Nonlocal gradient mechanics of nanobeams for non-smooth fields

Nonlocal continuum theories are investigated in the case of non-smooth fields representing the most general condition in mechanics of nanobeams. The treatment starts from the gen-eral formulation of elasticity provided by the abstract form of nonlocal gradient theory for nanobeams. The equivalent differential problem is then derived to reverse the constitutive law. Such a formulation requires prescription of non-classical interface conditions at discontinuity abscissae that play a fundamental role to close the relevant differential problem. In this paper, the simplest constitutive interface conditions not involving spatial convolutions are established, thus providing a significant improvement of the treatment contributed in Caporale et al. (2022) in which interface conditions are complexly formulated in terms of spatial convolutions. The developed differential scheme is fundamental for theoretical and computational purposes and plays a key role for strain-driven based models for which inversion of the constitutive law is essential to explicitly get the unknown solution fields. Exemplar continuum problems are finally analyzed and discussed to show merits and effectiveness of the proposed formulation in comparison with previous treatments in literature.

Automated summary

Nonlocal continuum theories are applied to investigate the mechanics of nanobeams under non-smooth fields. The study starts with the general formulation of elasticity in nanobeams based on the abstract form of nonlocal gradient theory. The equivalent differential problem is derived to determine the constitutive law, and the simplest constitutive interface conditions not involving spatial convolutions are established.