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

We analyse the G-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.

Automated summary

We investigated the G-convergence of general non-local convolution type functionals with varying densities dependent on the space variable and symmetrized gradient. The limit is a local free-discontinuity functional, characterized by an asymptotic cell formula for the bulk term. This leads to a homogenization result in the stochastic setting.