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Research Papers

On Partially Debonded Circular Inclusions in Finite Plane Elastostatics of Harmonic Materials

[+] Author and Article Information
X. Wang1

Department of Civil Engineering, and Department of Applied Mathematics, University of Akron, Akron, OH 44325-3905xuwang_sun@hotmail.com

E. Pan

Department of Civil Engineering, and Department of Applied Mathematics, University of Akron, Akron, OH 44325-3905

1

Corresponding author.

J. Appl. Mech 76(1), 011012 (Nov 05, 2008) (5 pages) doi:10.1115/1.3000023 History: Received April 14, 2008; Revised June 19, 2008; Published November 05, 2008

We investigate a partially debonded circular elastic inclusion embedded in a particular class of harmonic materials by using the complex variable method under finite plane-strain deformations. A complete (or full-field) solution is derived. It is observed that the stresses in general exhibit oscillatory singularities near the two tips of the arc shaped interface crack. Particularly the traditional inverse square root singularity for stresses is observed when the asymptotic behavior of the harmonic materials obeys a constitutive restriction proposed by Knowles and Sternberg (1975, “On the Singularity Induced by Certain Mixed Boundary Conditions in Linearized and Nonlinear Elastostatics  ,” Int. J. Solids Struct., 11, pp. 1173–1201). It is also found that the number of admissible states under finite plane deformations for given external loads can be two, one, or even zero.

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Grahic Jump Location
Figure 1

An arc crack along the interface between a circular inclusion and the matrix

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