An Investigation Of Effective Modulus On The Electro-magneto-elastic Composites Containing Mutil-coated Fibers

Multi-coating electro-magneto-elastic structure is a typical smart composite, therange in the basic unit cell and the variety of material properties of strength phase material(fiber) and multi-coating structure have a significant impact on local electro-magneto-elastic field and macroscopic effective properties. Therefore, the study of the Multi-coating electro-magneto-elastic composites has a very important significance. This paperdedicate to the research on the stress of local field and macroscopic effective propertieswith material microstructure parameters (especially the Multi-coating and fiber) of theelectro-magneto-elastic composites with doubly periodic Multi-coating fibers under anti-plane shear coupled with inplane electro-magnetic load.By use of the concept of Eshelby’s equivalent inclusion, a problem of doubly-periodic generalized eigenstains for electro-magneto-elastic materials, which is equivalentto the heterogeneous materials problem (doubly periodic Multi-coating electro-magneto-elastic fiber composites), is constructed by the introduction of non-uniform generalizedeigenstains in the doubly-periodic cylindrical regions of a uniform solid whose propertiesare the same as the matrix properties of originally heterogeneous materials, equivalentequations are established between non-homogeneous electro-magneto-elastic compositematerials and homogeneous electro-magneto-elastic composite materials with generalizedeigenstains. By using Laurent series expansion and the results of doubly quasi-periodicRiemann boundary value problem, combined with continuity conditions of generalizedstress and compatibility conditions of generalized displacement, the electro-magneto-elastic field is obtained in series form. The solutions can be used to analyze the electro-magneto-elastic field within unit cell, and predict the effective electro-magneto-elasticmodulus of the electro-magneto-elastic composite materials.Programming by using symbolic computation software Mathematica, interfacialstress and the electro-magneto-elastic effective modulus are calculated. Comparisons withexisting results demonstrate the accuracy of the present method. Numerical analyses showthat the ranges in the basic unit cell and the variety of material properties of fiber andmulti-coating structure have a significant impact on local electro-magneto-elastic field and macroscopic effective properties. Conclusions obtained from this paper are useful compl-ements to the study of the composites.