Singular field decomposition based on path-independent integrals

Abstract

A method is developed by which the field generated by a source (measured or numerically evaluated) is decomposed in a series of singular self-equilibrating linear elastic field components. These elementary sources form an elastic equivalent of the real source, the set of their magnitudes representing a ‘spectral decomposition’ of the investigated field. The decomposition is performed using path–independent interaction integrals computed through the field of interest, far from the source. The method may be used to investigate internal field sources, such as dislocations, as well as sources of field perturbation, such as crack tips or wedges. The method is applied to the analysis of the core structure of an edge dislocation in aluminium. The dislocation is represented in an atomistic simulation and a model core is sought in the form of a series of multipoles or elementary linear elastic field sources. The field of the dislocation is composed from the Volterra solution and higher–order components induced by the nonlinear behaviour of the material in the core region. The magnitude of the component elementary sources is determined from the numerically evaluated field far from the core. This expansion characterizes the core structure. Its variation associated with the core deformation as the dislocation is loaded against the Peierls barrier is investigated.

Acknowledgement

This work is an extension of earlier work performed by one of the authors (R.C.P.) in collaboration with Professor K. S. Kim.