Eshelby's paradox, its universality and resolution

Eliot Fried
Washington University in St. Louis
Mechanical and Aerospace Engineering

In 1980, after 30 years of seminal work on point, line, and wall defects in solids, Eshelby turned his attention to the study of disclinations in nematic liquid crystals. Working within the context of the Ericksen--Leslie theory, Eshelby calculated the force between a pair of parallel disclinations at rest. He found that force to be expressible entirely in terms of the Cauchy traction exerted on the defect core and, thus, to be of a Newtonian nature. Based on his experience with solids, Eshelby expected that his calculation would yield a configurational force analogous to those acting on material inhomogeneities, dislocations, cracks, grain boundaries, and phase interfaces and to yield a trivial Newtonian force. Eshelby interpreted his result as an intrinsic fallacy of the theory.

In this talk, it will be shown that Eshelby's paradox is not peculiar to the Ericksen--Leslie theory. Rather, that paradox arises whenever the spatial (as opposed to a referential) description is employed. Further, it will be demonstrated that a resolution to Eshelby's paradox is provided by Gurtin's approach to the theory of configurational forces.