Numerical methods for stress analysis are increasingly being employed in the micromechanics of solids. In this paper, the boundary integral equation (BIE) method for two-dimensional general anisotropic elasticity, based on the quadratic isoparametric element formulation, is extended to treating some inclusion problems. All the cases analysed involved an elliptical zirconia inclusion in an alumina matrix, noting that ZrO2-Al2O3 is an advanced ceramic increasingly used in structural applications. The BIE results are compared with those calculated using Eshelby's equivalent inclusion approach where possible, and excellent agreements between them are obtained. The present work demonstrates the suitability of using this numerical technique for analysing such problems and, in particular, the ease with which it may be used even in the case of general anisotropy.
The Journal of Strain Analysis for Engineering Design
Department of Mechanical and Aerospace Engineering

Tan, C, Gao, Y.L., & Afagh, F. (1992). Anisotropic stress analysis of inclusion problems using the boundary integral equation method. The Journal of Strain Analysis for Engineering Design, 27(2), 67–76. doi:10.1243/03093247V272067