SYMPOSIA PAPER Published: 01 January 1992

Traction Boundary Integral Equation (BIE) Formulations and Applications to Nonplanar and Multiple Cracks


The hypersingular Somigliana identity for the stress tensor is used as the basis for a traction boundary integral equation (BIE) suitable for numerical application to nonplanar cracks and to multiple cracks. The variety of derivations of hypersingular traction BIE formulations is reviewed and extended for this problem class. Numerical implementation is accomplished for piecewise-flat models of curved cracks, using local coordinate system integrations. A nonconforming, triangular boundary element implementation of the integral equations is given. Demonstration problems include several three-dimensional approximations to planestrain fracture mechanics problems, for which exact or highly accurate numerical solutions exist. In all cases, the use of a piecewise-flat traction BIE implementation is shown to give excellent results.

Author Information

Cruse, TA
Vanderbilt University, Nashville, TN
Novati, G
Politecnico di Milano, Milan, Italy
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Developed by Committee: E08
Pages: 314–332
DOI: 10.1520/STP23712S
ISBN-EB: 978-0-8031-5193-2
ISBN-13: 978-0-8031-1440-1