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