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Petersburg Department of Steklov Institute of Mathematics

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PREPRINT 3/1999

C. MALYSHEV
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THE DISLOCATION STRESS FUNCTIONS FROM THE DOUBLE CURL T(3)-GAUGE EQUATION:
LINEARITY AND A LOOK BEYOND

This preprint was accepted January 25, 1999

Contact:
` C. Malyshev `

ABSTRACT:
$T(3)$-gauge model of defects based on the gauge Lagrangian
quadratic in the gauge field strength is considered. The equilibrium
equation of the medium is fulfilled by the double curl Kr\"oner's
ansatz for stresses. The problem of replication of the static edge
dislocation along third axis is analysed under a special, though
conventional, choice of this ansatz.
The translational gauge equation is shown to constraint the
functions parametrizing the ansatz (the stress functions) so that the
resulting stress component $\sigma_{3 3}$ is not that of the edge
defect. Another translational gauge equation with the double curl
differential operator is shown to reproduce both the stress functions,
as well as the stress tensors, of the standard edge and screw
dislocations. Non-linear extension of the newly proposed translational
gauge equation is given to correct the linear defect solutions in next
orders. New gauge Lagrangian is suggested in the Hilbert--Einstein form.

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