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A well-posed stress-driven mixture is proposed for Timoshenko nano-beams. Themodel is a convex combination of local and nonlocal phases and circumvents someproblems of ill-posedness emerged in strain-driven Eringen-like formulationsfor structures of nanotechnological interest. The nonlocal part of the mixtureis the integral convolution between stress field and a bi-exponential averagingkernel function characterized by a scale parameter. The stress-driven mixtureis equivalent to a differential problem equipped with constitutive boundaryconditions involving bending and shear fields. Closed-form solutions ofTimoshenko nano-beams for selected boundary and loading conditions areestablished by an effective analytical strategy. The numerical results exhibita stiffening behavior in terms of scale parameter.

A stress-driven local-nonlocal mixture model for Timoshenko nano-beams