Here, L-J parameters for the carbon atoms of the buckyball and ε CC = 0.27647 kJ/mol as used in the original parametrization of Girifalco [33] and van der Waals interaction govern in the plate-buckyball interaction. R428 A time integration step of 1 fs is used, and periodical boundary conditions are applied in the x y plane to eliminated the boundary effect. Single buckyball mechanical behavior Atomistic simulation result The distinctive mechanical behavior of a single buckyball should underpin the overall energy absorption ability of a buckyball assembly. The force F and displacement W are normalized as FR/Eh 3

and W/D, respectively, where R, h, D, and E are the radius, effective thickness, diameter, and effective Young’s modulus of the buckyball, respectively. Considering that bending is involved during the buckyball compression, h = 0.66

nm and E = 5 TPa [34, 35]. Here a crushing speed at 0.01 m/s is employed to mimic quasi-static loading, because the normalized force-displacement curves are verified to be the same at various loading rates from 0.1 to 0.001 m/s in trial simulations. The force-displacement response under both quasi-static and a representative dynamic impact loading (with impact speed of 50 m/s and energy of 1.83 eV) are studied, as shown in Figure  2. Two obvious force-drops could be observed in low-speed crushing, while only one prominent force-drop exists in dynamic loading which is related to the less-evident snap-through deformation shape. Figure 2 Normalized force displacement curves at both low-speed crushing and impact loading. The entire process from the Selumetinib ic50 beginning of loading to the bowl-forming morphology can be divided into four phases. Morphologies of C720 are shown at the corresponding normalized displacements. The entire compression process could be divided into four phases according to the FR/Eh 3 ~ W/D curve, i.e., buckling (W/D < 10%), post-buckling (10% ≤ W/D < 30%), densification (30% ≤ W/D < 40%), and inverted-cap-forming phase (W/D > 40%). Upon the ricochet of P-type ATPase the plate, the deformation remains as a bowl shape

with great volume shrinkage. The stabilization of such a buckled morphology is owing to a lower system potential energy in the buckled configuration due to van der Waals interaction; similar energy dissipation mechanism in CNT network is also revealed by [36]. The derivative of curve undergoes a sudden change at the same W/D value but in two completely different loading rates, suggesting that the sudden force-drop points are highly dependent on the buckyball deformation rather than the loading rate. And theoretical insights may be obtained from the four-phase deformation. Phenomenological mechanical models Note that due to the property of FR/Eh 3 ~ W/D curve, among the phases of compression process, those with significant reduction of force (Figure  2) are relatively unimportant for energy absorption and not included in the modeling effort.