Impact-Induced Wave Propagation in Graphene: A Finite Element Shell Model Using MD-Derived Stiffness

Graphene can be a promising material for flexible body armor owing to its exceptional in-plane strength and out-of-plane flexibility. However, finite element (FE) simulations of impact-induced wave propagation often deviate from molecular dynamics (MD) predictions: conventional shell assumptions yield higher cone and transverse wave velocities and underestimate out-of-plane flexibility due to overestimated bending stiffness. To address this, membrane and bending stiffness were independently derived from MD-based tensile and bending tests and incorporated into the FE shell model. The improved model accurately reproduces MD results for wave propagation velocities (cone, transverse, and axial) and displacement responses (in-plane and out-of-plane) under hypervelocity projectile impact. Parametric analysis reveals that cone wave propagation is highly sensitive to projectile velocity and mass, while target size and temperature play a minor role. The initial stage of cone propagation is dominated by momentum transfer, whereas the late-stage behavior is influenced by dissipation and wave reflections. Overall, the study demonstrates that MD-derived stiffness values, particularly bending, substantially enhance the predictive capability of FE simulations. These insights can further support perforation and failure analysis under extreme impact conditions.