Second strain gradient elasticity of nano-objects. (December 2016)

• Record Type: Journal Article
• Authors: Cordero, Nicolas M.; Forest, Samuel; Busso, Esteban P.
• Is Part Of: Journal of the mechanics and physics of solids. Volume 97(2016:Dec.)
• Page Start: 92
• Page End: 124
• Publication Date: 2016-12
• Subjects: Third gradient elasticity -- Second strain gradient -- Surface energy -- Surface stress -- Micromorphic continuum -- Nano-wire -- Nano-porous material -- Mechanics of nano-objects -- Apparent elastic moduli; Mechanics, Applied -- Periodicals; Solids -- Periodicals; Mechanics -- Periodicals; Mécanique appliquée -- Périodiques; Solides -- Périodiques; Mechanics, Applied; Solids; Periodicals; 531.05
• DOI: 10.1016/j.jmps.2015.07.012
• Languages: English
• ISSNs: 0022-5096

Abstract

Abstract: Mindlin's second strain gradient continuum theory for isotropic linear elastic materials is used to model two different kinds of size-dependent surface effects observed in the mechanical behaviour of nano-objects. First, the existence of an initial higher order stress represented by Mindlin's cohesion parameter, b 0, makes it possible to account for the relaxation behaviour of traction-free surfaces. Second, the higher order elastic moduli, c i, coupling the strain tensor and its second gradient are shown to significantly affect the apparent elastic properties of nano-beams and nano-films under uni-axial loading. These two effects are independent from each other and allow for separated identification of the corresponding material parameters. Analytical results are provided for the size-dependent apparent shear modulus of a nano-thin strip under shear. Finite element simulations are then performed to derive the dependence of the apparent Young modulus and Poisson ratio of nano-films with respect to their thickness, and to illustrate hole free surface relaxation in a periodic nano-porous material.