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Research Papers

Three-Phase Inclusions of Arbitrary Shape With Internal Uniform Hydrostatic Stresses in Finite Elasticity

[+] Author and Article Information
Xu Wang

School of Mechanical and Power Engineering,  East China University of Science and Technology, 130 Meilong Road, Shanghai 200237, Chinaxuwang_sun@hotmail.com

Peter Schiavone1

Department of Mechanical Engineering,  University of Alberta, 4-9 Mechanical Engineering Building, Edmonton, Alberta, Canada T6G 2G8p.schiavone@ualberta.ca

1

Corresponding author.

J. Appl. Mech 79(4), 041012 (May 09, 2012) (6 pages) doi:10.1115/1.4006240 History: Received July 25, 2011; Revised November 21, 2011; Posted February 28, 2012; Published May 09, 2012; Online May 09, 2012

We study the internal stress field of a three-phase two-dimensional inclusion of arbitrary shape bonded to an unbounded matrix through an intermediate interphase layer when the matrix is subjected to remote uniform in-plane stresses. The elastic materials occupying all three phases belong to a particular class of compressible hyperelastic harmonic materials. Our analysis indicates that the internal stress field can be uniform and hydrostatic for some nonelliptical shapes of the inclusion, and all of the possible shapes of the inclusion permitting internal uniform hydrostatic stresses are identified. Three conditions are derived that ensure an internal uniform hydrostatic stress state. Our rigorous analysis indicates that for the given material and geometrical parameters of the three-phase inclusion of a nonelliptical shape, at most, eight different sets of remote uniform Piola stresses can be found, leading to internal uniform hydrostatic stresses. Finally, the analytical results are illustrated through an example.

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Copyright © 2012 by American Society of Mechanical Engineers
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Figures

Grahic Jump Location
Figure 1

Three-phase composite with a nonelliptical inclusion

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Figure 2

The mapped ξ-plane

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Figure 3

The permissible real values of p1 and p2 appearing in Eqs. 30,31

Grahic Jump Location
Figure 4

The permissible real values of p1 and p3 appearing in Eqs. 32,33

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