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

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Abstract

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.

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Authors and Affiliations

  1. Department of Structures for Engineering and Architecture, University of Naples Federico II, via Claudio 21, 80125, Naples, Italy

    Giovanni Romano, Raffaele Barretta & Marina Diaco

  2. Department of Civil and Mechanical Engineering, University of Cassino and Southern Lazio, via Di Biasio 43, 03043, Cassino, FR, Italy

    Raimondo Luciano

Authors
  1. Giovanni Romano
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  2. Raimondo Luciano
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  3. Raffaele Barretta
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  4. Marina Diaco
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Correspondence to Raffaele Barretta.

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Communicated by Andreas Öchsner.

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Romano, G., Luciano, R., Barretta, R. et al. Nonlocal integral elasticity in nanostructures, mixtures, boundary effects and limit behaviours. Continuum Mech. Thermodyn. 30, 641–655 (2018). https://doi.org/10.1007/s00161-018-0631-0

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  • DOI: https://doi.org/10.1007/s00161-018-0631-0

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