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In this paper we study the asymptotic behaviour of a family of randomfree-discontinuity energies $E_\varepsilon$ defined on a randomly perforateddomain, as $\varepsilon$ goes to zero. The functionals $E_\varepsilon$ modelthe energy associated to displacements of porous random materials that candevelop cracks. To gain compactness for sequences of displacements with boundedenergies, 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 randomperforations cannot come too close to one another. The limit energy is thenobtained in two steps. As a first step we apply a general result of stochasticconvergence of free-discontinuity functionals to a modified, coercive versionof $E_\varepsilon$. Then the effective volume and surface energy densities areidentified by means of a careful limit procedure.

Stochastic homogenisation of free-discontinuity functionals in random perforated domains