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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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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