Discrete-Continuum Transition

A Discussion of the Continuum Limit

Abstract

In recent years, the striving towards a proper understanding of plastic deformation on different scales led to a substantial progress in the development of advanced dislocation based material models. In this paper the limits of a continuum representation of dislocation dynamics in the discrete to continuous transition regime are discussed. Using 2d discrete dislocation dynamic simulations, a systematic investigation of ensemble averages of a bounded structure is presented considering a varying number of dislocations. Based on the results, the question, how we can evaluate the conditions under which a discrete system behaves similarly to a homogenized continuum system, is discussed.