Exact variational nonlocal stress modeling with asymptotic higher-order strain gradients for nanobeams

Lim, C. W. and Wang, C. M. (2007) Exact variational nonlocal stress modeling with asymptotic higher-order strain gradients for nanobeams. Journal of Applied Physics, 101 5: . doi:10.1063/1.2435878

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Author Lim, C. W.
Wang, C. M.
Title Exact variational nonlocal stress modeling with asymptotic higher-order strain gradients for nanobeams
Journal name Journal of Applied Physics   Check publisher's open access policy
ISSN 0021-8979
1089-7550
Publication date 2007-01-01
Year available 2006
Sub-type Article (original research)
DOI 10.1063/1.2435878
Open Access Status File (Publisher version)
Volume 101
Issue 5
Total pages 7
Place of publication Melville, NY, United States
Publisher A I P Publishing LLC
Language eng
Abstract This article presents a complete and asymptotic representation of the one-dimensional nanobeam model with nonlocal stress via an exact variational principle approach. An asymptotic governing differential equation of infinite-order strain gradient model and the corresponding infinite number of boundary conditions are derived and discussed. For practical applications, it explores and presents a reduced higher-order solution to the asymptotic nonlocal model. It is also identified here and explained at length that most publications on this subject have inaccurately employed an excessively simplified lower-order model which furnishes intriguing solutions under certain loading and boundary conditions where the results become identical to the classical solution, i.e., without the small-scale effect at all. Various nanobeam examples are solved to demonstrate the difference between using the simplified lower-order nonlocal model and the asymptotic higher-order strain gradient nonlocal stress model. An important conclusion is the discovery of significant over- or underestimation of stress levels using the lower-order model, particularly at the vicinity of the clamped end of a cantilevered nanobeam under a tip point load. The consequence is that the design of a nanobeam based on the lower-order strain gradient model could be flawed in predicting the nonlocal stress at the clamped end where it could, depending on the magnitude of the small-scale parameter, significantly over- or underestimate the failure criteria of a nanobeam which are governed by the level of stress.
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
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