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TECHNICAL PAPERS

Defect Green’s Function of Multiple Point-Like Inhomogeneities in a Multilayered Anisotropic Elastic Solid

[+] Author and Article Information
B. Yang

Department of Mechanical and Aerospace Engineering, Florida Institute of Technology, Melbourne, FL 32901e-mail: boyang@fit.edu

J. Appl. Mech 71(5), 672-676 (Nov 09, 2004) (5 pages) doi:10.1115/1.1781179 History: Received August 28, 2003; Revised April 15, 2004; Online November 09, 2004
Copyright © 2004 by ASME
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References

Lee, J. A., and Mykkanen, D. L., 1987, Metal and Polymer Matrix Composites, Noyes Data Corp, Park Ridge, NJ.
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Mura, T., 1987, Micromechanics of Defects in Solids, Martinus Nijhoff, Boston.
Mindlin,  R. D., 1936, “Force at a Point in the Interior of a Semi-Infinite Solid,” Physica (Amsterdam), 7, pp. 195–202.
Love, A. E. H., 1944, A Treatise on the Mathematical Theory of Elasticity, Dover, New York.
Ting, T. C. T., 1996, Anisotropic Elasticity, Oxford University Press, Oxford, UK.
Pan,  E., and Yuan,  F. G., 2000, “Three-Dimensional Green’s Functions in Anisotropic Bimaterials,” Int. J. Solids Struct., 37, pp. 5329–5351.
Yang,  B., and Pan,  E., 2002, “Three-Dimensional Green’s Functions in Anisotropic Trimaterials,” Int. J. Solids Struct., 39, pp. 2235–2255.
Yang,  B., and Pan,  E., 2002, “Efficient Evaluation of Three-Dimensional Green’s Functions in Anisotropic Elastostatic Multilayered Composites,” Eng. Anal. Boundary Elem., 26, pp. 355–366.
Pan,  E., and Yang,  B., 2001, “Elastostatic Fields in an Anisotropic Substrate due to a Buried Quantum Dot,” J. Appl. Phys., 90, pp. 6190–6196.
Yang,  B., and Pan,  E., 2003, “Elastic Fields of Quantum Dots in Multilayered Semiconductors: A Novel Green’s Function Method,” ASME J. Appl. Mech., 70, pp. 161–168.
Yang,  B., and Tewary,  V. K., 2003, “Continuum Dyson’s Equation and Defect Green’s Function in a Heterogeneous Anisotropic Solid,” Mech. Res. Commun., 31, pp. 405–414.
Yang,  B., and Pan,  E., 2002, “Elastic Analysis of an Inhomogeneous Quantum Dot in Multilayered Semiconductors Using a Boundary Element Method,” J. Appl. Phys., 92, pp. 3084–3088.
Tewary,  V. K., 1973, “Green-Function Method for Lattice Statics,” Adv. Phys., 22, pp. 757–810.
Schaffler, F., 2001, “Silicon-Germanium (Si1−xGex),” Properties of Advanced Semiconductor Materials, M. E. Levinshtein, S. L. Rumyantsev, and M. S. Shur, eds., John Wiley and Sons, New York.

Figures

Grahic Jump Location
(a) A multilayered solid embedded with multiple inhomogeneities; (b) a “clean” multilayered solid as reference to (a). Both structures are subjected to a unit point force along one of the axes at X . A global coordinate system is established with the x3-axis being perpendicular to the top surface and pointing inward the substrate.
Grahic Jump Location
A Si/Ge superlattice with (a) 3 cubic Ge-QDs and (b) 11×11 semispherical QDs
Grahic Jump Location
Variation of (nonzero) normalized strain components along the line, (x1,x2=0,x3=0) on the top surface induced by the three buried cubic QDs as shown in Fig. 2(a). The solid lines indicate the present solution of point-like QDs, and the dashed lines with symbols indicate the BE solution of finite-size QDs with the size as indicated.
Grahic Jump Location
Contour plot of the normalized hydrostatic strain εkk on the top surface in the case of 11×11 array of semispherical QDs as shown in Fig. 2(b). The magnitude of the contours can be read from the next Fig. 5.
Grahic Jump Location
Diagonal variation of the normalized hydrostatic strain εkk from (−3,−3) to (3,3) in Fig. 4, showing the magnitude and maximum and minimum locations

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