arXiv subjects

Cesare Davini

Publications and source records attributed to Cesare Davini.

5 recordsLinked to original sources

arXiv2019

An atomistic-based Föppl-von Kármán model for graphene

We deduce a non-linear continuum model of graphene for the case of finite out-of-plane displacements and small in-plane deformations. On assuming that the lattice interactions are governed by the Brenner's REBO potential of 2nd generation and that self-stress is present, we introduce discrete strain measures accounting for up-to-the-third neighbor interactions. The continuum limit turns out to depend on an average (macroscopic) displacement field and a relative shift displacement of the two Bravais lattices that give rise to the hexagonal periodicity. On minimizing the energy with respect to the shift variable, we formally determine a continuum model of Föppl-von Kármá type, whose constitutive coefficients are given in terms of the atomistic interactions.

cond-mat.mes-hall↗

arXiv2017

A 2D metamaterial with auxetic out-of-plane behavior and non-auxetic in-plane behavior

Customarily, in-plane auxeticity and synclastic bending behavior (i.e. out-of-plane auxeticity) are not independent, being the latter a manifestation of the former. Basically, this is a feature of three-dimensional bodies. At variance, two-dimensional bodies have more freedom to deform than three-dimensional ones. Here, we exploit this peculiarity and propose a two-dimensional honeycomb structure with out-of-plane auxetic behavior opposite to the in-plane one. With a suitable choice of the lattice constitutive parameters, in its continuum description such a structure can achieve the whole range of values for the bending Poisson coefficient, while retaining a membranal Poisson coefficient equal to 1. In particular, this structure can reach the extreme values, $-1$ and $+1$, of the bending Poisson coefficient. Analytical calculations are supported by numerical simulations, showing the accuracy of the continuum formulas in predicting the response of the discrete structure.

physics.app-ph↗

arXiv2017

A new material property of graphene: the bending Poisson coefficient

The in-plane infinitesimal deformations of graphene are well understood: they can be computed by solving the equilibrium problem for a sheet of isotropic elastic material with suitable stretching stiffness and Poisson coefficient $ν^{(m)}$. Here, we pose the following question: does the Poisson coefficient $ν^{(m)}$ affect the response to bending of graphene? Despite what happens if one adopts classical structural models, it does not. In this letter we show that a new material property, conceptually and quantitatively different from $ν^{(m)}$, has to be introduced. We term this new parameter bending Poisson coefficient; we propose for it a physical interpretation in terms of the atomic interactions and produce a quantitative evaluation.

cond-mat.mtrl-sci↗

arXiv2017

A REBO-potential-based model for graphene bending by $Γ$-convergence

An atomistic to continuum model for a graphene sheet undergoing bending is presented. Under the assumption that the atomic interactions are governed by a harmonic approximation of the 2nd-generation Brenner REBO (reactive empirical bond-order) potential, involving first, second and third nearest neighbors of any given atom, we determine the variational limit of the energy functionals. It turns out that the $Γ$-limit depends on the linearized mean and Gaussian curvatures. If some specific contributions in the atomic interaction are neglected, the variational limit is non-local.

math-ph↗

arXiv2017

The Gaussian Stiffness of Graphene deduced from a Continuum Model based on Molecular Dynamics Potentials

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.

cond-mat.mtrl-sci↗