We present a generalized contact computation model for arbitrarily shaped polyhedra to simplify the contact analysis in discontinuous deformation analysis. A list of generalized contact constraints can be established for contacting polyhedra during contact detection. Each contact constraint contains information for 2 contact points, unique contact plane, and related contact modes (open, locked, or sliding). Computational aspects of the generalized contact model include identification of contact positions and contact modes, uniform penalty formulation of generalized contact constraint, and uniform updating of contact modes and contact planes in the open-close iteration. Compared with previous strategies, the generalized contact computation model has a simpler data structure and fewer memory requirements. Meanwhile, it simplifies the penalty formulation and facilitates the open-close iteration check while producing enough accuracy. Illustrative examples show the ability of the method to handle the full range of polyhedral shapes.

A fast direct search (FDS) algorithm is presented to increase the efficiency of contact detection for convex polygonal and polyhedral particles. All contact types are detected using only a small subset of these contact types: vertex-to-edge for polygons while vertex-to-face and edge-to-edge for polyhedra. First, an initial contact list is generated. Then in subsequent steps the contact list is updated by checking only local boundaries of the blocks and their separation. An exclusion algorithm is applied to avoid unnecessary examination for particles that are near but not-in-contact. The benchmark tests show that the FDS produces significant speed-up in various cases.