Research Papers

N-Phase Elliptical Inhomogeneities With Internal Uniform Stresses in Plane Elasticity

[+] Author and Article Information
Xu Wang

School of Mechanical Engineering, Zhengzhou University, Zhengzhou, Henan 450001, P. R. China; Center for Composite Materials, University of Delaware, Newark, DE 19716

J. Appl. Mech 77(4), 041018 (Apr 19, 2010) (11 pages) doi:10.1115/1.4000929 History: Received September 16, 2009; Revised November 29, 2009; Published April 19, 2010; Online April 19, 2010

We investigate the problem of an N-phase elliptical inhomogeneity in plane elasticity. The elliptical inhomogeneity is bonded to the unbounded matrix through the intermediate (N2) interphases, and the matrix is subjected to remote uniform stresses. We observe that the stress field inside the elliptical inhomogeneity is still uniform when the following two conditions are satisfied: (i) The formed interfaces are (N1) confocal ellipses, and (ii) the interphases and the matrix possess the same shear modulus but different Poisson’s ratios. In Appendixes , we also discuss an arbitrary number of interacting arbitrary shaped inhomogeneities embedded in an infinite matrix, and an N-phase inhomogeneity with (N1) interfaces of arbitrary shape. Here all the phases comprising the composite possess the same shear modulus but different Poisson’s ratios. The results in the main body and in Appendixes are further extended in Appendix to finite plane strain deformations of compressible hyperelastic harmonic materials.

Copyright © 2010 by American Society of Mechanical Engineers
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