A review of size-dependent continuum mechanics models for micro-and nano-structures

MA Roudbari, TD Jorshari, C Lü, R Ansari… - Thin-Walled …, 2022 - Elsevier
Recently, the mechanical behavior of micro-/nano-structures has sparked an ongoing
debate, which leads to a fundamental question: what steps can be taken to investigate the …

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 …

Constitutive boundary conditions and paradoxes in nonlocal elastic nanobeams

G Romano, R Barretta, M Diaco… - International Journal of …, 2017 - Elsevier
A debated issue, in applications of Eringen's nonlocal model of elasticity to nanobeams, is
the paradox concerning the solution of simple beam problems, such as the cantilever under …

Size-dependent transverse and longitudinal vibrations of embedded carbon and silica carbide nanotubes by nonlocal finite element method

Ö Civalek, B Uzun, MÖ Yaylı, B Akgöz - The European Physical …, 2020 - epjplus.epj.org
In this study, free vibration analyses of embedded carbon and silica carbide nanotubes lying
on an elastic matrix are performed based on Eringen's nonlocal elasticity theory. These …

Nonlocal elasticity in nanobeams: the stress-driven integral model

G Romano, R Barretta - International Journal of Engineering Science, 2017 - Elsevier
Nonlocal elastic models have attracted an increasing amount of attention in the past years,
due to the promising feature of providing a viable simulation for scale effects in nano …

[HTML][HTML] Bending of Euler–Bernoulli beams using Eringen's integral formulation: a paradox resolved

J Fernandez-Saez, R Zaera, JA Loya… - International Journal of …, 2016 - Elsevier
The Eringen nonlocal theory of elasticity formulated in differential form has been widely used
to address problems in which size effect cannot be disregarded in micro-and nano …

On the analysis of microbeams

Ç Demir, Ö Civalek - International Journal of Engineering Science, 2017 - Elsevier
The most widely used theory in the analysis of nanostructures is Eringen's nonlocal elasticity
theory. But many researchers have mentioned that this theory has a paradox for the …

Vibrations of Bernoulli-Euler beams using the two-phase nonlocal elasticity theory

J Fernández-Sáez, R Zaera - International Journal of Engineering Science, 2017 - Elsevier
In this work the problem of the in-plane free vibrations (axial and bending) of a Bernoulli–
Euler nanobeam using the mixed local/nonlocal Eringen elasticity theory is studied. The …

A unified integro-differential nonlocal model

P Khodabakhshi, JN Reddy - International Journal of Engineering Science, 2015 - Elsevier
In this paper a unified integro-differential nonlocal elasticity model is presented and its use
in the bending analysis of Euler–Bernoulli beams is illustrated. A general (for an elastic …

Nonlocal continuum-based modeling of mechanical characteristics of nanoscopic structures

H Rafii-Tabar, E Ghavanloo, SA Fazelzadeh - Physics Reports, 2016 - Elsevier
Insight into the mechanical characteristics of nanoscopic structures is of fundamental interest
and indeed poses a great challenge to the research communities around the world. These …