Gradient elasticity and flexural wave dispersion in carbon nanotubes

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Some links between recent gradient thermo-elasto-plasticity theories and the thermomechanics of generalized continua (2010, background): “More recently, generalized continuum elasticity theories of a nonlocal or gradient type have also been used to capture the mechanical behavior of nanotubes, e.g. (Zhang et al., 2005; Wang and Hu, 2005; Askes and Aifantis, 2009).”
A review on the mechanics of nanostructures (2018, background): “This stiffness hardening can be estimated incorporating surface effects [75-80] or strain gradients [52, 53, 81-86].”
Gradient elasticity in statics and dynamics: An overview of formulations, length scale identification procedures, finite element implementations and new results (2011, methodology): “For the Timoshenko beam theory, we have provided solutions for the angular frequency in (Askes and Aifantis, 2009) which demonstrate that cut-off frequencies do not occur if combined strain/inertia gradients are used.”