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A modified approximation of the exponential Cauchy‐Born rule for arbitrary shell‐like nanostructures
Author(s) -
Findeisen Claudio,
Wackerfuß Jens
Publication year - 2014
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201410270
Subject(s) - planar , cauchy distribution , finite element method , shell (structure) , exponential function , mathematics , mathematical analysis , physics , materials science , computer science , composite material , computer graphics (images) , thermodynamics
The mechanical behaviour of shell‐like nanostructures, such as carbon nanotubes (CNT) can be described within the continuum mechanics by a generalisation of the Cauchy‐Born (CB) rule, introduced by Arroyo and Belytschko [1]. However, the finite element approximation presented in the literature requires the reference configuration to be planar. In case the configuration of interest is initially not planar, a preprocessing step is required that isometrically maps the planar reference configuration into the initial configuration. In order to calculate more complex structures, in this paper an extended finite element approximation is presented which is applicable to shell‐like atomic structures, whose reference configuration does not need to be planar and consequently the afore‐mentioned steps are no longer necessary. The accuracy of the proposed model is verified by two numerical examples. (© 2014 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)