Model-free data-driven computational mechanics (DDCM) [Kirchdoerfer & Ortiz, 2016] is a new paradigm for simulations in solid mechanics. As in the classical method, the boundary value problem is formulated with physics-based PDEs such as the balance of momentum and compatibility equations, which together define the admissibility conditions. However, DDCM does not use phenomenological constitutive laws to close the problem. Instead it uses directly data on material response, originating from either exper- iments or micro-physical simulations, in order to reduce constitutive modeling bias. The problem is solved in phase space where the admissibility conditions define a manifold and the material behavior is represented by a set of material points. DDCM aims to find the admissible state that best matches the material points. The DDCM framework has been formulated and used to solve problems in statics and dynamics, for multi- scale modeling, and has been coupled to classical solvers such as the finite element method to run simulations more efficiently. In this work, DDCM is applied to a frictional interface. Data-driven finite-thickness cohesive elements are sandwiched between two linear elastic bodies solved with FEM. The material response database is populated from micro-physical discrete simulations of two contacting rough surfaces sliding against each other. Through interactions between the interface, the bulk and the boundary conditions, complex behaviors such as dynamically propagating slip fronts arise.