Homogenisation of high-contrast brittle materials

Caterina Ida Zeppieri; Caterina Ida Zeppieri

doi:10.3934/mine.2020009

Mathematics in Engineering

2020, Volume 2, Issue 1: 174-202. doi: 10.3934/mine.2020009

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Homogenisation of high-contrast brittle materials

Caterina Ida Zeppieri ^,

Angewandte Mathematik, WWU Münster. Einsteinstrasse 62, 48149 Münster, Germany

Received: 13 October 2019 Accepted: 26 November 2019 Published: 31 December 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.
- Γ-convergence,
- homogenisation,
- free-discontinuity problems,
- high-contrast materials,
- porous materials,
- brittle fracture
Citation: Caterina Ida Zeppieri. Homogenisation of high-contrast brittle materials[J]. Mathematics in Engineering, 2020, 2(1): 174-202. doi: 10.3934/mine.2020009

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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.

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