A unified methodology for computing the stresses around an arbitrarily-shaped hole in isotropic or anisotropic materials

Abstract

A unified semi-analytical solution based on graphical conformal mapping and complex variable methods is proposed to calculate the in-plane stress around an arbitrarily-shaped hole in isotropic or anisotropic materials. The method requires only the outline coordinates of the hole, the elastic moduli of the material, and the magnitude and direction of the far-field stresses. Comparison with many published results for a wide range of shapes, such as triangles, squares, ovaloids, and ellipses, has been carried out to validate the method. The method has also been applied to a highly irregular geometry that has been observed in a breakout of a subsurface borehole. The solution is essentially closed-form, in the sense that it can be explicitly expressed in terms of the mapping coefficients, and parameters that depend only on the elastic moduli of the materials. With such a degree of flexibility, the method will be useful to study the effect of hole geometry on the stress distribution around holes in isotropic or anisotropic materials.