Accepted Paper

Inserted: 27 dec 2022
Last Updated: 11 may 2023

Journal: Proceedings of the Royal Society Edinburgh Sect. A
Pages: 27
Year: 2023

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.

Keywords: Non-local approximation, variational fracture, free discontinuity problems, deterministic and stochastic homogenisation, functions of bounded deformations, Gamma-convergence.

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