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Handbook of Nonlocal Continuum Mechanics for Materials and Structures pp 1–11Cite as

Fractional Nonlocal Continuum Mechanics and Microstructural Models

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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.

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Authors and Affiliations

  1. Skobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, 119991, Moscow, Russia

    Vasily E. Tarasov

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  1. Vasily E. Tarasov
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Correspondence to Vasily E. Tarasov .

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Editors and Affiliations

  1. Department of Civil and Environmental Engineering, Louisiana State University, Baton Rouge, USA

    George Z. Voyiadjis

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Tarasov, V.E. (2017). Fractional Nonlocal Continuum Mechanics and Microstructural Models. In: Voyiadjis, G. (eds) Handbook of Nonlocal Continuum Mechanics for Materials and Structures. Springer, Cham. https://doi.org/10.1007/978-3-319-22977-5_15-1

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  • DOI: https://doi.org/10.1007/978-3-319-22977-5_15-1

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  • Print ISBN: 978-3-319-22977-5

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