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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.
|Number of pages||40|
|Journal||Archive for Rational Mechanics and Analysis|
|Early online date||28 Mar 2019|
|Publication status||Published - 1 Aug 2019|
ASJC Scopus subject areas
- Mathematics (miscellaneous)
- Mechanical Engineering
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- 1 Finished
Dislocation Patterns Beyond Optimality
Engineering and Physical Sciences Research Council
1/10/16 → 30/09/18
Project: Research council