Nonlocal integral elasticity in nanostructures, mixtures, boundary effects and limit behaviours

Nonlocal elasticity is addressed in terms of integral convolutions for structural models of any dimension, that is bars, beams, plates, shells and 3D continua. A characteristic feature of the treatment is the recourse to the theory of generalised functions (distributions) to provide a unified presentation of previous proposals. Local-nonlocal mixtures are also included in the analysis. Boundary effects of convolutions on bounded domains are investigated, and analytical evaluations are provided in the general case. Methods for compensation of boundary effects are compared and discussed with a comprehensive treatment. Estimates of limit behaviours for extreme values of the nonlocal parameter are shown to give helpful information on model properties, allowing for new comments on previous proposals. Strain-driven and stress-driven models are shown to emerge by swapping the mechanical role of input and output fields in the constitutive convolution, with stress-driven elastic model leading to well-posed problems. Computations of stress-driven nonlocal one-dimensional elastic models are performed to exemplify the theoretical results.