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Fractional Nonlocal Continuum Mechanics and Microstructural Models

  • Vasily E. TarasovEmail author
Reference work entry

Abstract

Models of physical lattices with long-range interactions for nonlocal continuum are suggested. The lattice long-range interactions are described by exact fractional-order difference operators. Continuous limit of suggested lattice operators gives continuum fractional derivatives of non-integer orders. The proposed approach gives a new microstructural basis to formulation of theory of nonlocal materials with power-law nonlocality. Moreover these lattice models, which is based on exact fractional differences, allow us to have a unified microscopic description of fractional nonlocal and standard local continuum.

Keywords

Non-local continuum Lattice model Long-range interaction Fractional derivatives Exact differences 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Skobeltsyn Institute of Nuclear PhysicsLomonosov Moscow State UniversityMoscowRussia

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