A derivative-free upscaled theory for analysis of defects. (January 2019)

• Record Type: Journal Article
• Authors: Nowruzpour, Mohsen; Sarkar, Saikat; Reddy, J.N.; Roy, Debasish
• Is Part Of: Journal of the mechanics and physics of solids. Volume 122(2019)
• Page Start: 489
• Page End: 501
• Publication Date: 2019-01
• Subjects: Carbon nanotube -- Crack growth -- Upscaling -- Stochastic projection; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2018.09.018
• Languages: English
• ISSNs: 0022-5096

Abstract

Abstract: Notwithstanding its recent focus on microstructure-driven non-classical 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 derivative-free 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 Cauchy–Born 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 single-walled 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 first-of-its-kind 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.