A gradient Eringen model for functionally graded nanorods

Small-scale effects in nanorods with Young moduli which are functionally graded in the cross-section domain are investigated by nonlocal continuum mechanics. A gradient version of the Eringen uniaxial elastic model is proposed, improving thus the standard Eringen and gradient models of the elasticity theory. The ensuing nonlocal elastic equilibrium problem of a nanorod is formulated in variational terms by following a thermodynamic approach. Closed-form expressions of axial displacements and forces are established for cantilevers and fully clamped nanorods, by integrating the differential equation of elastic equilibrium under prescribed boundary conditions. New benchmarks for numerical analyses are thus detected. Merits of the new nonlocal model, in comparison with existing treatments, are also emphasized