4 research outputs found
Trajectories in a space with a spherically symmetric dislocation
We consider a new type of defect in the scope of linear elasticity theory,
using geometrical methods. This defect is produced by a spherically symmetric
dislocation, or ball dislocation. We derive the induced metric as well as the
affine connections and curvature tensors. Since the induced metric is
discontinuous, one can expect ambiguity coming from these quantities, due to
products between delta functions or its derivatives, plaguing a description of
ball dislocations based on the Geometric Theory of Defects. However, exactly as
in the previous case of cylindric defect, one can obtain some well-defined
physical predictions of the induced geometry. In particular, we explore some
properties of test particle trajectories around the defect and show that these
trajectories are curved but can not be circular orbits.Comment: 11 pages, 3 figure
Non-singular screw dislocations as the Coulomb gas with smoothed out coupling and the renormalization of the shear modulus
A field theory is developed for a thermodynamical description of array of
parallel non-singular screw dislocations in elastic cylinder. The partition
function of the system is considered in the functional integral form.
Self-energy of the dislocation cores is chosen in the form suggested by the
gauge-translational model of non-singular screw dislocation. It is shown that
the system of the dislocations is equivalent to the two-dimensional Coulomb
gas. The coupling potential is prevented from a short-distance divergency since
the core energies are taken into account. Two-point correlation functions of
the stress components are obtained. Renormalization of the shear modulus caused
by the presence of the dislocations is studied in the approximation of
non-interacting dislocation dipoles. It is demonstrated that the finite size of
the dislocation cores results in a modification of the renormalization law.Comment: 20 pages, LaTe