A Bridging Mechanism in the Homogenization of Brittle Composites with Soft Inclusions

Abstract

We provide a homogenization result for the energy-functional associated with a purely brittle composite whose microstructure is characterized by soft periodic inclusions embedded in a stiffer matrix. We show that the two constituents as above can be suitably arranged on a microscopic scale $\varepsilon$ to obtain, in the limit as $\varepsilon$ tends to zero, a homogeneous macroscopic energy-functional explicitly depending on the opening of the crack.