A Finite Element Procedure For Nonlinear Magnetoelectric Coupling Problems And Its Application

Magnetoelectric effect(ME)or its converse effect that is known as product tensor property in composites,which results from the mechanical strain interaction between piezoelectric and piezomagnetic phase,though neither of them has the ME.The ME response in composites can be several orders magnitude higher than that in those single phase multiferroic materials available so far,which makes it applicable in practice.As a new kind of smart material,ME composites provide great opportunities for potential application in devices such as Micro-Electro-Mechanical-System,magnetoelectric transducers,information storage,and microwave devices.Due to the strong nonlinear characteristic of constitute relations of ferroelectric and ferromagnetic phases which combine the composite,the response of ME composites under the electric or magnetic field should be nonlinear,the material properties usually depend on stress,bias magnetic field,and temperature nonlinearly.It is necessary to set up the fully coupled mechanical-magnetic-electric multi-field nonlinear analysis of ME composites.In this paper,an explicit-incremental Finite-Element-Method(FEM)which used to calculate the multi-field coupling of ME composite was proposed,and involved the following works:(1)First,based on the linear constitution of piezomagnetic phase and the system equivalent equation,using an explicit expression to account for the nonlinear relation between piezomagnetic coefficient(or magnetic permeability)and stress,bias magnetic field,an explicit-incremental FEM was given.And implementation of the method was applied using the subroutine USDFLD from software ABAQUS.The numerical result of quasi-static response in Giant Magnetostrictive Materials(GMM)validated the robustness,effectiveness,convergence.(2)By using the explicit-incremental FEM to simulate the dynamic response of Magnetostrctive Actuator under the stimulation of alternating magnetic field with presence of stress and bias field,the output of force,displacement,and frequency characteristic was presented.At the same time dependence of material damping,ratio of amplitude of alternating magnetic field and bias field on coupling response was also taken into account.The results gained by using linear and explicit-incremental FEM respectively demonstrated that large deviation would occur on the condition that the ratio of amplitude of alternating magnetic field and bias field is big.(3)By using the explicit-incremental FEM to calculate the quasi-static and dynamic response of ME laminated composites,the influence of the magnetic and electric polarized direction,stiffness of interface,stress levels,and boundary conditions on the ME coefficient was analyzed.The numerical results showed that stress and magnetic field has significant influence on nonlinear coupling,and different load order would get different results.