Review on nonlocal continuum mechanics: physics, material applicability, and mathematics

M Shaat, E Ghavanloo, SA Fazelzadeh - Mechanics of Materials, 2020 - Elsevier
The classical continuum mechanics assumes that a material is a composition of an infinite
number of particles each of which is a point that can only move and interact with its nearest …

[HTML][HTML] Exact solutions for the static bending of Euler-Bernoulli beams using Eringen's two-phase local/nonlocal model

YB Wang, XW Zhu, HH Dai - Aip Advances, 2016 - pubs.aip.org
Though widely used in modelling nano-and micro-structures, Eringen's differential model
shows some inconsistencies and recent study has demonstrated its differences between the …

Buckling analysis of Euler–Bernoulli beams using Eringen's two-phase nonlocal model

X Zhu, Y Wang, HH Dai - International Journal of Engineering Science, 2017 - Elsevier
The inconsistency of Eringen's nonlocal differential model, as applied to investigate
nanostructures, has recently triggered the study of nonlocal integral models. In this paper we …

Stress-driven nonlocal integral model for Timoshenko elastic nano-beams

R Barretta, R Luciano, FM de Sciarra, G Ruta - European Journal of …, 2018 - Elsevier
Size-dependent structural behavior of inflected Timoshenko elastic nano-beams is
investigated by nonlocal continuum mechanics. An innovative stress-driven integral model …

Size-dependent generalized thermoelasticity using Eringen's nonlocal model

YJ Yu, XG Tian, XR Liu - European Journal of Mechanics-A/Solids, 2015 - Elsevier
Ultrafast lasers, even the novel laser burst technology, have been widely using in numerous
applications, especially in micro-machining. The mechanism of ultrafast laser and matter …

Nonlocal inflected nano-beams: A stress-driven approach of bi-Helmholtz type

R Barretta, SA Fazelzadeh, L Feo, E Ghavanloo… - Composite …, 2018 - Elsevier
Size-dependent bending behavior of Bernoulli-Euler nano-beams is investigated by
elasticity integral theory. Eringen's strain-driven nonlocal integral formulation, providing the …

On integral and differential formulations in nonlocal elasticity

J Kaplunov, DA Prikazchikov… - European Journal of …, 2023 - Elsevier
The paper is concerned with comparative analysis of differential and integral formulations for
boundary value problems in nonlocal elasticity. For the sake of simplicity, the focus is on an …

Coupling of 2D discretized peridynamics with a meshless method based on classical elasticity using switching of nodal behaviour

A Shojaei, M Zaccariotto, U Galvanetto - Engineering Computations, 2017 - emerald.com
Purpose The paper aims to use a switching technique which allows to couple a nonlocal
bond-based Peridynamic approach to the Meshless Local Exponential Basis Functions …

The strain gradient elasticity via nonlocal considerations

T Gortsas, DG Aggelis, D Polyzos - International Journal of Solids and …, 2023 - Elsevier
Strain gradient elasticity and nonlocal elasticity are two enhanced elastic theories
intensively used over the last fifty years to explain static and dynamic phenomena that …

Analogies between nonlocal and local Bernoulli–Euler nanobeams

R Barretta, F Marotti de Sciarra - Archive of Applied Mechanics, 2015 - Springer
Small-scale effects in nanobeams are effectively described by the E ringen model of
nonlocal elasticity. The nonlocal elastostatic problem of B ernoulli–E uler nanobeams is …