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2019 | OriginalPaper | Buchkapitel

23. Fractional Nonlocal Continuum Mechanics and Microstructural Models

verfasst von : Vasily E. Tarasov

Erschienen in: Handbook of Nonlocal Continuum Mechanics for Materials and Structures

Verlag: Springer International Publishing

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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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Vorheriges Kapitel Finite Element Analysis of Thermodynamically Consistent Strain Gradient Plasticity Theory and Applications

Nächstes Kapitel Fractional Differential Calculus and Continuum Mechanics

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Titel: Fractional Nonlocal Continuum Mechanics and Microstructural Models
verfasst von: Vasily E. Tarasov
Verlag: Springer International Publishing
Buch: Handbook of Nonlocal Continuum Mechanics for Materials and Structures
Print ISBN: 978-3-319-58727-1

Electronic ISBN: 978-3-319-58729-5

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-319-58729-5_15

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