Micromechanics of defects in transversely isotropic elastic solids with interfaces

Abstract

The response of microstructural defects to internal and external fields is an important subject in materials science and engineering. The knowledge of elastic deformations due to defects is the first step towards understanding the fundamental effects of defects on the mechanical and physical properties of materials. A recently developed method for obtaining the explicit three- dimensional closed form elastic solution in solids with defects in the presence of an interface is reviewed. The interface is a planar boundary between two semi-infinite solids. The solids are either perfectly bonded together or in frictionless contact with each other at the planar interface. The defects are point defects, dislocations, disclinations, inclusions, elastic inhomogeneities, and thermal inhomogeneities. The method is a modified point force method. The elastic solution is expressed in terms of force double Green's functions in a simple form. The force double Green's functions are the partial derivatives of point force solutions. The only task in finding the solution is to find the appropriate surface or volume integral of functions of the distance from the defects to the point of interest. The integrals are the Newtonian potential of the defects with appropriate mass density and other biharmonic and harmonic potentials that are associated with the Newtonian potentials. The same method applies to both isotropic and transversely isotropic solids.