Exact results for the local fields and the effective moduli of fibrous composites with thickly coated fibers

Fibrous composites that consist of thickly coated cylindrical fibers embedded in a matrix are considered. All of the three phases of the composite are assumed to be transversely isotropic. The study consists of three parts. In the first part exact relations are derived for the influence functions that connect applied uniform overall fields to the induced local fields in piezomagnetoelectric systems. We consider the case of coated fibers with a concentrically circular cross section, and contrast the derived relations with the more limited ones that could be obtained in the case of coated fibers with an arbitrary cross section. The derivation is based on the ability to create uniform strain, electric and magnetic fields in the composite by the application of certain mechanical, electric, magnetic and thermal loadings. In the second part of the study, exact microstructure-independent connections are derived for a subgroup of the effective moduli of the homogenized piezomagnetoelectric composite which exhibits overall transverse isotropy. In the third part of the study, the derived exact connections between the effective moduli are reduced to the setting of thermoelasticity; allowing the coating to be thin and highly stiff or highly compliant, we make contact with the exact connections derived lately in the literature for two-phase fibrous thermoelastic composites with surface-stress-type and spring-type imperfect interfaces.