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Title: Exact variational nonlocal stress modeling with asymptotic higher-order strain gradients for nanobeams
Authors: Lim, C.W.
Wang, C.M. 
Issue Date: 2007
Citation: Lim, C.W., Wang, C.M. (2007). Exact variational nonlocal stress modeling with asymptotic higher-order strain gradients for nanobeams. Journal of Applied Physics 101 (5) : -. ScholarBank@NUS Repository.
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. © 2007 American Institute of Physics.
Source Title: Journal of Applied Physics
ISSN: 00218979
DOI: 10.1063/1.2435878
Appears in Collections:Staff Publications

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