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Meccanica
Published in: Meccanica 1/2016

01-05-2015

Three-dimensional lattice models with long-range interactions of Grünwald–Letnikov type for fractional generalization of gradient elasticity

Author: Vasily E. Tarasov

Published in: Meccanica | Issue 1/2016

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Abstract

Models of three-dimensional lattices with long-range interactions of Grünwald–Letnikov type for fractional gradient elasticity of non-local continuum are suggested. The lattice long-range interactions are described by fractional-order difference operators. Continuous limit of suggested three-dimensional lattice equations gives continuum differential equations with the Grünwald–Letnikov derivatives of non-integer orders. The proposed lattice models give a new microstructural basis for elasticity of materials with power-law type of non-locality. Moreover these lattice models allow us to have a unified microscopic description for fractional and usual (non-fractional) gradient elasticity continuum.
previous article Dual solutions of heat and mass transfer of nanofluid over a stretching/shrinking sheet with thermal radiation
next article Dynamic response of functionally graded cylinders due to time-dependent heat flux

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Metadata
Title
Three-dimensional lattice models with long-range interactions of Grünwald–Letnikov type for fractional generalization of gradient elasticity
Author
Vasily E. Tarasov
Publication date
01-05-2015
Publisher
Springer Netherlands
Published in
Meccanica / Issue 1/2016
Print ISSN: 0025-6455
Electronic ISSN: 1572-9648
DOI
https://doi.org/10.1007/s11012-015-0190-4

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