Abstract :
The title problem is considered for an elastic
circular tube of inner radius A and outer radius B.
The tube is made of a single component solid with
vacancies as its second component. The mole fraction
of the massive species is denoted by x1, while that of the
vacancies by x0 = 1 − x1. The tube is completely surrounded
by vacuum, serving as a reservoir of vacancies.
One of the standard elasticity boundary conditions is
applied at time t = 0, when the composition is uniform.
The ensuing coupled deformation and diffusion leads to
the evolving of A(t), B(t) and x1(R, t) as functions of
time. Since the single component solid is not in contact
with its vapor or liquid, the diffusion boundary condition
is always tied to the elasticity problem through a
surface condition that involves the normal configurational
traction. Our chemical potential has an energy
density term that serves as a source in the interior and
the boundary conditions for the diffusion problem are
such that the time rates of boundary accretion ˙A(t)
and ˙B (t) must simultaneously satisfy two dissipative
inequalities, one governed by the gradient of the internal
chemical potential and the other by the normal
configurational traction.
