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Second strain gradient elasticity of nano-objects

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, b0, makes it possible to account for the relaxation behaviour of traction-free surfaces. Second, the higher order elastic moduli, ci, 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.
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Nicolas M. Cordero, Samuel Forest, Esteban P. Busso. Second strain gradient elasticity of nano-objects. Journal of the Mechanics and Physics of Solids, Elsevier, 2016, 97, pp.92-124. ⟨10.1016/j.jmps.2015.07.012⟩. ⟨hal-01424985⟩



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