This paper deals with damage localized on interfaces between the fibres and the matrix in composite materials, which are often regarded as macro-scopically homogeneous solids with certain effective properties derived from information on phase properties and local geometry. This viewpoint is justified only for loading conditions that do not impair the integrity of the microstructure. In this contribution we start with a survey of models describing the transfer of elastic stresses from the matrix to the fiber. Then, the contact problems are formulated in a manner leading to a very fast Uzawa's algorithm (cf. (4)) for their solving. Debonding processes in the interfacial zone are illustrated by an example and discussed from the stability standpoint. A simple solution of the overall response of a damaged composite system is based on the TFA model. Finally, an approximative formula describes the size effect.
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