We analyze the Gamma-convergence of sequences of free-discontinuity functionals arising in the modeling of linear elastic solids with surface discontinuities, including phenomena as fracture, damage, or material voids. We prove compactness with respect to Gamma-convergence and represent the Gamma-limit in an integral form defined on the space of generalized special functions of bounded deformation (GSBD^p). We identify the integrands in terms of asymptotic cell formulas and prove a non-interaction property between bulk and surface contributions. In particular, our techniques allow to characterize relaxations of functionals on GSBD^p, and cover the classical case of periodic homogenization. Joint work with Matteo Perugini and Francesco Solombrino.