8. Inclusions

Inclusion is a foreign solid enclosed in the matrix. Due to the material discontinuity across the interface, stress distributions around the inclusion have a significant change. Some analytical solutions were presented in Hwu (Anisotropic elastic plates. Springer, New York, 2010) for certain specific situations in which the inclusions can be elastic or rigid whose shapes may be elliptical, line or polygon-like. Based upon these solutions, some matlab functions are designed. Sections 8.1 and 8.2 shows the functions for the problems with elastic or rigid inclusions subjected to a uniform load at infinity or a concentrated force at the matrix. The interactions between inclusion and dislocations are considered in Sect. 8.3, in which the dislocations may be located outside, inside or on the interface. By treating the crack as a distribution of dislocations, the inclusions with cracks outside, inside, penetrating, or along the interface are then considered in Sect. 8.4. Functions for common use and examples for inclusion problems are presented in the last two sections.