Benchmark Results for the Problem of Interaction Between a Crack and a Circular Inclusion

[+] Author and Article Information
J. Wang, S. G. Mogilevskaya, S. L. Crouch

Department of Civil Engineering, University of Minnesota, 500 Pillsbury Drive S.E., Minneapolis, MN 55455, USA

J. Appl. Mech 70(4), 619-621 (Aug 25, 2003) (3 pages) doi:10.1115/1.1598473 History: Received April 12, 2002; Revised February 22, 2003; Online August 25, 2003
Copyright © 2003 by ASME
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Helsing,  J., and Jonsson,  A., 2002, “On the Accuracy of Benchmark Tables and Graphical Results in the Applied Mechanics Literature,” ASME J. Appl. Mech., 69, pp. 88–90.
Wang, J., Mogilevskaya, S. G., and Crouch, S. L., 2001, “A Galerkin Boundary Integral Method for Nonhomogeneous Materials With Cracks,” Rock Mechanics in the National Interest, D. Elsworth, J. Tinucci, and K. Heasley, Balkema, Lisse, The Netherlands, pp. 1453–1460.
Mogilevskaya,  S. G., and Crouch,  S. L., 2001, “A Galerkin Boundary Integral Method for Multiple Circular Elastic Inclusions,” Int. J. Numer. Methods Eng., 52, pp. 1069–1106.
Mogilevskaya,  S. G., 1996, “The Universal Algorithm Based on Complex Hypersingular Integral Equation to Solve Plane Elasticity Problems,” Comput. Mech.,18, pp. 127–138.
Erdogan,  F., Gupta,  G. D., and Ratwani,  M., 1974, “Interaction Between a Circular Inclusion and an Arbitrarily Oriented Crack,” ASME J. Appl. Mech., 41, pp. 1007–1013.
Cheeseman,  B. A., and Santare,  M. H., 2000, “The Interaction of a Curved Crack With a Circular Inclusion,” Int. J. Fract., 103, pp. 259–277.
Linkov,  A. M., and Mogilevskaya,  S. G., 1994, “Complex Hypersingular Integrals and Integral Equations in Plane Elasticity,” Acta Mech., 105, pp. 189–205.


Grahic Jump Location
A straight (left) or circular arc (right) crack outside an inclusion under uniaxial or biaxial tension. This figure corresponds to Fig. 1 in Ref. 1.
Grahic Jump Location
Convergence of F1 and F2 at the left tip of the straight crack with increase of the number of terms of the Fourier series (the dotted lines denote Helsing and Jonsson’s results for c/a=0.5 and 1.0)




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