Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-26T21:54:15.392Z Has data issue: false hasContentIssue false
  • English
  • Français

Solution for a Crack Embedded in Multiply Confocally Elliptical Layers in Antiplane Elasticity

Published online by Cambridge University Press:  23 January 2015

Y.-Z. Chen
Y.-Z. Chen*
Affiliation:
Division of Engineering Mechanics, Jiangsu University, Jiangsu, China
*
*Corresponding author ([email protected])
Get access

Abstract

This paper provides a general solution for a crack embedded in multiply confocally elliptical layers in antiplane elasticity. In the problem, the elastic medium is composed of an inclusion, many confocally elliptical layers and the infinite matrix with different elastic properties. In addition, the remote loading is applied at infinity. The complex variable method and the conformal mapping technique are used. On the mapping plane, the complex potentials for the inclusion and many layers are assumed in a particular form with two undetermined coefficients. The continuity conditions for the displacement and traction along the interface between two adjacent layers are formulated and studied. By enforcing those conditions along the interface, the exact relation between two sets of two undetermined coefficients in the complex potentials for j-th layer and j + 1-th layer can be evaluated. From the traction free condition along the crack faces, the correct form of the complex potential for the cracked inclusion is obtained. Finally, many numerical results are provided.

Keywords

Stress intensity factorsCrack in inclusionMultiply dissimilar elliptical layersAntiplane elasticity
Type
Research Article
Information
Journal of Mechanics , Volume 31 , Issue 3 , June 2015 , pp. 261 - 267
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2014 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Eshelby, J.D., “The Determination of the Elastic Field of an Ellipsoidal Inclusion and Related Problems,” Proceedings of the Royal Society A, 241, pp. 376–396 (1957).Google Scholar
2.Mura, T., Micromechanics of Defects in Solids, Mar-tinus Nijhoff Publishers, Dordrecht (1987).CrossRefGoogle Scholar
3.Zhou, K., Hoh, H.J., Wang, X., Keer, L.M., Pang, J.H.L. and Song, B., “A Review of Recent Works on Inclusions,” Mechanics of Materials, 60, pp. 144–158 (2013).Google Scholar
4.Gong, S.X., “A Unified Treatment of the Elastic Elliptical Inclusion Under Antiplane Shear,” Archive of Applied Mechanics, 65, pp. 55–64 (1995).Google Scholar
5.Ru, C.Q., and Schiavone, P., “On the Elliptic Inclusion in Anti-Plane Shear,” Mathematics and Mechanics of Solids, 1, pp. 327–333 (1996)CrossRefGoogle Scholar
6.Chao, C.K., and Young, C.W., “On the General Treatment of Multiple Inclusions in Antiplane Elas-tostatics,” International Journal of Solids and Structures, 35, pp. 3573–3593 (1998).Google Scholar
7.Ru, C.Q., Schiavone, P., and Mioduchowski, A., “Uniformity of Stresses Within a Three-Phase Elliptic Inclusion in Anti-Plane Shear,” Journal of Elasticity, 52, pp. 121–128 (1999).CrossRefGoogle Scholar
8.Shen, M.H., Chen, S.N., and Chen, F.M., “Anti-plane Study on Confocally Elliptical Inhomogeneity Problem Using an Alternating Technique,” Archive of Applied Mechanics, 75, pp. 302–314 (2006).Google Scholar
9.Shen, M.H., Chen, S.N., and Chen, F.M., “Piezoelectric Study on Confocally Multicoated Elliptical Inclusion,” International Journal of Engineering Science, 43, pp. 1299–1312 (2005).Google Scholar
10.Chen, J.T., and Wu, A.C., “Null-Field Approach for the Multi-Inclusion Problem Under Antiplane Shears,” Journal of Applied Mechanics, 74, pp. 469–487 (2007).Google Scholar
11.Chen, J.T., Shen, W.C., and Wu, A.C., “Null-Field Integral Equations for Stress Field Around Circular Holes Under Anti-Plane Shear,” Engineering Analysis with Boundary Elements, 30, pp.205–217 (2006).Google Scholar
12.Chen, K.H., Chen, J.T., and Kuo, J.H., “Regularized Meshless Method for Antiplane Shear Problems,” International Journal for Numerical Methods in Engineering, 73, pp. 1251–1273 (2008).CrossRefGoogle Scholar
13.Lee, Y.T., and Chen, J.T., “Null-Field Approach for the Antiplane Problem with Elliptical Holes And/Or Inclusions,” Journal of Composites B, 44, pp. 283–294 (2013).Google Scholar
14.Ting, T.C.T., and Schiavone, P., “Uniform Antiplane Shear Stress Inside an Anisotropic Elastic Inclusion of Arbitrary Shape with Perfect or Imperfect Interface Bonding,” International Journal of Engineering Science, 48, pp. 67–77 (2010).CrossRefGoogle Scholar
15.Chen, Y.Z., “Closed form Solution for Eshelby's Elliptical Inclusion in Antiplane Elasticity Using Complex Variable,” Zeitschrift Fuer Angewandte Mathematik Und Physik, 69, pp. 1797–1805 (2013)Google Scholar
16.Chen, T., “A Confocally Multicoated Elliptical Inclusion Under Antiplane Shear: Some New Results,” Journal of Elasticity, 74, pp. 87–97 (2004).Google Scholar
17.Chen, Y.Z., Hasebe, N., and Lee, K.Y., Multiple Crack Problems in Elasticity, WIT Press, Southampton (2003).Google Scholar
18.Muskhelishvili, N.I., Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff, Gro-ningen (1953).Google Scholar