In the context of the linear theory of elasticity with eigenstrains, the radiated fields,
including inertia effects, and the energy-release rates (“driving forces”) of a spherically
expanding and a plane inclusion with constant dilatational eigenstrains are
calculated. The fields of a plane boundary with dilatational eigenstrain moving
from rest in general motion are calculated by a limiting process from the spherical
ones, as the radius tends to infinity, which yield the time-dependent tractions
that need to be applied on the lateral boundaries for the global problem to be
well-posed. The energy-release rate required to move the plane inclusion boundary
(and to create a new volume of eigenstrain) in general motion is obtained here for
a superposed loading of a homogeneous uniaxial tensile stress. This provides the
relation of the applied stress to the boundary velocity through the energy-rate balance
equation, yielding the “equation of motion” (or “kinetic relation”) of the plane
boundary under external tensile axial loading. This energy-rate balance expression
is the counterpart to the Peach-Koehler force on a dislocation plus the “self-force”
of the moving dislocation.