Boundary element analysis of cracks

Ammons, Bruce A.; Vable, Madhukar

doi:10.1016/0020-7683(95)00132-8

Cited by 14 publications

(7 citation statements)

References 7 publications

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“…The branches are located symmetrically on both sides of the main crack and inclined at = 45 • to it. It is noteworthy that at the function of the branch cracks, the relative COD and the integration of the traction should be satisfied, respectively, the continuity and equilibrium conditions derived by Ammons and Vable [46]. However, collocations at the branch point can be avoided using discontinuous element.…”

Section: Example 3 (Branched Crack Under a Far-field Tensile Stress Amentioning

confidence: 98%

“…In this example, 10 discontinuous quadratic elements are used for main crack surface, six elements for each branch when b/a = 0.6. The numerical results for this example were evaluated in Murakami [47] and were also solved by Ammons and Vable [46]. In Table IV, the normalized SIFs of the crack tips A and B are given for the ratio b/a = 0.6 and compared with those obtained by Ammons and Vable [46] and Murakami [47].…”

Section: Example 3 (Branched Crack Under a Far-field Tensile Stress Amentioning

confidence: 98%

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Modeling crack propagation path of anisotropic rocks using boundary element method

Ke¹,

Chen

et al. 2008

Num Anal Meth Geomechanics

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SUMMARYIn a cracked material, the stress intensity factors (SIFs) at the crack tips, which govern the crack propagation and are associated with the strength of the material, are strongly affected by the crack inclination angle and the orientation with respect to the principal direction of anisotropy. In this paper, a formulation of the boundary element method (BEM), based on the relative displacements of the crack tip, is used to determine the mixed-mode SIFs of isotropic and anisotropic rocks. Numerical examples of the application of the formulation for different crack inclination angles, crack lengths, and degree of material anisotropy are presented. Furthermore, the BEM formulation combined with the maximum circumferential stress criterion is adopted to predict the crack initiation angles and simulate the crack propagation paths. The propagation path in cracked straight through Brazilian disc specimen is numerically predicted and the results of numerical and experimental data compared with the actual laboratory observations. Good agreement is found between the two approaches. The proposed BEM formulation is therefore suitable to simulate the process of crack propagation.

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Section: Example 3 (Branched Crack Under a Far-field Tensile Stress Amentioning

confidence: 98%

Section: Example 3 (Branched Crack Under a Far-field Tensile Stress Amentioning

confidence: 98%

Modeling crack propagation path of anisotropic rocks using boundary element method

Ke¹,

Chen

et al. 2008

Num Anal Meth Geomechanics

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“…The crack was modelled using displacement discontinuities and integrated tractions were used to impose boundary conditions on the crack surface as elaborated in Ref. [18]. The displacement discontinuity density function was forced to zero at points A and B.…”

Section: Example 2: Pressurized Crack In An Infinite Planementioning

confidence: 99%

An hpr-mesh refinement algorithm for BEM

Maddi

Vable

2010

Engineering Analysis with Boundary Elements

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“…We next determine the grading function that minimizes the error in equation (21). From calculus of variations, the Euler equation can be written as below:…”

Section: Determining the Optimum Grading Function And Error Estimatesmentioning

confidence: 99%

An HR-method of mesh refinement for boundary element method

Ammons

Vable

1998

Int. J. Numer. Meth. Engng.

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This paper describes a mesh refinement technique for boundary element method in which the number of elements, the size of elements and the element end location are determined iteratively in order to obtain a user specified accuracy. The method uses¸ norm as a measure of error in the density function and a grading function that ensures that error over each element is the same. The use of grading function along with¸ norm makes the mesh refinement technique applicable to Direct and Indirect boundary element method formulation for a variety of boundary element method applications. Numerical problems in elastostatics, fracture mechanics, and bending of plate solved using Direct and Indirect method in which the density functions are approximated by Linear Lagrange, Quadratic Lagrange or Cubic Hermite polynomials validate the effectiveness of the proposed mesh refinement technique.

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Boundary element analysis of cracks

Cited by 14 publications

References 7 publications

Modeling crack propagation path of anisotropic rocks using boundary element method

Modeling crack propagation path of anisotropic rocks using boundary element method

An hpr-mesh refinement algorithm for BEM

An HR-method of mesh refinement for boundary element method

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