Phase Transformations in Electrically Conductive Ferromagnetic Shape-Memory Alloys, Their Thermodynamics and Analysis

Abstract

We derive a thermodynamically consistent general continuum-mechanical model describing mutually coupled martensitic and ferro/paramagnetic phase transformations in electrically-conductive magnetostrictive materials such as NiMnGa. We use small-strain and eddy-current approximations, yet large velocities and electric current injected through the boundary are allowed. Fully nonlinear coupling of magneto-mechanical and thermal effects is considered. The existence of energy-preserving weak solutions is proved by showing convergence of timediscrete approximations constructed by a carefully designed semi-implicit regularized scheme.

Thermomechanics of hydrogen storage in metallic hydrides: modeling and analysis

“…We will prove this theorem in Section 4 by a semi-implicit time discretisation in a more or less constructive manner, except the fixed-point argument behind the boundary-value sub-problems (28c)-(19c) and (18d)-(29d) and selection of converging subsequences. The additional properties (27) follow from (40f) and ( 46). The H 2 -regularity of χ is a standard consequence of (27d).…”

On morphoelastic rods

“…where ζ is a possibly nonsmooth dissipation potential such that 0 ∈ ∂ζ(0), and ζ( G) is its subdifferential set at G. Non-smooth dissipation potentials are customary in the mathematical modeling of materials that display hysteresis [15,50], for instance, in the modeling of shape memory alloys [46,47] and ferromagnetic materials [43,45]. Of course, the argument following (90) would not apply in this case.…”

A nonlinear theory for fibre-reinforced magneto-elastic rods

“…These works used a direct approach to formulate the equilibrium equations based on the conservation laws of continuum mechanics. Such an approach has the advantage to making possible the coupling between magneto-elasticity with other evolutionary phenomena whose mathematical description is not of variational type [35,36]. The same approach was applied by Dorfmann and Ogden [16] to formulate the equilibrium equation of magnetoelasticity at finite strains, and by DeSimone and Podio-Guidugli [15] for ferromagnetic solids.…”