Inserted: 13 jul 2020
Last Updated: 13 jul 2020
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 $L^\infty(0,T;L^2)$.