A Phenomenological Constitutive Model for Ferroelectric Ceramics and Ferromagnetic Materials

Abstract

This Contribution is concerned with a macroscopic nonlinear constitutive law for ferromagnetic alloys and ferroelectric ceramics. It accounts for the hysteresis effects which occur in the considered class of materials. The uniaxial model is thermodynamically motivated and based on the definition of a specific free energy function and a switching criterion. The strains and the magnetic or electric field strength are additively split into a reversible and an irreversible part. Analogous to plasticity, the irreversible quantities serve as internal variables. A one-to-one-relation between the two internal variables provides conservation of volume during polarization or magnetization process. The material model is able to approximate the ferromagnetic or ferroelectric hysteresis curves and the related butterfly hysteresis curves. An extended approach for ferrimagnetic behavior which occurs in ferromagnetic materials is presented. A main aspect of the constitutive model is its numerical treatment. The model is embedded in a three dimensional finite element formulation. The usage of the irreversible field strength permits the application of algorithms known from the treatment of computational inelasticity.