Analysis of Functionally Graded Magneto-Electro-Elastic Composites Using Hybrid/Mixed Finite Elements and Node-Wise Material Properties

A new class of hybrid/mixed finite elements, denoted “HMFEM-C”, has been developed for modeling magneto-electro-elastic (MEE) materials. These elements are based on assuming independent strain-fields, electric and magnetic fields, and collocating them with the strain-fields, electric and magnetic fields derived from the primal variables (mechanical displacements, electric and magnetic potentials) at some cleverly chosen points inside each element. The newly developed elements show significantly higher accuracy than the primal elements for the electric, magnetic as well as the mechanical variables. HMFEM-C is invariant through the use of the element-fixed local orthogonal base vectors, and is stable since it is not derived from a multi-field variational principle; hence it completely avoids LBB conditions that govern the stability of hybrid/mixed elements. In this paper, node-wise material properties are used in order to better simulate the spatial material grading of the functionally graded materials (FGM). A computer code was developed, validated and used to calculate the three magnetoelectric (ME) voltage coefficients for piezoelectric-piezomagnetic (PE-PM) composites, namely, the out-of-plane, transverse and in-plane ME voltage coefficients. The effects of the piezoelectric phase volume fraction as well as the mechanical boundary conditions and loadings on the ME voltage coefficients are investigated. Also, the effects of grading functions in PE-PM composites with functionally graded layers, as well as single-layered functionally graded magneto-electro-elastic materials, on the three ME voltage coefficients are presented.