Non-local elasticity theory as a continuous limit of 3D networks of pointwise interacting masses

Abstract

Small oscillations of an elastic system of point masses (particles) with a nonlocal interaction are considered. We study the asymptotic behavior of the system, when number of particles tends to infinity, and the distances between them and the forces of interaction tends 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.