  A lower semicontinuity result and a relaxation formula for free discontinuity
functionals with non-standard growth in the bulk energy are provided. Our
analysis is based on a non-trivial adaptation of the blow-up (Ambrosio 1994)
and of the global method for relaxation (Bouchitt\'e et al. 1998) to the
setting of generalized special function of bounded variation with Orlicz
growth. Key tools developed in this paper are an integral representation result
and a Poincar\'e inequality under non-standard growth.
