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Homogenisation of high-contrast brittle materials

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

This contribution is part of the Special Issue: Variational Models in Elasticity
Guest Editors: Lucia De Luca; Marcello Ponsiglione
Link: https://www.aimspress.com/newsinfo/1369.html

Special Issues: Variational Models in Elasticity

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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Keywords Γ-convergence; homogenisation; free-discontinuity problems; high-contrast materials; porous materials; brittle fracture

Citation: Caterina Ida Zeppieri. Homogenisation of high-contrast brittle materials. Mathematics in Engineering, 2020, 2(1): 174-202. doi: 10.3934/mine.2020009


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