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We study stochastic homogenisation of free-discontinuity surface functionalsdefined on piecewise rigid functions which arise in the study of fracture inbrittle materials. In particular, under standard assumptions on the density, weshow that there exists a $\Gamma$-limit almost surely and that it can berepresented by a surface integral. In addition, the effective density can becharacterised via a suitable cell formula and is deterministic under anergodicity assumption. We also show via $\Gamma$-convergence that thehomogenised functional defined on piecewise rigid functions can be recoveredfrom a Griffith-type model by passing to the limit of vanishing elasticdeformations.

Stochastic homogenisation for functionals defined on asymptotically piecewise rigid functions