Efficient Green's Function Modeling of Line and Surface Defects in Multilayered Anisotropic Elastic and Piezoelectric Materials
B. Yang; and V. K. Tewary

doi:10.3970/cmes.2006.015.165
Source CMES: Computer Modeling in Engineering & Sciences, Vol. 15, No. 3, pp. 165-178, 2006
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Keywords Anisotropy, Defects, Dislocations, Elasticity, Fourier transforms, Green's function, Multilayers, Piezoelectricity, Semiconductors, Steps, Stroh formalism.
Abstract Green's function (GF) modeling of defects may take effect only if the GF as well as its various integrals over a line, a surface and/or a volume can be efficiently evaluated. The GF is needed in modeling a point defect, while integrals are needed in modeling line, surface and volumetric defects. In a matrix of multilayered, generally anisotropic and linearly elastic and piezoelectric materials, the GF has been derived by applying 2D Fourier transforms and the Stroh formalism. Its use involves another two dimensions of integration in the Fourier inverse transform. A semi-analytical scheme has been developed previously for efficient evaluation of the GF. In this paper, an efficient scheme for evaluation of the line and surface integrals of the GF is presented. These integrals are obtained by carrying out the integration over the physical domain analytically and then over the transform domain numerically. The efficiency is thus comparable to that in the evaluation of the GF. The high efficiency in the evaluation of the surface integral is of particular value to the modeling of dislocations due to the lack of a line-defect treatment of this group of defects (originally, of uniform planar distribution of force dipoles) in a multilayered heterogeneous matrix. Numerical examples of nitride semiconductors with strong piezoelectric effect are presented to demonstrate the efficiency and accuracy of the present scheme.
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