Analysis of Crack Interaction Problem by the Numerical Manifold Method

2012 ◽  
Vol 446-449 ◽  
pp. 797-801 ◽  
Author(s):  
Hui Hua Zhang
Keyword(s):  
Numerical Manifold Method ◽  
Crack Interaction ◽  
Multiple Crack ◽  
Linear Elastic ◽  
Cover System ◽  
Crack Problems ◽  
Elastic Fracture ◽  
Numerical Manifold ◽  
Physical Boundary ◽  
Interaction Problem

Due to the use of mathematical cover system and physical cover system, the numerical manifold method (NMM) is very suitable for discontinuity problems, especially for multiple crack problems. In the NMM, the mathematical cover system is independent of the physical boundary, and in this case, fully regular mathematical elements can be used. In the present paper, the NMM, combined with the rectangular mathematical elements, is applied to solve crack interaction problems in the linear elastic fracture mechanics (LEFM). To verify the present method, a typical numerical example is investigated and the results agree well with the reference solutions.

Investigation of the Accuracy of the Numerical Manifold Method on n-Sided Regular Elements for Crack Problems

2012 ◽  
Vol 157-158 ◽  
pp. 1093-1096
Author(s):  
Hui Hua Zhang ◽  
Jia Xiang Yan
Keyword(s):  
Numerical Manifold Method ◽  
Quadrilateral Element ◽  
Regular Elements ◽  
Linear Elastic ◽  
Quadrilateral Elements ◽  
Crack Problems ◽  
Elastic Crack ◽  
Triangular Elements ◽  
Numerical Manifold ◽  
Better Than

The numerical manifold method (NMM) is a representative among different numerical methods for crack problems. Due to the independence of physical domain and the mathematical cover system, totally regular mathematical elements can be used in the NMM. In the present paper, the NMM is applied to solve 2-D linear elastic crack problems, together with the comparison study on the accuracy of n-sided regular mathematical elements, i.e., the triangular elements (n=3), the quadrilateral elements (n=4) and the hexagonal elements (n=6). Our numerical results show that among different elements, the regular hexagonal element is the best and the quadrilateral element is better than the triangular one.

On the Topology Update of the Numerical Manifold Method for Multiple Crack Propagation

2021 ◽  
pp. 2150030
Author(s):  
Jun He ◽  
Shuling Huang ◽  
Xiuli Ding ◽  
Yuting Zhang ◽  
Dengxue Liu
Keyword(s):  
Crack Initiation ◽  
Crack Propagation ◽  
Numerical Method ◽  
Crack Tip ◽  
Search Method ◽  
Numerical Manifold Method ◽  
Crack Initiation And Propagation ◽  
Multiple Crack ◽  
Initiation And Propagation ◽  
Numerical Manifold

Crack initiation and propagation are the two key issues of concern in the geotechnical engineering. In this study, the numerical manifold method (NMM) is applied to simulate crack propagation and the topology update of the NMM for multiple crack propagation is studied. The crack-tip asymptotic interpolation function is incorporated into the NMM to increase the accuracy of the crack-tip stress field. In addition, the Mohr-Coulomb criterion with tensile cut off is adopted to be the crack propagation criterion to judge the direction of crack initiation and propagation. Then a crack tip searching method is developed to automatically update the position of the crack tips. The inapplicability of the original loop search method in the NMM is also illustrated and a novel loop search method based on manifold elements is developed for physical loop updating. Moreover, methods for the manifold element updating and physical cover updating are provided. Based on the above study, the developed numerical method is capable to simulate multiple crack propagation. At last, typical rock rupture problems are numerically simulated to manifest the effectiveness of the developed numerical method.

scholarly journals Numerical Manifold Method for the Forced Vibration of Thin Plates during Bending

2014 ◽  
Vol 2014 ◽  
pp. 1-11
Author(s):  
Ding Jun ◽  
Chen Song ◽  
Wen Wei-Bin ◽  
Luo Shao-Ming ◽  
Huang Xia
Keyword(s):  
Dynamic Equation ◽  
Degrees Of Freedom ◽  
Solution Process ◽  
Thin Plates ◽  
Numerical Manifold Method ◽  
Bending Vibration ◽  
Linear Elastic ◽  
Spline Basis ◽  
Generalized Degrees Of Freedom ◽  
Numerical Manifold

A novel numerical manifold method was derived from the cubic B-spline basis function. The new interpolation function is characterized by high-order coordination at the boundary of a manifold element. The linear elastic-dynamic equation used to solve the bending vibration of thin plates was derived according to the principle of minimum instantaneous potential energy. The method for the initialization of the dynamic equation and its solution process were provided. Moreover, the analysis showed that the calculated stiffness matrix exhibited favorable performance. Numerical results showed that the generalized degrees of freedom were significantly fewer and that the calculation accuracy was higher for the manifold method than for the conventional finite element method.

ARBITRARY DISCONTINUITIES IN THE NUMERICAL MANIFOLD METHOD

2011 ◽  
Vol 08 (02) ◽  
pp. 315-347 ◽  
Author(s):  
XINMEI AN ◽  
GUOWEI MA ◽  
YONGCHANG CAI ◽  
HEHUA ZHU
Keyword(s):  
Solid Mechanics ◽  
Shear Bands ◽  
Partition Of Unity ◽  
Physical Problem ◽  
Numerical Manifold Method ◽  
Problem Domain ◽  
Material Interfaces ◽  
Cover System ◽  
Local Approximations ◽  
Numerical Manifold

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.

Evaluation of the SIF for the Multiple Crack Problems

2014 ◽  
Vol 638-640 ◽  
pp. 66-70
Author(s):  
Jun Yu Liu ◽  
Ping Zhang ◽  
Meng Han Liao ◽  
Bao Kuan Ning
Keyword(s):  
Stress Intensity ◽  
Orthotropic Material ◽  
High Accuracy ◽  
Mode I ◽  
Multiple Cracks ◽  
Intensity Factors ◽  
Multiple Crack ◽  
Crack Problems ◽  
Elastic Fracture ◽  
Scaled Boundary Finite Element

In elastic fracture mechanics the evaluation of the stress intensity factor (SIF) for multiple cracks problems is an important issue. In the paper the scaled boundary finite element method (SBFEM) is used to solve the SIF of mode I of multiple crack problems. The solving domain is partitioned into several sub-domains according to the number of cracks. Every sub-domain has its own scaling center. The characteristics of the SBFEM are preserved in every sub-domain. Numerical examples show that the SBFEM is effective with high accuracy in evaluating the multiple cracks fracture problems. It can be applied to treat the anisotropic materials conveniently. The stress intensity factors of unequal double-edged cracks in orthotropic material are provided.

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