Constitutive boundary conditions for nonlocal strain gradient elastic nano-beams

Nonlocal strain gradient integral model of elasticity, extension of the fully nonlocal integral law, is widely adopted to assess size effects in nano-beams. The bending moment is sum of convolutions of elastic curvature and of its derivative with a smoothing kernel. For nanomechanical problems on unbounded domains, such as in wave propagation, the nonlocal strain gradient integral relation is equivalent to a differential law with constitutive...