Gradient Theory of Media with Conserved Dislocations: Application to Microstructured Materials

  • Sergey Lurie
  • Petr Belov
  • Natalia Tuchkova
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 21)


In the paper, a rigorous continuous media model with conserved dislocations is developed. The important feature of the newly developed classification is a new kinematic interpretation of dislocations, which reflects the connection of dislocations with distortion, change in volume (porosity), and free forming. Our model generalizes those previously derived by Mindlin, Cosserat, Toupin, Aero–Kuvshinskii and so on, and refines some assertions of these models from the point of view of the account of adhesive interactions.


Helmholtz Equation Adhesive Interaction Gradient Theory Gradient Model Interphase Layer 
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© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Inst. of Applied Mechanics of RASMoscowRussia
  2. 2.Dorodnicyn Computing Centre of RASMoscowRussia

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