A Constitutive Model for Magnetostrictive Materials - Theory and Finite Element Implementation

A 3D macroscopic constitutive law for hysteresis effects in magnetostrictive materials is presented and a finite element implementation is provided. The novel aspect of the thermodynamically consistent model is an additive decomposition of the magnetic and the strain field in a reversible and an irreversible part. Employing the irreversible magnetic field is advantageous for a finite element implementation, where the displacements and magnetic scalar potential are the nodal degrees of freedom. To consider the correlation between the irreversible magnetic field and the irreversible strains a one-to-one relation is assumed. The irreversible magnetic field determines as internal variable the movement of the center of a switching surface. This controls the motion of the domain walls during the magnetization process. The evolution of the internal variables is derived from the magnetic enthalpy function by the postulate of maximum dissipation, where the switching surface serves as constraint. The evolution equations are integrated using the backward Euler implicit integration scheme. The constitutive model is implemented in a 3D hexahedral element which provides an algorithmic consistent tangent stiffness matrix. A numerical example demonstrates the capability of the proposed model to reproduce the ferromagnetic hysteresis loops of a Terfenol-D sample. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)