Nonlocal Gradient Mechanics of Elastic Beams Under Torsion

Nonlocal gradient mechanics of elastic beams subject to torsion is established by means of a variationally consistent methodology, equipped with suitable functional spaces of test fields. The proposed elasticity theory is the generalization of size-dependent models recently contributed in literature to assess size-effects in nano-structures, such as modified nonlocal strain gradient and strain- and stress-driven local/nonlocal elasticity formulations. General new ideas are elucidated by examining the torsional behavior of elastic nano-beams. Equivalence between nonlocal integral convolutions and differential problems subject to variationally consistent boundary conditions is demonstrated for special averaging kernels. The variational procedure leads to well-posed engineering problems in nano-mechanics. Elasto-static responses and free vibrations of nano-beams under torsion are analyzed applying an effective analytical solution technique. Nonlocal strain- and stress-driven gradient models of elasticity can efficiently predict both stiffening and softening structural responses, and thus, notably characterize small-scale phenomena in structures exploited in modern Nano-Electro-Mechanical-Systems (NEMS).