  In this paper we investigate the effect of a Signorini-type interface
condition on the asymptotic behaviour, as $\varepsilon$ tends to zero, of
problems posed in $\varepsilon$-periodic domains with inclusions. The
Signorini-type condition is expressed in terms of two complementary equalities
involving the jump of the solution on the interface and its conormal derivative
via a parameter $\gamma$. Our problem models the heat exchange in a medium
hosting an $\varepsilon$-periodic array of thermal conductors in presence of
impurities distributed on some regions of the interface. Different limit
problems are obtained according to different values of $\gamma$.
