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

Abstract

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.

The contact problem of a circular rigid punch on piezomagnetic materials

“…Because of the lack and the uncertainty of the coefficients of Terfenol-D, we grouped the data from different sources (van der Burgt (1953), Dapino et al (1997), Kannan and Dasgupta (1997), Moffet et al (1991) and Ryu et al (2001)) in six examples, which all have the same elastic coefficients and differ in the piezomagnetic and permeability constants. In each example the uncoupled results are shown too, revealing the effect of the coupling phenomenon.…”

Multiphysics and Thermodynamic Formulations for Equilibrium and Non-equilibrium Interactions: Non-linear Finite Elements Applied to Multi-coupled Active Materials

“…An alternative 2-D staggered formulation was proposed in [61], assuming non-linearity only for the magnetic field. A fully coupled 3-D and dynamic FEM was formulated in [73]. The hysteretic behavior was modeled using thermodynamically consistent models in [84], [76], [85], [71].…”

“…5 and (66). The derivatives of D in the Maxwell stress expressions and in (73) are from its definitions 3×1 vectors. Due to the form of the first two equations (71), these derivatives are equal to those of P present in f P M (third of (71) Since it is useful in a hysteresis simulation of ferroelectric materials, it has been assumed that the properties ǫ, µ may vary with the corresponding field although not with time.…”

Coupled axisymmetric finite element model of a hydraulically amplified magnetostrictive actuator for active powertrain mounts

“…Benbouzid [10] presented a 2D bidirectionally coupled magnetostatic model with Terfenol-D constitutive behavior incorporated using surface splines. Kannan and Dasgupta [11] formulated a 2D magnetostatic model with bi-directionally coupled magnetomechanical relations, current induced magnetic fields and electromagnetic body forces. Zhou et al [12] developed a 2D dynamic finite element model of a unimorph actuator with one way magnetomechanical coupling.…”