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Abstract
In this paper we study the stochastic homogenisation of free-discontinuity functionals. Assuming stationarity for the random volume and surface integrands, we prove the existence of a homogenised random free-discontinuity functional, which is deterministic in the ergodic case. Moreover, by establishing a connection between the deterministic convergence of the functionals at any fixed realisation and the pointwise Subadditive Ergodic Theorem by Akcoglou and Krengel, we characterise the limit volume and surface integrands in terms of asymptotic cell formulas.
Original language | English |
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Pages (from-to) | 935–974 |
Number of pages | 40 |
Journal | Archive for Rational Mechanics and Analysis |
Volume | 233 |
Issue number | 2 |
Early online date | 28 Mar 2019 |
DOIs | |
Publication status | Published - 1 Aug 2019 |
ASJC Scopus subject areas
- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering
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Dive into the research topics of 'Stochastic homogenisation of free-discontinuity problems'. Together they form a unique fingerprint.Projects
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Dislocation Patterns Beyond Optimality
Scardia, L. (PI)
Engineering and Physical Sciences Research Council
1/10/16 → 30/09/18
Project: Research council