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Non-local approximation of free-discontinuity problems in linear elasticity and application to stochastic homogenisation (2212.13759v1)
Published 28 Dec 2022 in math.AP and math.FA
Abstract: We analyse the $\Gamma$-convergence of general non-local convolution type functionals with varying densities depending on the space variable and on the symmetrized gradient. The limit is a local free-discontinuity functional, where the bulk term can be completely characterized in terms of an asymptotic cell formula. From that, we can deduce an homogenisation result in the stochastic setting.