The Filon construct for moving dislocations

Abstract

Filon’s construct, originally developed for plane isotropic linear elastostatics, examines the difference between solutions to the same boundary value problem but for two different values of the elastic moduli, and relates the difference solution to one occurring in a corresponding stationary dislocation problem. This paper generalises the result to three-dimensional linear elastodynamics with particular reference to moving dislocations. Also studied is the inverse procedure which derives the pair of elastodynamical problems from a given distribution of dislocations. Body-forces and an auxiliary plastic distortion tensor are novel and essential features of the argument. Specialisation to the static and quasi-static theories is straightforward. The inverse Filon construct is illustrated by the stationary edge dislocation and uniformly moving screw dislocation in a homogeneous isotropic linear elastic whole space.