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

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.

Keywords:

• Timoshenko elastic nano-beams
• size effects
• nonlocal integral theory
• analytical modeling
• CNT
• reduced Young modulus

Additional information

Funding

The financial support of the Italian Ministry for University and Research (P.R.I.N. National Grant 2017, Project code 2017J4EAYB; University of Naples Federico II Research Unit) is gratefully acknowledged.