Eur. Phys. J. Special Topics 193, 193-204 (2011)
https://doi.org/10.1140/epjst/e2011-01391-5

Regular Article

A fractional calculus approach to nonlocal elasticity

Department of Structural Engineering and Geotechnics, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

^a e-mail: pietro.cornetti@polito.it

Received: 1 December 2010
Revised: 27 January 2011
Published online: 4 April 2011

Abstract

If the attenuation function of strain is expressed as a power law, the formalism of fractional calculus may be used to handle Eringen nonlocal elastic model. Aim of the present paper is to provide a mechanical interpretation to this nonlocal fractional elastic model by showing that it is equivalent to a discrete, point-spring model. A one-dimensional geometry is considered; the static, kinematic and constitutive equations are presented and the governing fractional differential equation highlighted. Two numerical procedures to solve the fractional equation are finally implemented and applied to study the strain field in a finite bar under given edge displacements.