A nonlinear Galerkin finite-element theory for modeling magnetostrictive smart structures

Materials such as Terfenol-D that are capable of giant magnetostriction are increasingly being used for sensing and actuation in active and adaptive structures. Designers of such adaptive structures need robust analytical and modeling tools for solving coupled electro-magneto - mechanical boundary value problems. While linear piezoelectric analysis is a standard feature of several general-purpose commercial finite-element codes, there are fewer tools for addressing the strong nonlinearities inherent in this class of problems. Electro-magneto - mechanical interactions manifest themselves not only through constitutive nonlinearities, but also through nonlinear terms in the governing equations. There have been recent works to deal with the constitutive nonlinearities in electrostriction and piezoelectricity, but a general computational framework for the comprehensive treatment of both these types of nonlinearity in magnetostrictives has not yet been developed. This paper presents a quasi-static variational principle and finite-element scheme to model the nonlinear interactions between mechanical and magnetic fields in magnetostrictive materials, incorporating both types of nonlinearity mentioned above. The basis of the finite-element scheme is presented here and applied to simulation of the actuation response of two actuator configurations. While the nonlinear scheme developed is of general three-dimensional nature, the application examples utilize material property data that pertain to the crystalline and geometrical symmetry of commercially produced Terfenol-D.