Submitted Paper

Inserted: 28 jan 2026
Last Updated: 28 jan 2026

Year: 2026

Abstract:

We study the $Γ$-convergence of sequences of free discontinuity functionals with linear growth defined in the space ${\rm BD}$ of functions with bounded deformation. We prove a compactness result with respect to $Γ$-convergence and outline the main properties of the $Γ$-limits, which lead to an integral representation result. The corresponding integrands are obtained by taking limits of suitable minimisation problems on small cubes. These results are then used to study the deterministic and stochastic homogenisation problem for a large class of free discontinuity functionals defined in ${\rm BD}$.