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

摘要

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 3D 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 formations are also discussed in this paper. Computational results obtained from the newly proposed scheme will be presented in a future paper.!19