Generalization of the micromechanics multi-coating approach to coupled fields composite materials with eigenfields: Effective properties

A generalization of the micromechanics multi-coating scheme to coupled fields composite materials with eigenfields is presented in this work. The key ingredients required to succeed in this generalization are: (i) the use of pseudo-tensors to represent the properties of the composite material phases and the proper handling of the induced pseudo-tensorial relations, (ii) the introduction of eigenfields, and (iii) the derivation of the interfacial operators for coupled fields material with eigenfields to account for the jump of the gradient of the potential fields. The model is used to compute the thermo-magneto-electro-elastic effective properties of piezomagnetic composite material and the results agree well with numerical predictions reported in the literature. This general framework may be useful to compute the effective properties of composite materials containing functionally graded inhomogeneities or composite materials with inhomogeneous interphases. The use of this micromechanics scheme for optimal design of such smart composite materials will be discussed elsewhere.