scholarly journals Application of the linearly independent numerical manifold method in modeling the complex crack problems

2016 ◽  
Author(s):  
Dongdong Xu ◽  
Xiaobing Wang ◽  
Yujie Sun
Keyword(s):  
Numerical Manifold Method ◽  
Linearly Independent ◽  
Crack Problems ◽  
Complex Crack ◽  
Numerical Manifold ◽  
Complex Crack Problems

Stress Intensity Factor for Interfacial Cracks in Bi-Materials Using Incompatible Numerical Manifold Method

2011 ◽  
Vol 327 ◽  
pp. 109-114
Author(s):  
Gao Feng Wei ◽  
Hong Fen Gao ◽  
Hai Hui Jiang
Keyword(s):  
Stress Intensity ◽  
Interfacial Crack ◽  
Partition Of Unity ◽  
Complex Stress ◽  
Element Approximation ◽  
Numerical Manifold Method ◽  
Displacement Fields ◽  
Interfacial Cracks ◽  
Crack Problems ◽  
Numerical Manifold

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.

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.

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.

scholarly journals Time-dependent deformation and failure of granite based on the virtual crack incorporated numerical manifold method

2021 ◽  
Vol 133 ◽  
pp. 104070
Author(s):  
Xian-yang Yu ◽  
Tao Xu ◽  
Michael J. Heap ◽  
Patrick Baud ◽  
Thierry Reuschlé ◽  
...  
Keyword(s):  
Time Dependent ◽  
Numerical Manifold Method ◽  
Deformation And Failure ◽  
Numerical Manifold
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