Omer, Netta; Yosibash, Zohar On the path independency of the point-wise \(J\) integral in three-dimensions. (English) Zbl 1197.74122 Int. J. Fract. 136, No. 1-4, 1-36 (2005). Summary: The asymptotic solution in the vicinity of a crack front in a three-dimensional (3-D) elastic domain is provided explicitly following the general framework in [M. Costabel, M. Dauge and Z. Yosibash, SIAM J. Math. Anal. 35, No. 5, 1177–1202 (2004; Zbl 1141.35363)]. Using it, we show analytically for several fully 3-D displacement fields (which are neither plane strain nor plane stress) that the pointwise path-area \(J_{X_1}\) -integral in 3-D is path-independent. We then demonstrate by numerical examples, employing \(p\)-finite element methods, that good numerical approximations of the path-area \(J_{X_1}\) -integral may be achieved which indeed show path independency. We also show that computation of the path part of the \(J_{X_1}\) on a plane perpendicular to the crack front is path dependent. However, one may still use this path integral computed at several radii, followed by the application of Richardson’s extrapolation technique (as \(R\rightarrow 0\)) to obtain a good estimate for \(J_{X_1}\)-integral. Cited in 10 Documents MSC: 74R10 Brittle fracture 74G05 Explicit solutions of equilibrium problems in solid mechanics Keywords:edge stress intensity functions; high order finite elements; \(J\)-integral Citations:Zbl 1141.35363 PDFBibTeX XMLCite \textit{N. Omer} and \textit{Z. Yosibash}, Int. J. Fract. 136, No. 1--4, 1--36 (2005; Zbl 1197.74122) Full Text: DOI References: This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.