TY - JOUR

T1 - Enrichment of three-dimensional numerical manifold method with cover-based contact theory for static and dynamic mechanical response analysis

AU - Kang, Ge

AU - Ni, Ke song

AU - Zhuang, Xiaoying

AU - Rabczuk, Timon

AU - Ning, You jun

AU - Chen, Peng wan

N1 - Funding Information: The authors gratefully acknowledge financial support from the National Natural Science Foundation of China , Grants No. 12102048 ; China Postdoctoral Science Foundation Funded Project, Grants No. 2021M700429; and Beijing Natural Science Foundation, Grants No. L212017.

PY - 2023/10

Y1 - 2023/10

N2 - 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.

AB - 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.

KW - Cover-based contact

KW - Dynamic impact

KW - Program framework

KW - Slope instability

KW - Three-dimensional numerical manifold method

UR - http://www.scopus.com/inward/record.url?scp=85162127917&partnerID=8YFLogxK

U2 - 10.1016/j.apm.2023.05.021

DO - 10.1016/j.apm.2023.05.021

M3 - Article

AN - SCOPUS:85162127917

VL - 122

SP - 524

EP - 554

JO - Applied mathematical modelling

JF - Applied mathematical modelling

SN - 0307-904X

ER -