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The superb mechanical properties make graphene an ideal candidate material for impact protection. Combining molecular dynamics simulations and theoretical analyses, the deformation and failure modes, energy absorption of single-layer graphene under ballistic impact are investigated. According to numerical and theoretical results, the expression for residual velocity of projectile after impact is given. The dependence of deformation and failure modes, energy absorption mechanisms, specific penetration energy (SPE) on impact velocity is analyzed. The results show that during low-velocity impact, there are conical deformation region (CDR), star-like crack and monoatomic carbon chain in graphene. Energy absorption mechanisms of graphene are mainly local deformation and fracture. With increasing impact velocity, the size of CDR decreases. The star-like crack gradually transforms into circular hole. When impact velocity is high enough, carbon atoms within projectile projection area in graphene will be ejected in the form of debris. The kinetic energy (KE) loss of projectile is converted into KE of debris carbon atoms and fracture energy of carbon bonds. Besides, it is also found that SPE (dominant factors are deformation of conical region and KE increments) exhibits a decreasing–increasing trend with increasing impact velocity. When impact velocity is the same, SPE decreases with increasing projectile diameter. [Display omitted] • Energy absorption of graphene under ballistic impact is studied by MD simulations. • The expression for residual velocity of rigid projectile after impact is given. • The dependence of deformation and failure modes on impact velocity is discussed. • Energy absorption mechanism of graphene during impact process is analyzed. • The effect of impact velocity on specific penetration energy is studied. [ABSTRACT FROM AUTHOR]