  We study the dynamics of visco-elastic materials coupled by a common cohesive
interface (or, equivalently, {two single domains separated by} a prescribed
cohesive crack) in the anti-plane setting. We consider a general class of
traction-separation laws featuring an activation threshold on the normal
stress, softening and elastic unloading. In strong form, the evolution is
described by a system of PDEs coupling momentum balance (in the bulk) with
transmission and Karush-Kuhn-Tucker conditions (on the interface). We provide a
detailed analysis of the system. We first prove existence of a weak solution,
employing a time discrete approach and a regularization of the initial data.
Then, we prove our main results: the energy identity and the existence of {
solutions} with acceleration in $L^\infty (0,T; L^2)$.
