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.
ASJC Scopus subject areas
- Mathematics (miscellaneous)
- Mechanical Engineering
Cagnetti, F., Dal Maso, G., Scardia, L., & Zeppieri, C. I. (2019). Stochastic homogenisation of free-discontinuity problems. Archive for Rational Mechanics and Analysis, 233(2), 935–974. https://doi.org/10.1007/s00205-019-01372-x