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.

A variational statement of the nonlinear boundary value problem of magneto-mechanical interactions in magnetostrictive materials is presented. Some of the complexities arising out of the nature of these interactions are pointed out. A finite element code developed on the basis of a linearized version of the above variational statement is used to model the behavior of an idealized magnetostrictive actuator. The strong influence of coupling constants on the induced magnetic field is demonstrated through our coupled finite element analysis. Errors that are possible in uncoupled analyses are illustrated and the need for fully coupled analyses of general two or three dimensional actuator configurations is brought out.

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.

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FE Robustness: comparing sheet metal forming variation and finite element models AIP Conf.Abstract. Stamping processes are routinely validated and optimized using simulation tools. Process optimization, carried out manually or automatically, establishes a single set of conditions capable of producing a good part, without any consideration of the robustness of the stamping process. This paper presents a new approach to virtual validation of stamping processes that simultaneously, and in a natural fashion, also provides valuable feedback on process robustness over the entire production lifetime of a given part. Uncontrollable variabilities in material and process conditions -as they actually occur under production conditions -are taken into account in a true "simulation" of stamping processes, providing quantitative measures of robustness as well as a clear picture of sensitive dependencies between critical panel quality attributes and controllable process conditions. The latter is important to identifying meaningful countermeasure options available to influence and improve production quality, and to minimize overall production cost.