Solution of stress intensity factors of multiple cracks in plane elasticity with eigen COD formulation of boundary integral equation

Guo, Zhansheng; Ma, Hang

doi:10.1007/s11741-011-0716-1

Cited by 7 publications

(3 citation statements)

References 22 publications

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“…It can be known that the computed results of the proposed approach are quite agreed with Chen and Chong [8]. The accuracy has been greatly improved compared with the author's previous work [9] as well.…”

Section: A Plate With Two Symmetrically Inclined Crackssupporting

confidence: 67%

Solution of stress intensity factors for 2-D multiple crack problems by the fast multipole boundary element method

Guo¹,

Liu²,

2013

Boundary Elements and Other Mesh Reduction Methods XXXVI

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The fast multipole boundary element method (BEM) based on both singular and hypersingular boundary integral equations (BIEs) for 2-D elasticity is applied to study 2-D multiple crack problems in this work. For multiple crack problems, the degrees of freedom (DOFs) and the size of the matrices can increase quickly as the number of cracks increases, which prohibits the use of the conventional BEM. In this study, constant line elements are used to discretize the crack surfaces and other boundaries. There is no use of the special quarter-point elements at crack tips in the present approach. To account for the need for accuracy, a relatively larger number of constant elements is required on the surfaces of cracks. By applying the fast multipole BEM, the increased computational work can be dealt with readily on desktop PCs. Results of the computed stress intensity factors using crack opening displacements (CODs) near the crack tips are presented in this paper. It is found that the fast multipole BEM with constant elements can predict the stress intensity factors of cracks in 2-D plates with sufficient accuracy and efficiency. Keywords: fast multipole boundary element method, 2-D crack problems, constant boundary elements, stress intensity factors.

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Section: A Plate With Two Symmetrically Inclined Crackssupporting

confidence: 67%

Solution of stress intensity factors for 2-D multiple crack problems by the fast multipole boundary element method

Guo¹,

Liu²,

2013

Boundary Elements and Other Mesh Reduction Methods XXXVI

Self Cite

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“…Figure 6a represents a model of two non-collinear symmetrical cracks with 2a and inclination with centers that are 2.2a away from one another under uniaxial tensile stress. Figure 6 displays different solutions [by Sih (1973), Chen and Chang (1989), Guo and Ma (2011), Guo et al (2013)] for K I for two symmetrical non-collinear cracks with several inclination . In the figure, the dots are the values obtained by this methodology for the two tips of the crack inclined by 20° and 0° from the horizontal line.…”

Section: Non-collinear Cracksmentioning

confidence: 99%

Fracture Assessment of Quasi-brittle Rock Simulated by Modified Discrete Element Method

Gheibi

Holt

2020

Rock Mech Rock Eng

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New developments of an in-house hybrid code, named Modified Discrete Element Method (MDEM) are presented in the paper. The new developments are on the treatment of pre-existing and propagating fractures in quasi-brittle materials. These developments are the embedment of Linear Elastic Fracture Mechanics (LEFM) and elastic-softening crack band model-based methodologies in the MDEM and their application in lab and reservoir scale. Using the first methodology, MDEM can calculate stress intensity factors, K I and K II using the internal contact forces of particles. K I and K II are calculated independent of boundary conditions and geometrical configuration with acceptable accuracy level. The methodology has been also used in reservoir scale to study the rupture likelihood of faults and fractures due to fluid injection. This methodology enables the code to model mode I and mode II failures and propagation direction based on the fracturing model proposed by Rao et al. (Int J Rock Mech Min Sci 40(3): 355-375, 2003). Using the second methodology, the MDEM can model nonlinear behavior of quasi-brittle materials including or excluding preexisting cracks based on fracture energy. A model was verified against an experiment of a three point bend test with a notch. The numerically obtained force-crack mouth opening curve was reasonably comparable to the experimental test. The analysis was repeated for three other mesh sizes and the results are less mesh size dependent. Finally, it was shown that MDEM has the potential in studying fracture mechanics of quasi-brittle materials both in lab and large-scale investigations.

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“…To overcome these weaknesses of the above mentioned algorithms, the concept of the eigen crack opening displacement (COD) are firstly proposed in author's previous paper in ref. [25] and reintroduced in the present paper as shown in Section 2.1. Based on the concept of eigen COD, the basic format of eigen COD BIEs and its iterative fashion are established step by step with a small size of final system matrix in refs.…”

Section: Introductionmentioning

confidence: 98%

Numerical Comparison Research on the Solution of Stress Intensity Factors of Multiple Crack Problems

Guo¹

2020

APM

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Solution of stress intensity factors of multiple cracks in plane elasticity with eigen COD formulation of boundary integral equation

Cited by 7 publications

References 22 publications

Solution of stress intensity factors for 2-D multiple crack problems by the fast multipole boundary element method

Solution of stress intensity factors for 2-D multiple crack problems by the fast multipole boundary element method

Fracture Assessment of Quasi-brittle Rock Simulated by Modified Discrete Element Method

Numerical Comparison Research on the Solution of Stress Intensity Factors of Multiple Crack Problems

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