Journal of Mathematical Physics, Analysis, Geometry
2019, vol. 15, No 2, pp. 203-224   https://doi.org/10.15407/mag15.02.203     ( to contents , go back )
https://doi.org/10.15407/mag15.02.203

Nonlocal Elasticity Theory as a Continuous Limit of 3D Networks of Pointwise Interacting Masses

Mariya Goncharenko

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine
E-mail: marusya61@yahoo.co.uk

Eugen Khruslov

B. Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, 47 Nauky Ave., Kharkiv, 61103, Ukraine
E-mail: khruslov@ilt.kharkov.ua

Received January 22, 2018, revised April 13, 2018

Abstract

Small oscillations of an elastic system of point masses (particles) with a nonlocal interaction are considered. The asymptotic behavior of the system is studied when a number of particles tend to infinity and the distances between them and the forces of interaction tend to zero. The first term of the asymptotic is described by the homogenized system of equations, which is a nonlocal model of oscillations of elastic medium.

Mathematics Subject Classification 2000: 35Q70, 35Q74, 35B27.
Key words: nonlocal elasticity, homogenization, integral model, Eringen model.

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