Integrity bases for cubic nonlinear magnetostriction

A so-called smart material is a that the seat of one or more multiphysical coupling. One key points in development constitutive laws these materials, either at local global scale, to formulate free energy density (or enthalpy) from vectors, tensors, given order and for class symmetry, depending on symmetry classes crystal constituting representative volume element. This article takes as support study stress magnetization couple (?,m) involved phenomena magnetoelastic coupling cubic medium. Several studies indeed show non-monotonic sensitivity magnetic susceptibility magnetostriction certain soft materials under stress. Modeling such phenomenon requires introduction second term Gibbs density. polynomial formulation two variables preferred over tensorial formulation. For class, this allows express easily any bi-degree ? m (i.e. tensors formulation). rigorous systematic method essential obtain high-degree magneto-mechanical terms build function which invariant by action (octahedral) group. aim, theoretical computer tools Invariant Theory, allow mathematical description nonlinear magneto-elasticity, are introduced. Minimal integrity bases algebra pair (m,?), proper (orientation-preserving) full groups, then proposed. The minimal basis group constituted 60 invariants, while (the interest magneto-elasticity) made up 30 invariants. These invariants formulated (coordinate free) intrinsic manner, using generalized cross product write some them. counting independent multi-degree (m,?) performed. It shown accordingly it possible list without error all parameters useful coupled behavior basis. technique applied derive general expressions ??(?,m) domains scale exhibiting symmetry. classic results an isotropic medium recovered.