Homogenisation of high-contrast brittle materials

Abstract

This paper is an overview on some recent results concerning the variational analysis of static fracture in the so-called high-contrast brittle composite materials. The paper is divided into two main parts. The first part is devoted to establish a compactness result for a general class of free-discontinuity functionals with degenerate (or high-contrast) integrands. The second part is focussed on some specific examples which show that the degeneracy of the integrands may lead to non-standard limit effects, which are specific to this high-contrast setting.

Keywords

• γ-convergence
• homogenisation
• free-discontinuity problems
• high-contrast materials
• porous materials
• brittle fracture