Axial and flexional behaviour of elastic nano-beams by stress-driven two-phase elasticity

Size-dependent structural behaviour of axially functionally graded nanobeams with non-uniform cross-section under axial and transversal loads is investigated by two-phase integral stress-driven elasticity. An effective nonlocal model is used by introducing a convex combination of the purely nonlocal integral stress-driven relation with a local phase. The stress-driven nonlocal model does not show ill-posedness behaviours such as the Eringen strain-driven model and leads to well-posed elastostatic nonlocal problems in all cases of technical interest. In particular, the integral convolution of the two-phase mixture is obtained by considering the bi-exponential kernel. A nanocantilever subject to an axial or a transversal force at the tip is considered. The nonlocal integral stress-driven model is solved and transversal and axial displacements are evaluated