A derivative-free upscaled theory for analysis of defects

Nowruzpour, Mohsen and Sarkar, Saikat and Reddy, JN and Roy, Debasish (2019) A derivative-free upscaled theory for analysis of defects. In: JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS, 122 . pp. 489-501.

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Abstract

Notwithstanding its recent focus on microstructure-driven nonclassical aspects, a breakthrough model in continuum mechanics that can evolve the macroscopic deformation of a solid body undergoing fracture whilst systematically incorporating the microstructural information remains elusive. In addressing this issue, we presently obtain, based on the molecular level information, a derivativefree balance law pertaining to a higher scale of interest and useful in a continuum or discrete setting. Derived using a probabilistic projection technique, the law exploits certain microstructural information in a weakly unique manner. The projection generalizes the notion of directional derivative and, depending on the application, may be interpreted as a discrete CauchyBorn map with the structure of the classical deformation gradient emerging in the infinitesimal limit. As an illustration, we use the Tersoff-Brenner potential and obtain a discrete macroscopic model for studying the deformation of a singlewalled carbon nanotube (SWCNT). The macroscopic (or continuum) model shows the effect of chirality - a molecular phenomenon - in its deformation profile. We also demonstrate the deformation of a fractured SWCNT, which is a firstofitskind simulation, and predict crack branching phenomena in agreement with molecular dynamics simulations. As another example, we have included simulation results for fractured SWCNT bundle with a view to establishing our claim regarding the efficacy of the proposed method. (C) 2018 Elsevier Ltd. All rights reserved.

Item Type:	Journal Article
Publication:	JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS
Publisher:	PERGAMON-ELSEVIER SCIENCE LTD
Additional Information:	Copy right for this article belong to PERGAMON-ELSEVIER SCIENCE LTD
Keywords:	Carbon nanotube; Crack growth; Upscaling; Stochastic projection
Department/Centre:	Division of Mechanical Sciences > Civil Engineering
Date Deposited:	06 Dec 2018 10:50
Last Modified:	06 Dec 2018 10:50
URI:	http://eprints.iisc.ac.in/id/eprint/61206

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