Magnetic shape-memory alloys: thermomechanical modelling and analysis

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.     

A three-dimensional model describing stress-induced solid phase transformation with permanent inelasticity

The employment of shape memory alloys (SMA) in a large number of applications in the fields of aeronautical, biomedical, and structural engineering has been the motivation for an increasing interest in the direction of a correct and exhaustive modeling of their macroscopic behaviour.