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The theoretical basis and performance characteristics of two new methods for the computation of the coefficients of the terms of asymptotic expansions at reentrant corners from finite-element solutions are presented. The methods, called the contour integral method (CIM) and the cutoff function method (CFM), are very efficient: the coefficients converge to their true values as fast as the strain energy, or faster.
In order to make the presentation as simple as possible, we assume that the elastic body is homogeneous and isotropic, is loaded by boundary tractions only, and, in the neighborhood of the reentrant corner, has stress-free boundaries. The methods described herein can be adapted to cases without such restrictions.
finite-element methods, p, -extension, fracture mechanics, elasticity, stress-intensity factors, mixed mode, extraction methods, convergence, error estimate
Professor of mechanics and director, Center for Computational Mechanics, Washington University, St. Louis, MO
Research professor, Institute for Physical Science and Technology, University of Maryland, College Park, MD