Journal of Mathematical Sciences

, Volume 213, Issue 5, pp 750–755 | Cite as

The Einstein-Like Field Theory and Renormalization of the Shear Modulus

  • C. Malyshev

The Einstein-like field theory is developed to describe an elastic solid containing distribution of screw dislocations with finite-sized core. The core self-energy is given by a gauge-translational Lagrangian that is quadratic in torsion tensor and corresponding to the three-dimensional Riemann–Cartan geometry. The Hilbert–Einstein gauge equation plays the role of unconventional incompatibility law. The stress tensor of the modified screw dislocations is smoothed within the core. The renormalization of the shear modulus caused by proliferation of dipoles of nonsingular screw dislocations is studied. Bibliography: 23 titles.


Shear Modulus Screw Dislocation Dislocation Core Torsion Tensor Dislocation Dipole 
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© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.St.Petersburg Department of the Steklov Mathematical InstituteITMO UniversitySt. PetersburgRussia

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