Exact connections between the effective elastic moduli of fibre-reinforced composites with general imperfect interfaces

Transversely isotropic composites consisting of an elastic matrix reinforced by unidirectional elastic fibres of circular cross-section are studied. The displacement and traction vectors at the interface between a fibre and the matrix are assumed to be simultaneously discontinuous and governed by a general isotropic imperfect interface model. It is first proved that piecewise uniform strain fields transversely isotropic about the fibre direction can be generated inside such a composite. The existence of these piecewise uniform strain fields is then exploited so as to derive two exact connections between the five effective elastic moduli of the composite. These two exact connections are finally shown to cover as particulars cases all the relevant results reported in the literature for fibre-reinforced composites.