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The local destruction and deformation characteristics of a concrete target impacted by a rigid projectile were analyzed, and the similarity laws for local damage effects in the concrete target were studied utilizing the rigid-plastic, internal friction, and modified hydrodynamic models. For a thin target, the impact factor is the only factor controlling the low-velocity impact process. For a thick target impacted by a projectile at intermediate velocity, internal friction is the main factor contributing to the energy dissipation. The impact factor, the toughness factor, and the dynamic factor together determine the penetration process. However, for a thick target impacted at high velocity, the impact factor and hardness factor together determine the penetration process. The penetration depth shows a 2/3 power relationship with impact velocity. For thick targets, similarity laws change along with impact velocity. The radii ratio between the projectile and penetration tunnel is proportional to the projectile’s diameter for intermediate velocity impact and only shows a relationship with the impact velocity for high velocity penetration.