Unified nonlocal rational continuum models developed from discrete atomistic equations

Patra, Amit K and Gopalakrishnan, S and Ganguli, Ranjan (2018) Unified nonlocal rational continuum models developed from discrete atomistic equations. In: INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES, 135 . pp. 176-189.

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Abstract

In this paper, a unified nonlocal rational continuum enrichment technique is presented for improving the dispersive characteristics of some well known classical continuum equations on the basis of atomistic dispersion relations. This type of enrichment can be useful in a wide range of mechanical problems such as localization of strain and damage in many quasibrittle structures, size effects in microscale elastoplasticity, and multiscale modeling of materials. A novel technique of transforming a discrete differential expression into an exact equivalent rational continuum derivative form is developed considering the Taylor's series transformation of the continuous field variables and traveling wave type of solutions for both the discrete and continuum field variables. An exact equivalent continuum rod representation of the 1D harmonic lattice with the non-nearest neighbor interactions is developed considering the lattice details. Using similar enrichment technique in the variational framework, other useful higher-order equations, namely nonlocal rational Mindlin Herrmann rod and nonlocal rational Timoshenko beam equations, are developed to explore their nonlocal properties in general. Some analytical and numerical studies on the high frequency dynamic behavior of these novel nonlocal rational continuum models are presented with their comparison with the atomistic solutions for the respective physical systems. These enriched rational continuum equations have crucial use in studying high-frequency dynamics of many nano-electro-mechanical sensors and devices, dynamics of phononic metamaterials, and wave propagation in composite structures. These new models can help to circumvent the biggest problem regarding size and time restrictions in many atomistic simulations. (C) 2017 Elsevier Ltd. All rights reserved.

Item Type:	Journal Article
Publication:	INTERNATIONAL JOURNAL OF MECHANICAL SCIENCES
Additional Information:	Copy right for this article belong to the PERGAMON-ELSEVIER SCIENCE LTD, THE BOULEVARD, LANGFORD LANE, KIDLINGTON, OXFORD OX5 1GB, ENGLAND
Department/Centre:	Division of Mechanical Sciences > Aerospace Engineering(Formerly Aeronautical Engineering)
Date Deposited:	02 Mar 2018 14:56
Last Modified:	02 Mar 2018 14:56
URI:	http://eprints.iisc.ac.in/id/eprint/59056

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