TY - JOUR
T1 - On the path independency of the point-wise J integral in three-dimensions
AU - Omer, Netta
AU - Yosibash, Zohar
PY - 2005/11
Y1 - 2005/11
N2 - 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, 2004, SIAM Journal of Mathematical Analysis, 35(5), 1177-1202. Using it, we show analyticall y for several fully 3-D displacement fields (which are neither plane strain nor plane stress) that the pointwise path-area JX1-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 JX1-integral may be achieved which indeed show path independency. We also show that computation of the path part of the JX1 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 → 0) to obtain a good estimate for JX1-integral.
AB - 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, 2004, SIAM Journal of Mathematical Analysis, 35(5), 1177-1202. Using it, we show analyticall y for several fully 3-D displacement fields (which are neither plane strain nor plane stress) that the pointwise path-area JX1-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 JX1-integral may be achieved which indeed show path independency. We also show that computation of the path part of the JX1 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 → 0) to obtain a good estimate for JX1-integral.
KW - Edge stress intensity functions
KW - High order finite elements
KW - J -integral
UR - http://www.scopus.com/inward/record.url?scp=33244496222&partnerID=8YFLogxK
U2 - 10.1007/s10704-005-3934-7
DO - 10.1007/s10704-005-3934-7
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AN - SCOPUS:33244496222
SN - 0376-9429
VL - 136
SP - 1
EP - 36
JO - International Journal of Fracture
JF - International Journal of Fracture
IS - 1-4
ER -