Development of three-dimensional numerical manifold method with cover-based contact theory

Numerical manifold method (NMM) is a typical continuous-discontinuous coupling method. It unifies the continuous and discontinuous theories in the same program framework. In the present work, based on the cover-based contact theory, the specific solution of contact covers under five different positional relationships is given in detail, and the contact judgement conditions and contact cover solution formulas under each positional relationship are proposed. By converting the contact into the relationship between reference point a₀ and the outer boundary of entrance block E (A, B), the contact algorithm between 3D blocks is implemented and programmed. The developed code is initially calibrated by two simple models, and its correctness is quantitatively verified by the motion of the inclined sliding model. Finally, it is applied to more complex structural deformation and dynamic collision problems. The 3D-NMM developed in the present work can be used for structural kinematics, structural deformation and dynamic collision problems, and has broad application prospects in the field of structural mechanics.