A GENERALIZED AND EFFICIENT METHOD FOR FINITE COVER GENERATION IN THE NUMERICAL MANIFOLD METHOD

2013 ◽  
Vol 10 (05) ◽  
pp. 1350028 ◽  
Author(s):  
YONGCHANG CAI ◽  
XIAOYING ZHUANG ◽  
HEHUA ZHU

The numerical manifold method (NMM) based on the concept of finite covers and the partition of unity (PU) provides a unified framework to analyze continuum and discontinuum without changing predefined mesh in a discretized way. The NMM has been applied in the modeling of fluid structure interaction as well as in rock mechanics including the analysis of block system, jointed rock and fractured body, showing particular advantages over other PU based methods. Unlike other PU methods, the degrees of freedoms in the NMM are associated with the physical covers, rather than the nodes, which allow it to be naturally adapted to the changing geometries in analyzing complex discontinuum such as multiple intersecting cracks and branched cracks. Despite these recent advances, there is no publication available to date describing the physical cover generation of the NMM in a systematic way or giving a general principle of cover numbering, which has practically limited a wider application of the NMM. To address this issue, a generalized cover generation method is developed in the paper based on the concept of "detached physical cover" where manifold elements belonging to the same mathematical cover and having common mathematical edges are collected to form a new detached physical cover. The present method has a concise formulation for implementation, and is effective and generally applicable for dealing with interfaces, inclusions or discontinuities of complex geometry. A test example is performed showing the correctness, robustness and efficiency of the proposed method.

2011 ◽  
Vol 08 (02) ◽  
pp. 315-347 ◽  
Author(s):  
XINMEI AN ◽  
GUOWEI MA ◽  
YONGCHANG CAI ◽  
HEHUA ZHU

An overview of modeling arbitrary discontinuities within the numerical manifold method (NMM) framework is presented. The NMM employs a dual cover system, namely mathematical covers (MCs) and physical covers (PCs), to describe a physical problem. MCs are constructed totally independent of geometries of the problem domain, over which a partition of unity is defined. PCs are the intersections of MCs and the problem domain, over which local approximations with unknowns to be determined are defined. With such a dual cover system, arbitrary discontinuities involving jumps, kinks, singularities, and other nonsmooth features can be modeled in a convenient manner by constructing special PCs and designing tailored local approximations. Several typical discontinuities in solid mechanics are discussed. Among them are the simulations of material boundaries, voids, brittle cracks, cohesive cracks, material interfaces, interface cracks, dislocations, shear bands, high gradient zones, etc.


2022 ◽  
Vol 9 ◽  
Author(s):  
Xing-Chao Lin ◽  
Qiang Zhang ◽  
Jiufeng Jin ◽  
Guangming Chen ◽  
Jin-Hang Li

On the basis of the numerical manifold method, this work introduces the concept of stress intensity factor at the crack tip in fracture mechanics and proposes the utilisation of artificial joint technology to ensure the accuracy of joint geometric dimensions in the element generation of the numerical manifold method. The contour integral method is used to solve the stress intensity factor at the joint tip, and the failure criterion and direction of crack propagation at the joint tip are determined. Element reconstruction and crack tracking are implemented in crack propagation, and a simulation programme of the entire process of deformation, failure, propagation and coalescence of jointed rock masses is developed. The rationality of the proposed method is verified by performing the typical uniaxial compression test and direct shear test.


2011 ◽  
Vol 327 ◽  
pp. 109-114
Author(s):  
Gao Feng Wei ◽  
Hong Fen Gao ◽  
Hai Hui Jiang

Incompatible numerical manifold method (INMM) uses interpolation functions based on the concept of partition of unity, and considers the asymptotic solution and the discontinuity of displacement. This paper describes the application of INMM to bi-material interfacial crack. The two dimensional near-tip asymptotic displacement functions are added to the trial function approximation. This enables the domain to be modeled by manifold elements without explicitly meshing the crack surfaces. The crack-tip enrichment functions are chosen as those that span the asymptotic displacement fields for an interfacial crack. The INMM facilitates the incorporation of the oscillatory nature of the singularity within a conforming manifold element approximation. The complex stress intensity factors for bi-material interfacial cracks are numerically evaluated. Good agreement between the numerical results and the analytical solutions for benchmark interfacial crack problems is realized.


2018 ◽  
Vol 35 (7) ◽  
pp. 2429-2458
Author(s):  
Yuanqiang Chen ◽  
H. Zheng ◽  
Wei Li ◽  
Shan Lin

Purpose The purpose of this paper is to propose a new three-node triangular element in the framework of the numerical manifold method (NMM), which is designated by Trig3-MLScns. Design/methodology/approach The formulation uses the improved parametric shape functions of classical triangular elements (Trig3-0) to construct the partition of unity (PU) and the moving least square (MLS) interpolation method to construct the local approximation function. Findings Compared with the classical three-node element (Trig3-0), the Trig3-MLScns element has a higher order of approximations, much better accuracy and continuous nodal stress. Moreover, the linear dependence problem associated with many PU-based methods with high-order approximations is eliminated in the present element. A number of numerical examples indicate the high accuracy and robustness of the Trig3-MLScns element. Originality/value The proposed element inherits the individual merits of the NMM and the MLS.


2015 ◽  
Vol 61 ◽  
pp. 153-171 ◽  
Author(s):  
Lei He ◽  
Xinmei An ◽  
Xiaoying Liu ◽  
Zhiye Zhao ◽  
Shengqi Yang

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