Archive of Applied Mechanics

, Volume 89, Issue 3, pp 467–483 | Cite as

Non-uniform plastic deformations of crystals undergoing anti-plane constrained shear

  • K. C. LeEmail author
  • Y. Piao


The present paper studies non-uniform plastic deformations of crystals undergoing anti-plane constrained shear. The asymptotically exact energy density of crystals containing a moderately large density of excess dislocations is found by the averaging procedure. This energy density is extrapolated to the cases of extremely small or large dislocation densities. Taking into account the configurational temperature and the density of redundant dislocations, we develop the thermodynamic dislocation theory for non-uniform plastic deformations and use it to predict stress–strain curves and dislocation densities.


Dislocations Thermodynamics Energy Disorder temperature Size effect 



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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Materials Mechanics Research GroupTon Duc Thang UniversityHo Chi Minh CityVietnam
  2. 2.Faculty of Civil EngineeringTon Duc Thang UniversityHo Chi Minh CityVietnam
  3. 3.Lehrstuhl für Mechanik - MaterialtheorieRuhr-Universität BochumBochumGermany

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