Taking the cue from two recent papers,\ud
Fraternali et al. (J Mech Phys Solids 60:1137–1144,\ud
2012), and Fraternali et al. (Appl Phys Lett 105:201903,\ud
2014), we sample numerically the impulsive dynamics\ud
of chains consisting of T3 tensegrity modules. We\ud
concentrate on illustrating the effects of the kinetic\ud
coupling between axial strain and twist, a distinguishing\ud
feature of T3 modules that was switched off in the cited\ud
papers; in addition, we demonstrate by examples that\ud
another feature of T3 modules, their ‘handedness’,\ud
induces certain peculiar behaviors in chains made of\ud
both left-handed and right-handed modules. In our\ud
study, we consider a number of T3 chains, different in\ud
composition and subject to various end conditions
We consider a discrete model of a graphene sheet with atomic interactions governed by a harmonic approximation of the 2nd-generation Brenner potential that depends on bond lengths, bond angles, and two types of dihedral angles. A continuum limit is then deduced that fully describes the bending behavior. In particular, we deduce for the first time an analytical expression of the Gaussian stiffness, a scarcely investigated parameter ruling the rippling of graphene, for which contradictory values have been proposed in the literature. We disclose the atomic-scale sources of both bending and Gaussian stiffnesses and provide for them quantitative evaluations.
A continuum model for a graphene sheet undergoing infinitesimal in–plane deformations is derived
by applying the arguments of homogenization theory. The model turns out to coincide with that found by various
authors with different methods, but it avoids, in particular, anticipations on the validity of any properly adjusted or
generalized Cauchy-Born rule. The constitutive equation for stress and the effective Young modulus and Poisson
ratio are explicitly given in terms of the bond constants
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