Published Paper
Inserted: 29 nov 2019
Last Updated: 13 jul 2023
Journal: Math. Eng.
Volume: 2
Number: 1
Pages: 174--202
Year: 2020
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: Brittle fracture, $\Gamma$-convergence, Free-discontinuity problems, homogenisation, high-contrast materials, porous materials
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