Prediction of non-linear electromagnetoelastic properties for piezoelectric/piezomagnetic fibre reinforced composites

Abstract

Abstract

In this paper, the constitutive equations for the non-linear electromagnetothermoelastic properties of piezoelectric/piezomagnetic fibre reinforced composites (PEMFRC) materials are presented. These equations are derived on the basis of the thermodynamic principle using Gibbs free energy expanded into a Taylor series, emphasis being placed on quadratic non-linearities. The coupling effects between any two independent variables such as the preload and the electric and magnetic fields are included in these equations. Subsequently, the non-linear constitutive equations and isofield assumptions are employed to derive the closed-form formulae required for the present XY PEMFRC non-linear model and YX PEMFRC non-linear model. These two models can be used to predict the effective non-linear electromagnetoelastic properties of PEMFRC materials. Single- and double-loading conditions are introduced when deriving the required closed-form formulae for the effective non-linear electromagnetoelastic constants of PEMFRC materials. Using the present models, a parametric study is conducted for both LiNbO₃/CoFe₂O₄ and PZT-5H/CoFe₂O₄ PEMFRC materials. For the effective non-linear electromagnetoelastic properties along the fibre direction, the corresponding closed-form formulae proposed in this paper are consistent with those derived using the rule of mixtures. For the case of the piezoelectric fibre volume fraction V_f = 1 and the electric field H_n = 0, the constitutive equations proposed in this paper for the non-linear behaviour of PEMFRC materials are the same as those available in the literature for purely piezoelectric materials.