On the derivation of the elastic properties of lattice nanostructures: The case of graphene sheets

Buckling Analysis of Single-Layer Graphene Sheets Using Molecular Mechanics

“…In the present study, we propose a buckling analysis of single-layer graphene sheets through a molecular mechanics model which extends those used in our previous works (Genoese et al, 2017(Genoese et al, , 2018a(Genoese et al, ,b, 2019 in order to account for binary, ternary and quaternary interactions between the atoms. They are described using a geometrically exact setting and introducing Morse and cosine potential functions, equipped with a proper set of parameters.…”

“…Among them, ab-initio simulations (Kudin et al, 2001;Baumeier et al, 2007;Liu et al, 2007) are the most accurate tools available to investigate the behavior of nanomaterials, including their mechanics, but they demand a lot of computer power and so they are not always feasible for systems with very many atoms. For this reason, increasing attention has been given to molecular dynamics/statics formulations (Liew et al, 2004;Lu et al, 2009;Xiao et al, 2009;Zhao et al, 2009;Georgantzinos et al, 2012;Silvestre et al, 2012;Berinskii and Borodich, 2013;Davini, 2014;Theodosiou and Saravanos, 2014;Gamboa et al, 2015;Korobeynikov et al, 2015Korobeynikov et al, , 2018Budarapu et al, 2017;Davini et al, 2017;Genoese et al, 2017Genoese et al, , 2018aGenoese et al, ,b, 2019Hossain et al, 2018;Sgouros et al, 2018;Singh and Patel, 2018b) or their structural-mechanical approximations (e.g., nanoscale equivalent beam and truss models; Sakhaee-Pour, 2009a,b;Georgantzinos et al, 2010;Alzebdeh, 2012;Giannopoulos, 2012;Tserpes, 2012;Firouz-Abadi et al, 2016;Rafiee and Eskandariyun, 2017;Savvas and Stefanou, 2018) and to continuum models (Chang, 2010;Aminpour and Rizzi, 2016;Ghaffari et al, 2018;Singh and Patel, 2018a;Zhang et al, 2018).…”

“…Most of the research on graphene has focused on its rigidities, the frequencies of free vibration, and tensile failure properties and this has produced also a refinement of the parameters of simple bonding potentials (Genoese et al, 2017;Hossain et al, 2018;Korobeynikov et al, 2018), such as the DREIDING, the Stillinger-Weber or the modified Morse potentials. Currently, molecular statics formulations based on these potentials are considered to be the best compromise at the atomistic scale in non-linear contexts, where the simplicity of the models is a major requirement.…”

“…They are described using a geometrically exact setting and introducing Morse and cosine potential functions, equipped with a proper set of parameters. To this regard, following the reasoning already proposed in Genoese et al (2017Genoese et al ( , 2018aGenoese et al ( , 2019, a constitutive problem is solved only for purposes of giving a new parametrization of the dihedral potential. Then, by solving the equilibrium equations of the atomistic system through the arc-length strategy, we obtain the critical and postcritical behaviors of graphene under compression in the zigzag and in the armchair directions and shear.…”

Comparing quantum, molecular and continuum models for graphene at large deformations

“…Subsequently in this paper, relevant discussion on this aspect from our findings are reported. In MD and MM simulations, the accuracy of the results depends on the potential defining [15] 2000 Ab-initio 1.100 1.100 0.340 [16] 2006 Molecular structural mechanics 1.096--1.125 1.106--1.201 0.340 (Tersoff-Brenner) [17] 2006 DFT 1.250 1.250 0.340 [18] 2007 Ab-initio 1.050 1.050 0.334 [3] 2008 Experimental (nano indentation) 1 \pm 0.100 1 \pm 0.100 0.335 [19] 2009 DFT 0.964 0.964 0.340 [20] 2009 Molecular structural mechanics 1.040 1.042 0.340 [21] 2009 Quantum molecular dynamics 1.100 0.600 0.335 [22] 2009 Orthogonal tight-binding and MD 1.01 \pm 0.030 1.01 \pm 0.030 0.335 [23] 2009 Truss-type analytical models with AMBER 1.378 1.303 NA with MORSE 1.379 1.957 NA [24] 2010 MD (AIREBO) 0.890 0.830 NA [25] 2010 Molecular structural mechanics 0.721 0.737 0.340 [14] 2010 MD (Tersoff) 1.130 1.050 0.335 [26] 2010 Molecular mechanics (MM3) 3.380 3.400 0.100 [27] 2012 MD (AIREBO) 1.097 0.961 0.335 [28] 2013 Molecular structural mechanics and MD 1.070 1.070 0.335 [29] 2014 Molecular structural mechanics 1.100 1.100 0.34 (Modified MORSE) [30] 2017 Space frame approach with AMBER 0.780 0.819 NA with MORSE 0.890 0.938 NA [31] 2018 Multiscale model (MM3) 0.927 0.927 0.335 atomic interactions. For carbonaceous structures, popular potentials are: MM3 [32], Tersoff [33], the first and second generation reactive empirical bond order (REBO) [34,35], adaptive intermolecular reactive empirical bond order (AIREBO) [36], and ReaxFF [37].…”