Oscillating Infinitesimal Prismatic Dislocation Loops in Thin Films

The steady-state elastic responses of infinite isotropic solids and thin films to the oscillating infinitesimal prismatic dislocation loops are investigated. The film can be free standing, in smooth contact with or perfectly bonded to a rigid substrate. The solutions are expressed in terms of Helmholtz potentials with unknown coefficients, which will be determined by solving a set of simultaneous liner algebraic equations. The simultaneous algebraic equations are constructed by using the boundary conditions on the plane containing the dislocation loop and on the surfaces of the film. The method can be easily extended to multilayered solids.