Size-Dependent Elastic State of Ellipsoidal Nano-Inclusions Incorporating Surface∕Interface Tension

[+] Author and Article Information
P. Sharma

Department of Mechanical Engineering,  University of Houston, Houston, TX 77204psharma@uh.edu

L. T. Wheeler

Department of Mechanical Engineering,  University of Houston, Houston, TX 77204

A more rigorous calculation say using the multi-band k.p. method or tight binding approach is required for accurate electronic band structure calculation. For our purposes, the approximation in Eq. 36 is sufficient to illustrate our point.

J. Appl. Mech 74(3), 447-454 (Apr 12, 2006) (8 pages) doi:10.1115/1.2338052 History: Received October 01, 2005; Revised April 12, 2006

Using a tensor virial method of moments, an approximate solution to the relaxed elastic state of embedded ellipsoidal inclusions is presented that incorporates surface∕interface energies. The latter effects come into prominence at inclusion sizes in the nanometer range. Unlike the classical elastic case, the new results for ellipsoidal inclusions incorporating surface∕interface tension are size-dependent and thus, at least partially, account for the size-effects in the elastic state of nano-inclusions. For the pure dilatation case, exceptionally simple expressions are derived. The present work is a generalization of a previous research that addresses simplified spherical inclusions. As an example, the present work allows us, in a straightforward closed-form manner, the study of effect of shape on the size-dependent strain state of an embedded quantum dot.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Schematic of the problem

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Figure 2

Schematic of the solution

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Figure 3

Schematic of the problem for the isolated ellipsoidal particle under a surface tension

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Figure 4

(a)–(d): Effect of shape on size-dependent dilatation of ellipsoidal inclusions

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Figure 5

Effect of shape on size-dependent principal strains of ellipsoidal inclusion, a1=a2<a3, r=a3∕a1. (a) r=5 (b) r=2.5 (c) r=1.5.




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