Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Efficient Green?s Function Modeling of Line and Surface Defects in Multilayered Anisotropic Elastic and Piezoelectric Material



B. Yang, Vinod Tewary


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 small volume can be efficiently evaluated. The GF itself is needed in modeling a point defect while the integrals needed in modeling a line, a surface and a volumetric defect, respectively. In a matrix of multilayered generally anisotropic and linearly elastic and piezoelectric materials, the GF has been derived by applying the 2D Fourier transforms and the Stroh formalism. Its evaluation 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 integrating over the physical domain analytically and then over the transform domain numerically. The efficiency is thus as high as that in the evaluation of the GF. These line and surface integrals are applied to model a line defect (such as steps) and a surface defect (such as dislocations), respectively. The high efficiency in the evaluation of the surface integral is of particular value due to the lack of a line-defect approach of dislocations in the case of multilayered heterogeneous matrix, which must be modeled as original as a surface defect of force dipole. Numerical examples of nitride semiconductors with strong piezoelectric effect are presented to demonstrate the efficiency and accuracy of the present scheme.
Engineering Analysis With Boundary Elements


anisotropy, defects, dislocations, elasticity, Fourier transforms, Green?s function, multilayers, piezoelectricity, semiconductors, steps, Stroh formalism.


Yang, B. and Tewary, V. (2006), Efficient Green?s Function Modeling of Line and Surface Defects in Multilayered Anisotropic Elastic and Piezoelectric Material, Engineering Analysis With Boundary Elements, [online], (Accessed June 16, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created October 30, 2006, Updated October 12, 2021