### 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.