Buckling of thermalized elastic sheets

Thermally fluctuating, semiflexible sheets in simple shear flow

“…In this work, we focus on a sheet model of a particular size, so future work exploring a finite-size scaling analysis of the dynamical results presented is warranted. It is worth noting, though, that several recent works [60][61][62][63] exploring the finite-temperature buckling transition of 2D sheets lend support to the idea that several results in this work may very well apply directly to sheets of different sizes as long as properly renormalized elastic constants are used (see Conclusions for additional discussion).…”

Thermalized buckling of isotropically compressed thin sheets

“…As a result, in recent years, exploring the influence of external stresses on the mechanics of fluctuating membranes has been a topic of prime interest [29]. While there has been some theoretical work, both old [30] and new [31][32][33][34], complemented by more recent large scale numerical simulations [35][36][37][38][39][40], elucidating the role of boundaries in controlling the nonlinear mechanics and buckling of thermalized sheets, particularly for compressions which attempt to impose a nonzero Gaussian curvature, remains a challenging problem. Motivated by the above, in this paper, we pose and answer the following question -what is the finite temperature version of the buckling transition in an isotropically compressed thin sheet?…”

Anomalous thermal expansion in Ising-like puckered sheets

“…The coarse-grained model with no dilations [33] has been used to study the mechanical and thermal properties of 2D materials (e.g graphene) [16,17,28,46,56]. We fix κ = 1.0 and k = 100 and vary T from 0.1 to 0.4.…”

“…We first examine the thermal contraction of a pristine membrane (no dilations) to establish a point of comparison. Thermalized membranes have been studied extensively in MD and MC simulations of graphene and similar models [16,17,45,46], and their negative coefficient of thermal expansion α T has been calculated analytically using renormalization group [47].…”

“…Furthermore, thermal fluctuations also profoundly change the mechanics of atomically thin materials at long wavelengths. Simulations and experiments have revealed scale-dependent elastic parameters, with thermal fluctuations increasing the bending rigidity and decreasing in-plane stiffness [3,[15][16][17][18][19][20]. In addition, buckled configurations have been found (either via density functional theory or experiment) in atomically thin materials such as stanene, SnO, PbS, and borophane polymorphs [21][22][23][24][25][26], and there is interest in using topological defects and substitutional impurities to modify the configurations of graphene [27][28][29][30].…”