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.
Citation: Engineering Analysis With Boundary Elements
Pub Type: Journals
anisotropy, defects, dislocations, elasticity, Fourier transforms, Green?s function, multilayers, piezoelectricity, semiconductors, steps, Stroh formalism.