A framework to solve fast dynamic problems involving a non-smooth interface behavior with contact and decohesion is under concern. In previous works, unilateral contact and impact have been studied in explicit dynamics but no damage nor cohesion were involved. Combining a contact problem and a thermodynamically motivated damage model within the so-called CD-Lagrange explicit dynamics scheme is the aim of this work. To do so, RCCM macroscopic model of adhesion with damage of the interface is studied. The thermodynamic motivation of the model and the use of a symplectic explicit scheme creates a framework based on good energy balance. In this work, illustrations and feasibility are shown for small displacement problems.