, Tomáš, Stefanelli, Ulisse
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2014; Springer; Springer Nature B.V
• Subjects: Alloys; Analysis; Classical and Continuum Physics; Dynamical systems; Energy conservation; Engineering Thermodynamics; Ferromagnetism; Heat and Mass Transfer; Magnetism; Martensitic transformations; Mathematical models; Nonlinear dynamics; Original Article; Phase transitions; Physics; Physics and Astronomy; Shape memory; Shape-memory alloys; Specialty metals industry; Structural Materials; Theoretical and Applied Mechanics; Thermistors; Thermodynamics; Transformations; Martensitic Transformation; FePt; Weak Solution; Shape Memory Alloy; Martensite
• ISSN: 0935-1175; 1432-0959
• DOI: 10.1007/s00161-014-0339-8

A phenomenological model for the coupled thermo-electro-magneto-mechanical and phase-transformation behaviour of magnetic shape-memory alloys is advanced in small strains and eddy current approximation. The corresponding system of strongly nonlinear relations is tackled via a suitable enthalpy-like transformation. A fully implicit regularized time-discretization scheme is devised and proved to be stable and convergent. In particular, the convergence proof for discrete solutions entails that a suitably weak, energy-conserving solution to the continuous nonlinear system exists. Moreover, several particular models as e.g. ferro/paramagnetic transformation in ferromagnetic materials, martensitic transformation in shape memory allows, or just a simple thermistor problem are covered just as special cases.