On the Accuracy of Benchmark Tables and Graphical Results in the Applied Mechanics Literature

[+] Author and Article Information
J. Helsing

Department of Solid Mechanics and NADA, Royal Institute of Technology, SE-100 44 Stockholm, Sweden e-mail: helsing@nada.kth.se

A. Jonsson

Department of Solid Mechanics, Royal Institute of Technology, SE-100 44 Stockholm, Sweden

J. Appl. Mech 69(1), 88-90 (Aug 21, 2001) (3 pages) doi:10.1115/1.1427691 History: Received October 10, 2000; Revised August 21, 2001
Copyright © 2002 by ASME
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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 Elastic Inclusion,” Int. J. Fract., 103, pp. 259–277.
Helsing,  J., and Peters,  G., 1999, “Integral Equation Methods and Numerical Solutions of Crack and Inclusion Problems in Planar Elastostatics,” SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 59, pp. 965–982.


Grahic Jump Location
Left, a straight crack outside an inclusion under uniaxial tension. This is the setup of Erdogan, Gupta, and Ratwani 1 corresponding to their Table 3. Right, an arc-shaped crack outside a circular inclusion under biaxial tension. This is the setup of Cheeseman and Santare 2 corresponding to their Fig. 8.
Grahic Jump Location
Normalized mode I stress intensity factors of the setup in Fig. 8 in Cheeseman and Santare 2 (the right image of our Fig. 1) versus dimensionless distance for a circular arc-shaped crack interacting with an inclusion
Grahic Jump Location
Convergence of the stress intensity factor k11 of Erdogan, Gupta, and Ratwani 1 for c=2a in the left image of our Fig. 1. The mesh is uniformly refined. The number of distgretization points is N. Double precision arithmetic is used. The reference value k11=0.8497339474770513 is computed with 592, or more, discretization points in quadruple precision arithmetic. Relative errors smaller than machine epsilon as displayed as 1.11⋅10−16.



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