If the attenuation function of strain is expressed as a power law, the formalism of fractional calculus may be used to handle Eringen non-local elastic model. Aim of the present paper is to provide a mechanical interpretation to this non-local fractional elastic model by showing that it is equivalent to a discrete, point-spring model. A one-dimensional geometry is considered; static, kinematic and constitutive equations as well as the proper boundary conditions are derived and discussed.
Carpinteri, A., Cornetti, P., Sapora, A., Di Paola, M., Zingales, M. (2009). An explicit mechanical interpretation of Eringen non-local elasticity by means of fractional calculus. In Atti del 19. Congresso dell’Associazione Italiana di Meccanica Teorica e Applicata : Ancona, 14-17 settembre 2009. ancona : ares.
An explicit mechanical interpretation of Eringen non-local elasticity by means of fractional calculus
DI PAOLA, Mario;ZINGALES, Massimiliano
2009-01-01
Abstract
If the attenuation function of strain is expressed as a power law, the formalism of fractional calculus may be used to handle Eringen non-local elastic model. Aim of the present paper is to provide a mechanical interpretation to this non-local fractional elastic model by showing that it is equivalent to a discrete, point-spring model. A one-dimensional geometry is considered; static, kinematic and constitutive equations as well as the proper boundary conditions are derived and discussed.
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