▎ 摘　　要

Helical graphene nanoribbons (HGNRs) are a special structure made of single-layer graphene, which are of interest in the nanotechnology because of their unique mechanical features. Here we propose an asymmetrical nonlinear spring model (ANSM) for designing different HGNRs used in the dynamic nano-indentation testing. Both nonlinear static and dynamics behaviors of HGNRs are studied using molecular dynamics (MD) simulations and the ANSM, respectively. The interlayer van der Waals interactions, which play a key role in the mechanical behaviors of HGNRs, are quantitatively considered in the ANSM with quadratic and cubic nonlinearities. The response-frequency curves of forced vibrations in HGNRs show clear softening-type nonlinearity. In particular, a remarkable transformation from softening-type to hardening-type nonlinearity occurs with increasing contact stiffness in nonlinear dynamics behaviors of HGNRs. Checking against present static and linear dynamics results of MD simulations shows that the ANSM has high accuracy. The present study provides valuable physical insights for designing and assembling HGNR-based resonators.