An asymptotic multi-scale approach for beams via strain gradient elasticity: surface effects

- Journal title : Multiscale and Multiphysics Mechanics
- Volume 1, Issue 1, 2016, pp.15-33
- Publisher : Techno-Press
- DOI : 10.12989/mmm.2016.1.1.015

Title & Authors

An asymptotic multi-scale approach for beams via strain gradient elasticity: surface effects

Kim, Jun-Sik;

Kim, Jun-Sik;

Abstract

In this paper, an asymptotic method is employed to formulate nano- or micro-beams based on strain gradient elasticity. Although a basic theory for the strain gradient elasticity has been well established in literature, a systematic approach is relatively rare because of its complexity and ambiguity of higher-order elasticity coefficients. In order to systematically identify the strain gradient effect, an asymptotic approach is adopted by introducing the small parameter which represents the beam geometric slenderness and/or the internal atomistic characteristic. The approach allows us to systematically split the two-dimensional strain gradient elasticity into the microscopic one-dimensional through-the-thickness analysis and the macroscopic one-dimensional beam analysis. The first-order beam problem turns out to be different from the classical elasticity in terms of the bending stiffness, which comes from the through-the-thickness strain gradient effect. This subsequently affects the second-order transverse shear stress in which the surface shear stress exists. It is demonstrated that a careful derivation of a first strain gradient elasticity embraces "Gurtin-Murdoch traction" as the surface effect of a one-dimensional Euler-Bernoulli-like beam model.

Keywords

strain gradient elasticity;size effect;surface tension;asymptotic method;

Language

English

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