Anisotropic stress analysis of inclusion problems using the boundary integral equation method

Abstract

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.

A quadratic boundary element implementation in orthotropic elasticity using the real variable approach

“…; y= y h and xy = xy (0; y) q 0 (11) where w is the maximum central de ection, h is the plate thickness and q 0 is the maximum amplitude of the sinusoidally distributed load at the top surface. This problem was solved using eight quadratic elements for aspect ratio L=h = 4, although more elements were added for higher aspect ratios.…”

Treatment of Body-Force Volume Integrals in Bem by Exact Transformation for 2-D Anisotropic Elasticity

“…The explicit equations for constants A ij can be found in Tan et al 10 The corresponding traction fundamental solutions of equation (6) where n j are unit outward normal components at a boundary point (x 1 ; x 2 ).…”

Accurate modelling of rigid and soft inclusions in 2D elastic solids by the boundary element method

“…In this situation stress concentrations might appear along interfaces, particularly near corners, leading to material deterioration, which reduces the load capacity and the stiffness of the solid under analysis. Several improved BEM formulations have recently appeared to deal with some important inclusion cases in elastic domains emphasising the performance of using integral equations in this context [7][8][9].…”