Introduction

The main methods for treating the defect elasticity problems considered in this book are introduced. The chapter begins by reviewing the requirements that any solution for a defect elasticity problem must satisfy. A basic differential equation for the displacements whose solutions automatically satisfy these requirements is then formulated, and useful methods of solving it are described. These include its direct solution and various formalisms that expedite its solution under different conditions, including the Fourier transform approach, the Green's function method, and the sextic and integral formalisms.

Following this, the transformation strain method, which is applicable for many defect problems, is described. Here, the defect is introduced in the form of an appropriate stress-free transformation strain. The resulting elastic field is then found by methods involving the use of Green's functions or Fourier transforms.

Next, the stress function method for solving problems is introduced, and the Airy stress function method, which is applicable when plane strain conditions prevail, is described. Finally, the problem of finding solutions for defects in finite homogeneous regions bounded by interfaces, rather than in infinite regions, is outlined. The methods by which the boundary conditions at the interfaces, which exist in such cases, can be satisfied by the method of images and use of appropriate Green’s functions are described.