Dal Maso, GianniToader, Rodica2022-01-112022-01-112022-01-11https://openscience.sissa.it/handle/1963/35436SISSA 01/2022/MATEWe introduce a new space of generalised functions with bound ed variation to prove the existence of a solution to a minimum problem that arises in the variational approach to fracture mechanics in elasto plastic materials. We study the fine properties of the functions belonging to this space and prove a compactness result. In order to use the Direct Method of the Calculus of Variations we prove a lower semicontinuity result for the functional occurring in this minimum problem. Moreover, we adapt a nontrivial argument introduced by Friedrich to show that every minimizing sequence can be modified to obtain a new minimizing sequence that satisfies the hypotheses of our compactness result.engeneralised functions with bounded variationfracture mechanicselastoplastic materialssemicontinuitycompact minimizing sequencePreprint