Role of coupling terms in constitutive relationships of magnetostrictive materials

Abstract

Anhysteretic, coupled, linear and nonlinear constitutive relationship for magnetostrictive material is studied in this paper. Constitutive relationships of magnetostrictive material are represented through two equations, one for actuation and other for sensing, both of which are coupled through magneto-mechanical coefficient. Coupled model is studied without assuming any explicit direct relationship with magnetic field. In linear-coupled model, which is assumed to preserve the magnetic flux line continuity, the elastic modulus, the permeability and magneto-elastic constant are assumed as constant. In nonlinear-coupled model, the nonlinearity is decoupled and solved separately for the magnetic domain and mechanical domain using two nonlinear curves, namely the stress vs. strain curve and magnetic flux density vs. magnetic field curve. This is done by two different methods. In the first, the magnetic flux density is computed iteratively, while in the second, artificial neural network is used, where in the trained network will give the necessary strain and magnetic flux density for a given magnetic field and stress level. The effect of non-linearity is demonstrated on a magnetostrictive rod.