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

authored by: Ge Kang, Ke song Ni, Xiaoying Zhuang, Timon Rabczuk, You jun Ning, Peng wan Chen
Abstract: 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.
Organisation(s): Institute of Photonics
External Organisation(s): Beijing Institute of Technology
China Aerodynamics Research and Development Center
Tongji University
Bauhaus-Universität Weimar
Southwest Petroleum University China
Type: Article
Journal: Applied mathematical modelling
Volume: 122
Pages: 524-554
No. of pages: 31
ISSN: 0307-904X
Publication date: 10.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Modelling and Simulation, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.apm.2023.05.021 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{295caf3bd5564415965aa8108dd9798b,
title = "Enrichment of three-dimensional numerical manifold method with cover-based contact theory for static and dynamic mechanical response analysis",
abstract = "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.",
keywords = "Cover-based contact, Dynamic impact, Program framework, Slope instability, Three-dimensional numerical manifold method",
author = "Ge Kang and Ni, {Ke song} and Xiaoying Zhuang and Timon Rabczuk and Ning, {You jun} and Chen, {Peng wan}",
note = "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. ",
year = "2023",
month = oct,
doi = "10.1016/j.apm.2023.05.021",
language = "English",
volume = "122",
pages = "524--554",
journal = "Applied mathematical modelling",
issn = "0307-904X",
publisher = "Elsevier Inc.",
}

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