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

Abstract

We analyse the Γ-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.

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Keywords

non-local approximation, variational fracture, free discontinuity problems, functions of bounded deformations, Γ-convergence, deterministic and stochastic homogenisation

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