A novel methodology consisting of three hierarchical levels is proposed for the detection phase of contact mechanics simulations. The top level of the hierarchy uses kinematic information from the objects involved in the simulation to determine approximate collision times. These instants then determine when the engine resumes operation for further detection. By using bounding volume hierarchies, the second level of detection precludes contact by computing simple exclusion tests on bounding volumes of increasing tightness. When contact cannot be ruled out by using simple tests, the final level of detection comes into effect by using thorough checks on finite element primitives. To that purpose, a robust optimization-based formulation that does not rely on orthogonal projections is outlined. The detection framework can be used to predict the exact collision time among finite element discretizations. The performance of the proposed methodology is investigated with a set of examples.