The model of elastic multipole

Abstract

The idea of elastic multipole is based on a number of drastic simplifications. On the one hand, the theories of point-like multipoles are phenomenological as a point-like source cannot produce director distortions. On the other hand, only a spherical particle allows for analytical theory. I present a mathematically consistent analytical model of spherical elastic multipoles of a finite radius a. The core idea is to consider the general problem of a particle in an ambient distorted director field whose actual source is replaced by an equivalent source in the form of a large concentric sphere of radius ã. The solution obtained up to small terms ∼a/ã gives a simple universal tool to derive all particle's interactions. For an example, the interactions of elastic dipoles, quadrupoles, and monopoles with the ambient director, as well as their pair potentials are calculated by the straightforward differentiation. The assumptions underlying the model are discussed in detail. The main ideas of elastic multipoles and their tensorial structure, which are general and do not depend on the particular particle shape, are briefly presented.