A phenomenological constitutive model for magnetostrictive materials and ferroelectric ceramics

The contribution is concerned with a thermodynamic consistent constitutive model for magnetostrictive materials and ferroelectric ceramics. It captures the nonlinear phenomenological behavior which is described by hysteresis effects. Magnetostrictive alloys and ferroelectric ceramics belong to the multifunctional materials. In recent years these materials have become widely–used in actor and sensor applications. They characterize an inherent coupling between deformation and magnetic or electric field. Due to the similarities of the coupled differential equations a uniform approach is applied for both phenomena. The presented three–dimensional material model is thermodynamically motivated. It is based on the definition of a specific free energy function and a switching criterion. Furthermore an additive split of strain and the magnetic or electric field in a reversible and an irreversible part is suggested. The irreversible quantities serve as internal variables, which is analog to plasticity theory. A one–to–one–relation between the two internal variables provides conservation of volume for the irreversible strains. The presented material model can approximate the ferromagnetic or ferroelectric hysteresis curve and the related butterfly hysteresis. Furthermore an extended approach for ferrimagnetic behavior, which occurs in magnetostrictive materials, is presented. Some numerical simulations demonstrate the capability of the presented model. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)