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Schematic of model formulation for buckling induced delamination. (a) Equilibrium configuration of adhered multilayer system with length, L. (b) Cooperative buckling (no delamination). Under compressive load, P, system undergoes collective deformation, , with a rigidity, D 0 and curvature, . (c) Buckling induced delamination. Two elastic members undergo bending (discrete buckling), with rigidities D 1 and D 2 subject to identical (but directionally opposite) deformation ( ) and curvature ( ).
Hybrid molecular model: full atomistic graphene with idealized coarse-grain “model material.” The constructed multi-layer systems consist of either (a)mono- or (b) bi-layer rectangular sheets of graphene enclosed by idealized linear elastic coarse-grain material layers. The graphene layers are simulated using the AIREBO potential for carbon-carbon interactions, 20 while the outer layers are modeled as a homogeneous 2D elastic material via a developed coarse-grain formulation, 22,23 allowing systematic manipulation of bending stiffness (D) and adhesion energy ( ) and confirm the general validity of Eq. (6) .
Simulation snapshots of buckling. With (initial) low adhesion energy/stiffness, all systems delaminate. Systematic increase in adhesion strength results in a critical value as a function of buckling length (L e) and change in rigidity ( ). (a) Monolayer graphene, Å and eV, with critical adhesion energy of eV. (b) Bilayer graphene, Å and eV, with critical adhesion energy of eV. We observe the graphene does not undergo the same ideal deformation as assumed.
Plot of adhesion strength ( ) versus buckling length (L e); simulation results and prediction, mono- and bilayer graphene with model material rigidities of (a) 225 eV and (b) 100 eV. For a given adhesion strength, , cooperative buckling (no delamination) occurs if the effective buckling length exceeds the predicted value. Otherwise, delamination occurs. Error bars indicated uncertainty in calculating exact material lengths due to coarse-grain bond spacing ( Å).
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