The present paper studies non-uniform plastic deformations of crystalsundergoing anti-plane constrained shear. The asymptotically exact energydensity of crystals containing a moderately large density of excessdislocations is found by the averaging procedure. This energy density isextrapolated to the cases of extremely small or large dislocation densities. Byincorporating the configurational temperature and the density of redundantdislocations, we develop the thermodynamic dislocation theory for non-uniformplastic deformations and use it to predict the stress-strain curves and thedislocation densities.
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