Problems involving the mechanical behavior of composite materials, in particular, the effects of imperfect bonding at the fiber - matrix boundary, are receiving an increasing amount of attention in the literature. One of the most widely used mechanical models in describing an imperfect bonding condition is based on the premise that the tractions are continuous but displacements are discontinuous across the material interface. More specifically, jumps in the displacement components are assumed to be proportional, in terms of spring - factor type interface parameters, to their respective interface traction components (i.e. an imperfect interface).

The concept, of imperfect interface has been developed mainly to account for various damages at the fiber - matrix interface, for example, imperfect adhesions, microcracks and voids. In particular, in many composite materials, the actual interface usually exhibits inhomogeneous imperfections. Despite this fact, little attention has been given to study this more general and physically more realistic scenario of inhomogeneous interface damage and imperfection.

The objective of this study is to develop a general method for the rigorous solution of a single isotropic circular inclusion embedded within an infinite homogeneous matrix in plane elasticity. The bonding at the inclusion - matrix interface is considered to be imperfect with the ass\imption that the interface imperfections are circnmferentially inhomogeneous (i.e. the extent of damage at the fiber - matrix interface varies pointwise along the interface itself). In fact, for the first time, this dissertation systematically studies two physically significant types of inhomogeneous imperfect interfaces:​ that being the inhomogeneous spring - layer interface and the inhomogeneous non-slip interface.

Complex variable techniques are used to obtain exact closed - form solutions for the stress fields associated with the inhomogeneous imperfect interfaces. The results from these calculations are compared to the results when the imperfections are circnmferentially homogeneous. These comparisons illustrate that replacing the inhomogeneous imperfect, interface by its homogeneous counterpart will lead to significant errors in the stresses and even in the calculation of the average stresses induced within the inclusion. Hence, the inhomogeneity of interface damage and imperfection has an essential effect on the stress field and average stresses within the inclusion.