Homogenization of linearized elasticity in a two-component medium with slip displacement conditions

Abstract We consider the periodic homogenization of the linearized elasticity problem with slip displacement conditions for a two-scale composite of two solids. Such interface jumps in displacement arise e.g. in contact problems with imperfect bonding. Motivated by applications in carbon-fibre-reinforced concretes, we aim to investigate the impact of the length of the carbon fibres on the effective properties, which is why we assume one of the materials to be connected, whereas the other one is either connected or disconnected. The method of periodic unfolding is applied, deriving some new compactness results in passing, to determine the macroscopic limit problems rigorously, which show significant differences for the two cases.