Modelling issues and advances in nonlocal beams mechanics

Nonlocal continuum mechanics presents still open questions about applicability of integral constitutive theories to nanostructures of current interest in Engineering Science. Nevertheless, nonlocal elasticity is widely exploited to model size effects in small-scale structures since it represents an effective tool to avoid computationally expensive procedures. The known strain-driven approach proposed by Eringen has shown an intrinsic incompatibility between constitutive and equilibrium requirements when applied to structures. Such an issue has been acknowledged by the scientific community merely for bounded continua. For structural problems defined in unbounded domains, obstruction to equilibrium caused by the strain-driven formulation is a still open issue. The present contribution definitely proves inapplicability of the strain-driven spatial convolution to structural mechanics and proposes a consistent nonlocal approach for both bounded and unbounded structures. The presented methodology is based on stress-driven spatial convolutions, representing the key paradigm to formulate a well-posed theory of integral elasticity and to effectively model scale effects in nanobeams of applicative interest in Nano-Mechanics.