One-dimensional nonlocal and gradient elasticity: Closed-form solution and size effect

The equivalence between nonlocal and gradient elasticity models is investigated by making reference to one-dimensional boundary value problems equipped with two integral stress-strain laws proposed by Eringen (Nonlocal Continuum Field Theories (2002)). Corresponding closed-form solutions are derived through a procedure for the reduction of integral to differential equations. The reproduction of size effects in micro/nano rods is discussed. The differential formulation associated with the local/nonlocal model is shown to correspond to the strain-gradient formulation proposed by Aifantis (Mech. Mater. 35 (2003) 259-280). (C) 2012 Elsevier Ltd. All rights reserved.