Lattice model with power-law spatial dispersion for fractional elasticity

• Authors: Vasily Tarasov
• Languages of publication: EN

Abstracts

EN

A lattice model with a spatial dispersion corresponding to a power-law type is suggested. This model serves as a microscopic model for elastic continuum with power-law non-locality. We prove that the continuous limit maps of the equations for the lattice with the power-law spatial dispersion into the continuum equations with fractional generalizations of the Laplacian operators. The suggested continuum equations, which are obtained from the lattice model, are fractional generalizations of the integral and gradient elasticity models. These equations of fractional elasticity are solved for two special static cases: fractional integral elasticity and fractional gradient elasticity.

Keywords

EN

fractional derivatives; lattice model; spatial dispersion; elasticity; fractional elasticity

• Publisher: De Gruyter Open
• Journal: Open Physics
• Year: 2013
• Volume: 11
• Issue: 11
• Pages: 1580-1588

Dates

published

1 - 11 - 2013

online

10 - 12 - 2013

Contributors

author

Vasily Tarasov

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

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Identifiers

DOI

10.2478/s11534-013-0308-z