Calculation of T-stress for cracks in two-dimensional anisotropic elastic media by boundary integral equation method

A numerical procedure is proposed to compute the T-stress for two-dimensional cracks in general anisotropic elastic media. T-stress is determined from the sum of crack-face displacements which are computed via an integral equation of the boundary data. To smooth out the data in order to perform accu...

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Bibliographic Details
Published in:International journal of fracture 2018-05, Vol.211 (1-2), p.149-162
Main Authors: Tran, Han D., Mear, Mark E.
Format: Article
Language:English
Subjects:
Automotive Engineering
Boundary element method
Boundary integral method
Characterization and Evaluation of Materials
Chemistry and Materials Science
Civil Engineering
Classical Mechanics
Crack tips
Cracks
Displacement
Domains
Elastic anisotropy
Elastic media
Galerkin method
Integral equations
Materials Science
Mathematical analysis
Mechanical Engineering
Numerical differentiation
Original Paper
Stresses
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Summary:A numerical procedure is proposed to compute the T-stress for two-dimensional cracks in general anisotropic elastic media. T-stress is determined from the sum of crack-face displacements which are computed via an integral equation of the boundary data. To smooth out the data in order to perform accurately numerical differentiation, the sum of crack-face displacement is established in a weak-form integral equation in which the integration domain is simply the crack-tip element. This weak-form integral equation is then solved numerically using standard Galerkin approximation to obtain the nodal values of the sum of crack-face displacements. The procedure is incorporated in a weakly-singular symmetric Galerkin boundary element method in which all integral equations for the traction and displacement on the boundary of the domain and on the crack faces include (at most) weakly-singular kernels. To examine the accuracy and efficiency of the developed method, various numerical examples for cracks in infinite and finite domains are treated. It is shown that highly accurate results are obtained using relatively coarse meshes.
ISSN:0376-9429
1573-2673
DOI:10.1007/s10704-018-0280-0