Size-dependent elastic properties of nanosized structural elements

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Size-dependent elastic properties of unidirectional nano-composites with interface stresses (2007, methodology): “The material properties of the matrix are recorded from [11] for aluminium (Kf ¼ 75:2 GPa; mf ¼ 0:3Þ: Note that K is the isotropic bulk modulus and l is the shear modulus, which are related to Hill’s moduli by k ¼ K þ l=3; l ¼ p ¼ m: The free surface properties were extracted from the existing liter”
Anomalous Compliance and Early Yielding of Nanoporous Gold (2015, background): “Surface excess elasticity is an obvious explanation [79, 80], and is supported by the observation of large changes in the stiffness when the surface state is reversibly varied [35], yet an agreement on the sign of the surface excess elastic constants, stiffer or more compliant than bulk, has”
On the shell theory on the nanoscale with surface stresses (2011, background): “…us note that even for nanostructures as nanoshells, nanofilms, and nanoplates the continuum approach gives a satisfying coincidence with atomistic simulations, if one takes into account the appropriate constitutive equations, see e.g. (Kudin et al., 2001; Miller & Shenoy, 2000; Peng et al., 2008).”
Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films (2005, background): “More recently, Miller and Shenoy (2000) developed a simple model to incorporate surface stress in determining the size-dependent elastic modulus of plates and rods.”