Multiscale Approach for the Modeling of Chemo-Magneto-Thermo-Mechanical Couplings – Reversible Framework

Abstract

We focus in this paper on a multiscale modeling approach of the materials’ reversible behavior involving couplings of the chemo-magneto-thermo-mechanical type. It is shown that it is possible to take into account a large variety of these coupled environments by a unified approach using the springs of the scale change and the build of an appropriate Gibbs free energy function. The approach is well suited to situations where some fields can be considered homogeneous at a relevant scale and where free deformation can be defined.

Multiscale magneto-elastic modeling of magnetic materials including isotropic second order stress effect

“…In the following, g denotes a grain. It is supposed to be composed of several phases φ (typically ferrite, austenite, martensite,...), that may be separated in different variants (see [42,43] for more details) but remain at constant volume fraction in the modeling proposed 1 . α denotes a magnetic domain family inside the ferromagnetic phase considered and represents the lower scale.…”

“…7 A more complex formulation has been proposed recently [43] to take a possible phase transformation (ferromagnetic to ferromagnetic, or ferromagnetic to paramagnetic) or the existence of several variants into account. The total number of internal variables strongly depends on the number of grains, phases, variants and number of domain families inside each variant.…”

“…Local magnetic and mechanical loadings ( H gr and σ gr ) are then different from the global loadings ( H and σ). Typically the calculation of the local loadings are carried out on each grain through a self-consistent polycrystalline scheme [22], where loadings at the grain scale are derived from the macroscopic loadings, using equations (43) and (44). The gap between local and global quantities defines the demagnetizing field and the residual stress.…”