Tight-binding theory of graphene mechanical properties

Nonlocal Euler–Bernoulli beam theories with material nonlinearity and their application to single-walled carbon nanotubes

“…This section uses \left( {15,15} \right) SWCNTs to demonstrate the differences between the four theories. So the diameter is d=2.034\;\text{n}\text{m}, and the thickness is taken as h=0.34\;\text{n}\text{m}, the other physical and geometrical parameters are [15,22] [32,54]. The non-local parameter obtained by atomic calculations has also shown some confusion [17,31,55].…”

“…The stress or strain gradient models have been widely used to study carbon nanotubes (CNTs) and graphene [28][29][30]. Since the mechanical properties of graphene and CNTs have lacked thorough understanding based on quantum mechanics [32], determining the scale parameter e 0 is still a controversial open question [5,31]. Researchers calculated nonlinear elastic parameters for some materials through molecular dynamics (MD) and density functional theory (DFT), for example, CNTs [16], graphene [14], and silicon nanowires [13].…”

A Nonlinear Nonlocal Thermoelasticity Euler–Bernoulli Beam Theory and Its Application to Single-Walled Carbon Nanotubes

“…The parameters are shown in Table 1 . Determining the nonlocal parameter of SWCNTs is an open problem because there is an ambiguous understanding of the mechanical properties of a one-atom-thick nanostructure [ 22 , 23 ]. If the vibration frequency in CNTs is in the terahertz range, a conservative estimate is [ 8 ].…”

“…The stress gradient model has been widely used to describe the mechanical properties of CNTs and graphene [ 19 , 20 , 21 ]. As the mechanical properties of a single atomic layer require a more thorough understanding based on quantum mechanics [ 22 , 23 ], determining the scale parameter remains a controversial open question [ 24 ].…”

Nonlocal Euler-Bernoulli Beam Theories with Material Nonlinearity and their Application to Single-Walled Carbon Nanotubes

“…The stress or strain gradient model is widely used to study carbon nanotubes (CNTs) and graphene [28][29][30]. Nevertheless, determining the scale parameter of CNTs and graphene, 0 e , is still a controversial open question [5,31] since the mechanical properties' understanding based on the quantum mechanics has not been thoroughly proposed for graphene and CNTs [32]. The material nonlinearity has restricted nonlinear elastic parameters' calculations through molecular dynamics (MD) and density functional theory (DFT).…”