Enrichment of three-dimensional numerical manifold method with cover-based contact theory for static and dynamic mechanical response analysis

Based on the mathematical grid of 4-node tetrahedral finite element form, the dual cover system, weight function and displacement function of three-dimensional numerical manifold method (3D-NMM) are proposed. The derivation process of element stiffness matrix, inertial force matrix, loading point matrix, etc. are systematically demonstrated in the present work. Based on the cover-based contact theory, the contact detection algorithm among discrete 3D blocks is realized, and the 3D manifold framework is programmed. The accuracy of the developed code is firstly calibrated through two continuum deformation analysis: cantilever beam bending model and axial tensile model of thin plate with circular hole. Then it is applied to three complex discontinuous instability simulation (SHPB, brick wall structure and cliff slope) to verify the effectiveness and accuracy of the proposed contact algorithm. The classic Steven low velocity impact process is also simulated, and the deformation and failure of polymer bonded composites (PBC) are predicted, which further verifies the feasibility and robustness of the developed code in dealing with dynamic impact problems.