An explicit mechanical interpretation of Eringen non-local elasticity by means of fractional calculus

Keywords

Fractional calculus, Elasticity (physics), Mathematics, Calculus (dental), Constitutive equation

References

• Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical ModelsFrancesco Mainardi — 2010
• Fractals and fractional calculus in continuum mechanicsAlberto Carpinteri, Francesco Mainardi — 1997
• Fluid viscous device modelling by fractional derivativesVittorio Gusella, Gloria Terenzi — 1997
• ON FRACTIONAL INTEGRALS AND DERIVATIVESH. Kober — 1940
• Discrete random walk models for space-time fractional diffusionRudolf Gorenflo, Francesco Mainardi, Daniele Moretti — 2002
• Scaling Laws and Multiscale Approach in the Mechanics of Heterogeneous and Disordered MaterialsAlberto Carpinteri, Pietro Cornetti, Simone Puzzi — 2006
• Nonlocal elasticity and related variational principlesCastrenze Polizzotto — 2001
• A fractional calculus approach to the description of stress and strain localization in fractal mediaAlberto Carpinteri, Pietro Cornetti — 2002
• Gradient Effects at Macro, Micro, and Nano ScalesElias C. Aifantis — 1994

Cited by

• Wave propagation in fractional nonlocal elastic continuaAlberto Sapora, Pietro Cornetti, Alberto Carpinteri — 2013
• Nonlocal elasticity: an approach based on fractional calculusAlberto Carpinteri, Pietro Cornetti, Alberto Sapora — 2014
• Lattice model with power-law spatial dispersion for fractional elasticityVasily Tarasov — 2013
• Three-dimensional lattice models with long-range interactions of Grünwald–Letnikov type for fractional generalization of gradient elasticityVasily E. Tarasov — 2016
• Fractional Gradient Elasticity from Spatial Dispersion LawVasily E. Tarasov — 2013
• Lattice Model of Fractional Gradient and Integral Elasticity: Long-Range Interaction of Grunwald-Letnikov-Riesz TypeVasily E. Tarasov — 2014
• Wave propagation in nonlocal elastic continua modelled by a fractional calculus approachAlberto Sapora, Pietro Cornetti, Alberto Carpinteri — 2013
• Fractional Mechanics of Elastic Solids: Continuum AspectsVasily E. Tarasov — 2017
• Mathematical models for nonlocal elastic composite materialsGiuseppina Autuori, Federico Cluni, Vittorio Gusella — 2017
• Longitudinal waves in a nonlocal rod by fractional LaplacianGiuseppina Autuori, Federico Cluni, Vittorio Gusella — 2018
• Fractional derivative heat conduction modeling based on thermal elements combinationJun Fang, HongGuang Sun, Cuiping Zhang — 2019
• The fractional constitutive models for nonlocal material based on scattering wave equationsJun Fang, Sven Peter Näsholm, Wen Chen — 2020
• Fractional Calculus Applied to Fractal Media and Nonlocal ContinuaA. Carpinteri — 2021
• FRACTIONAL CALCULUS APPROACH FOR WAVE PROPAGATION IN NONLOCAL ONE DIMENSIONAL ELASTIC SOLIDS (FRACTIONAL CALCULUS)B. Yakaiah — 2017
• Fractional gradient elasticity from spatial dispersion lawVasily E. Tarasov — 2016

Related papers

• Elastic waves propagation in 1D fractional non-local continuumGiulio Cottone, Mario Di Paola, Massimiliano Zingales — 2009
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• Non-local continuum mechanics and fractional calculusK.A. Lazopoulos — 2006
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• Fractional Calculus and Waves in Linear Viscoelasticity: An Introduction to Mathematical ModelsFrancesco Mainardi — 2010
• Fractals and fractional calculus in continuum mechanicsAlberto Carpinteri, Francesco Mainardi — 1997
• Continuous limit of discrete systems with long-range interactionVasily E. Tarasov — 2006
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