Vol. 11, No. 4, 2016

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ISSN: 1559-3959
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