Journal of Mechanics of Materials and Structures Vol. 11, No. 4, 2016

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What discrete model corresponds exactly to a gradient elasticity equation?

Vasily E. Tarasov

Vol. 11 (2016), No. 4, 329–343

DOI: 10.2140/jomms.2016.11.329

Abstract

In this paper, we obtain exact discrete analogs of the gradient elasticity equations. The suggested discrete equations have differences represented by infinite series. Physically, these equations describe models of lattices with long-range interactions. Mathematically, unique difference equations correspond exactly to continuum gradient elasticity equations.

Keywords

elasticity, gradient elasticity, long-range interactions, exact discretization, difference equation

Milestones

Received: 9 August 2015

Revised: 16 February 2016

Accepted: 28 February 2016

Published: 4 August 2016

Authors

Vasily E. Tarasov
Skobeltsyn Institute of Nuclear Physics Lomonosov Moscow State University Leninskie gory GSP-1 Moscow 119991 Russia