Startseite Stochastic homogenisation of free-discontinuity functionals in randomly perforated domains
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Stochastic homogenisation of free-discontinuity functionals in randomly perforated domains

  • Xavier Pellet , Lucia Scardia EMAIL logo und Caterina Ida Zeppieri
Veröffentlicht/Copyright: 31. August 2023

Abstract

In this paper, we study the asymptotic behaviour of a family of random free-discontinuity energies E ε defined in a randomly perforated domain, as ε goes to zero. The functionals E ε model the energy associated to displacements of porous random materials that can develop cracks. To gain compactness for sequences of displacements with bounded energies, we need to overcome the lack of equi-coerciveness of the functionals. We do so by means of an extension result, under the assumption that the random perforations cannot come too close to one another. The limit energy is then obtained in two steps. As a first step, we apply a general result of stochastic convergence of free-discontinuity functionals to a modified, coercive version of E ε . Then the effective volume and surface energy densities are identified by means of a careful limit procedure.

MSC 2020: 49J45; 49Q20; 74Q05

Communicated by Irene Fonseca


Award Identifier / Grant number: ZE 1186/1-1

Award Identifier / Grant number: EP/V00204X/1

Award Identifier / Grant number: EP/V008897/1

Funding statement: The work of C. I. Zeppieri was supported by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) project number ZE 1186/1-1 and under the Germany Excellence Strategy EXC 2044-390685587, Mathematics Münster: Dynamics–Geometry–Structure. L. Scardia acknowledges support by the EPSRC under the grants EP/V00204X/1 and EP/V008897/1.

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Received: 2022-06-23
Accepted: 2023-07-03
Published Online: 2023-08-31
Published in Print: 2024-07-01

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Heruntergeladen am 22.9.2025 von https://www.degruyterbrill.com/document/doi/10.1515/acv-2022-0052/html
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