<title>New magnetic-field-based weighted-residual quasi-static finite element scheme for modeling bulk magnetostriction</title>

Abstract

Deformation control of smart structures and damage detection in smart composites by magneto-mechanical tagging are just a few of the increasing number of applications of polydomain, polycrystalline magnetostrictive materials that are currently being researched. Robust computational models of bulk magnetostriction will be of great assistance to designers of smart structures for optimization of performance and development of control strategies. This paper discusses the limitations of existing tools, and reports on the work of the authors in developing a three dimensional nonlinear continuum finite element scheme for magnetostrictive structures, based on an appropriate Galerkin variational principle and incremental constitutive relations. The unique problems posed by the form of the equations governing magneto-mechanical interactions as well as their impact on the proper choice of variational and finite element discretization schemes are discussed. An adaptation of vectorial edge functions for interpolation of magnetic field in hexahedral elements is outlined. The differences between the proposed finite element scheme and available formulations are also discussed in this paper. Computational results obtained from the newly proposed scheme will be presented in a future paper.

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

“…Further study, particularly of sensing applications and of more complex actuator/sensor and structural configurations that promote large magnetic field gradients, is needed to identify and to understand the circumstances where differences could be significant. A study of simple sensing applications is now underway and will be reported upon in a later paper [10].…”

“…Body couples are included only in an implicit sense (discussion in section 2). A modification of the present theory that also takes these body couples into account is currently underway and will be reported on elsewhere [10]. The inclusion of magnetic body forces and body couples adds a new complexity to the formulation and necessitates additional computation to establish Maxwell stresses and the magnetic contributions to Cauchy stresses.…”

“…Further, the contributions of the antisymmetric part of Cauchy stress σ [ij ] and of rotations ω ij to the energy of the magnetoelastic solid are ignored here, as an approximation. These contributions will be explored in a future paper [10].…”