Timoshenko nonlocal strain gradient nanobeams: Variational consistency, exact solutions and carbon nanotube Young moduli

TL;DR

This paper develops a variationally consistent nonlocal strain gradient model for Timoshenko nanobeams, specifically applied to carbon nanotubes, providing analytical solutions validated by molecular dynamics simulations.

Contribution

It introduces a novel nonlocal strain gradient approach for Timoshenko nanobeams that extends previous models to include scale effects and provides analytical estimates of CNT Young's moduli.

Findings

Analytical solutions for CNT Young's moduli are derived.

Model predictions are validated by molecular dynamics simulations.

The approach captures size-dependent mechanical behavior of CNTs.

Abstract

Carbon nanotubes (CNTs) are principal constituents of nanocomposites and nano-systems. CNT size-dependent response assessment is therefore a topic of current interest in Mechanics of Advanced Materials and Structures. CNTs are modeled here by a variationally consistent nonlocal strain gradient approach for Timoshenko nano-beams, extending the treatment in [Int. J. Eng. Science 143 (2019) 73-91] confined to slender structures. Scale effects are described by integral convolutions, conveniently replaced with differential and boundary nonlocal laws. The theoretical predictions, exploited to analytically estimate the reduced Young elastic modulus of CNTs, are validated by molecular dynamics simulations.