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The modeling of fracture problems within geometrically linear elasticity is often based on the space of generalized functions of bounded deformation GSBD p (Ω), p ∈ (1, ∞), their treatment is however hindered by the very low regularity of those functions and by the lack of appropriate density results. We construct here an approximation of GSBD p functions, for p ∈ (1, ∞), with functions which are Lipschitz continuous away from a jump set which is a finite union of closed subsets of C 1doi:10.1051/cocv/2018021 fatcat:ukvjrcrhmrdklablanh2uz4tuy