A new formulation of boundary element method for cracked anisotropic bodies under anti-plane shear.

*(English)*Zbl 1050.74052Summary: By applying integration by parts and other techniques to the traditional boundary integral formulation, a new boundary integral equation is derived to analyze cracked anisotropic bodies under anti-plane shear. The new boundary formulation uses dislocation density as unknown on the crack surface, from which the stress intensity factor \(K_{\text{III}}\) is determined near the crack tip. The boundary element method based on the new equation is established, in which the singular interpolation functions are introduced to model the singularity of dislocation density (on the order of \(1/{\sqrt r}\)) appropriately. The present traction boundary integral equation involves only singularity of order \(1/r\) (no hyper-singular terms appear), and all the singular integrals can be evaluated exactly. The equation and method can be directly used for anti-plane problems with cracks of any geometric shapes. Applications to isotropic and anisotropic cases are provided, and numerical results demonstrate the accuracy of our boundary element method.

##### MSC:

74S15 | Boundary element methods applied to problems in solid mechanics |

74R10 | Brittle fracture |

74E10 | Anisotropy in solid mechanics |

74G70 | Stress concentrations, singularities in solid mechanics |

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\textit{Y. Sun} et al., Comput. Methods Appl. Mech. Eng. 192, No. 22--24, 2633--2648 (2003; Zbl 1050.74052)

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