Limit behaviour of Eringen’s two-phase elastic beams

In this paper, the bending behaviour of small-scale Bernoulli–Euler beams is investigated by Eringen’s two-phase local/nonlocal theory elasticity. Bending moments are expressed in terms elastic curvatures a convex combination local and nonlocal contributions, that with non-negative scalar coefficients summing to unity. The contribution convolution integral curvature field suitable averaging kernel characterized scale parameter. relevant structural problem, well-posed for non-vanishing phases, preliminarily formulated exact solutions some simple beam problems recalled. Limit behaviours obtained solutions, analytically evaluated, studied diagrammed, do not fulfil equilibrium requirements kinematic boundary conditions. Accordingly, unlike alleged claims literature, such asymptotic fields cannot be assumed as purely This conclusion agrees known result which problem engineering interest admits no solution.