Rungamornrat, Jaroon; Mear, Mark E. Weakly-singular, weak-form integral equations for cracks in three-dimensional anisotropic media. (English) Zbl 1169.74549 Int. J. Solids Struct. 45, No. 5, 1283-1301 (2008). Summary: Singularity-reduced integral relations are developed for displacement discontinuities in three-dimensional, anisotropic linearly elastic media. An isolated displacement discontinuity is considered first, and a systematic procedure is followed to develop relations for the displacement and stress fields induced by the discontinuity. The singularity-reduced relation for the stress is particularly important since it is in a form which allows a weakly-singular, weak-form traction integral equation to be readily established. The integral relations obtained for a general displacement discontinuity are then specialized to an isolated crack and to dislocations; the relations for dislocations are introduced to emphasize their direct connection to corresponding results for cracks and to allow earlier independent findings for these two types of discontinuities to be put into proper context. Next, the singularity-reduced integral equations obtained for an isolated crack are extended to allow treatment of cracks in a finite domain, and a pair of weakly-singular, weak-form displacement and traction integral equations is established. These integral equations can be combined to obtain a final formulation which is in a symmetric form, and in this way they serve as the basis for a weakly-singular, symmetric Galerkin boundary element method suitable for analysis of cracks in anisotropic media. Cited in 2 ReviewsCited in 14 Documents MSC: 74R10 Brittle fracture 74B05 Classical linear elasticity 74E10 Anisotropy in solid mechanics Keywords:cracks; dislocations; integral equations; anisotropic; weakly-singular; boundary elements PDFBibTeX XMLCite \textit{J. Rungamornrat} and \textit{M. E. Mear}, Int. J. Solids Struct. 45, No. 5, 1283--1301 (2008; Zbl 1169.74549) Full Text: DOI References: [1] Bacon, D. J.; Barnett, D. M.; Scattergood, R. O.: Anisotropic continuum theory of lattice defects, Progress in materials science 23, 51-262 (1978) [2] Becache, E.; Nedelec, J. 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