Implementation of three-dimensional contact algorithm in numerical manifold method for the structural impact simulation

Structural impact often accompanies large amounts of contacts and leads to complex mechanical phenomena. In solid mechanics, the numerical manifold method (NMM) is proposed to address problems featuring continuous-discontinuous transitions by utilizing a dual coverage system encompassing both mathematical and physical covers. In the present work, a penalty contact algorithm for 3DNMM based on cover-based contact theory is programmed and applied to impact mechanics problems. The accuracy of the developed contact algorithm is firstly calibrated through free-falling blocks and collision blocks. The influence of contact parameters on contact convergence is systematically studied, and three preliminary criteria for how to set contact parameters are provided. The effectiveness of the contact algorithm is verified by conserving system momentum during block collisions. Subsequently, the contact algorithm is applied to Taylor rod and car-streetlight impact simulation, further confirming its effectiveness in modeling high-speed collisions, large displacements, and large deformations of structures. By comparing the 3DNMM results with those from Abaqus, the contact algorithm developed here performs exceptionally well in solving collision problems and produces results consistent with commercial software. The research results in the present work verify the applicability and accuracy of the proposed contact algorithm in solving structural dynamic impact problems. The present work also provides guidance for contact parameter setting in impact problems.