title: The constitutive relation and small scale parameter of nonlocal continuum mechanics for modelling carbon nanotubes.
abstract: In this paper, the constitutive relations of nonlocal elasticity theory are presented for application in the analysis of carbon nanotubes (CNTs) when modelled as Euler-Bernoulli beams, Timoshenko beams or as cylindrical shells. In particular, the shear stress and strain relation for the nonlocal Timoshenko beam theory is discussed in great detail due to a misconception by some researchers that the nonlocal effect should appear in this constitutive relation. Different theories for proposing the value of the small scale parameter are also introduced and a recommendation for the value from the standpoint of wave propagation of CNTs is given.
authors: Department of Mechanical and Manufacturing Engineering, University of Manitoba, Winnipeg, Manitoba, R3T 5V6, Canada.
authors: Q
authors: Q
authors: Wang
authors: C M
authors: CM
authors: Wang