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We analyse the $\Gamma$-convergence of general non-local convolution typefunctionals with varying densities depending on the space variable and on thesymmetrized gradient. The limit is a local free-discontinuity functional, wherethe bulk term can be completely characterized in terms of an asymptotic cellformula. From that, we can deduce an homogenisation result in the stochasticsetting.

Non-local approximation of free-discontinuity problems in linear elasticity and application to stochastic homogenisation