An extrinsic cohesive zone model for mixed mode I and mode II fracture that encompasses contact and Coulomb friction is developed in the framework of non-smooth mechanics. The model is extended to include the effects of dynamics with impact and sliding, and is discretised in time so that it can be written as a linear complementarity problem (LCP). The LCP is proved to have a solution, subject to a condition on the size of the time-step. Finally, we study the behaviour of the LCP system numerically, by observing the response of a simple test geometry to rapid loading, and observe the numerical method reproduces analytically predicted and experimentally observed behaviours, without requiring impracticably small time-steps.