Homogenisation of vectorial free-discontinuity functionals with cohesive type surface terms

The results on $\mathrm{\Gamma }$-limits of sequences of free-discontinuity functionals with bounded cohesive surface terms are extended to the case of vector-valued functions. In this framework, we prove an integral representation result for the $\mathrm{\Gamma }$-limit, which is then used to study deterministic and stochastic homogenisation problems for this type of functionals.