Inserted: 27 dec 2022
Last Updated: 11 may 2023
Journal: Proceedings of the Royal Society Edinburgh Sect. A
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.