A Dual Boundary Element Formulation for Three-Dimensional Fracture Analysis
Authors: A. WILDE, IT Innovation Centre, United Kingdom
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APPLIED MECHANICS REVIEWS
This volume presents the dual boundary element formulation which uses continuous elements in three dimensions, and applies it to the analysis of geomechanical fracture problems and fatigue crack growth. The method overcomes the mathematical degeneration associated with the solitary use of the displacement boundary integral equation for cracked bodies by introducing an additional independent boundary integral equation on one of the crack surfaces. Effective implementation is achieved through the use of accurate algorithms for the singular and near-singular integrals in the dual equations.
Two new approaches which enable discretisation of crack surfaces with continuous elements are considered, and special crack front elements to accurately model the square root variation of the displacement field near the crack front are developed. There is also discussion of implementation on MIMD computer architecture. The author then moves on to give two different techniques for the evaluation of stress intensity factors, both based on crack-opening-displacements, and to explore applications in seam extraction and in hydraulic fracture by the introduction of spring constraints between the crack surfaces. Finally, the method is extended to the analysis of fatigue crack growth, the accuracy and efficiency of which is demonstrated through a number of mixed-mode examples including both embedded and edge cracks.
Contents: Introduction; Basic Elasticity and Fracture Mechanics; The Boundary Element Method; The Three-Dimensional Dual Boundary Element Method; Enriched Elements for the Evaluation of the Traction BIE; The Dual Boundary Element Method for Three-Dimensional Crack Analysis; Application of the DBEM to Crack Analysis in Geomechanics; Application of the DBEM to Three-Dimensional Crack Growth Analysis; Conclusions; Bibliography; Appendices.