Reduced polynomial invariant integrity basis for in-plane magneto-mechanical loading

The description of the behavior a material subjected to multi-physics loadings requires formulation constitutive laws that usually derive from Gibbs free energies, using invariant quantities depending on considered physics and symmetries. On other hand, most crystalline materials can be described by their texture associated preferred directions strong symmetry (the so-called fibers). Moreover, among produced industrially, many are manufactured in form sheets or thin layers. This article has for object study magneto-mechanical coupling which is function stress $\sigma$ magnetization M. We consider with cubic whose one three fibers denoted as $\theta$, $\gamma$ $\alpha$ ' , enough so both in-plane quantities. propose an algorithm able linear relations between 30 invariants I k minimal integrity basis describing magneto-elastic problem, when they restricted loading conditions different fiber orientations. algorithm/program output reduced list cardinal 7 {100}-oriented $\theta$ fiber, 15 {110}-oriented 8 {111}-oriented fiber. reduction (compared initial 30) great help low-parameter macroscopic models.