Calculus of Variations and Geometric Measure Theory

C. I. Zeppieri

Homogenisation of high-contrast brittle materials

created by zeppieri1 on 29 Nov 2019


Accepted Paper

Inserted: 29 nov 2019
Last Updated: 29 nov 2019

Journal: Mathematics in Engineering
Year: 2019


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: Brittle fracture, $\Gamma$-convergence, Free-discontinuity problems, homogenisation, high-contrast materials, porous materials