Momentum-Transfer Framework Unifies High-Velocity Impact and Failure Across Materials, Geometries, and Scales
Materials that dissipate energy efficiently under high-speed impacts, from micrometeoroid strikes on spacecraft to ballistic penetration in protective systems, are essential for maintaining structural integrity in extreme environments. Yet, despite decades of study, predicting and comparing impact performance across materials, geometries, and length scales remains challenging because conventional projectile-impact models often rely on conservation-based or empirically partitioned descriptions that assume the projectile-target interaction is a closed system. Here, we relax this assumption and directly observe the momentum and energy transferred out of the projectile during impact. We find that the momentum transferred to the target consistently reaches its maximum at the ballistic-limit velocity, demonstrated through a coordinated suite of micro-projectile impact experiments spanning varied projectile diameters, target thicknesses, and impact velocities, and further supported by targeted macroscale tests. This behavior is reinforced across a broad range of independent studies encompassing metals, polymers, composites, sandwich panels, and reinforced concrete, with thicknesses ranging from nanometers to hundreds of millimeters and projectiles of spherical, blunt, ogive, and conical shape, under both normal and oblique impacts. Together, these observations reveal a consistent impact behavior across all available data: maximum momentum transfer occurs at the ballistic limit. Extending this bound into the energy absorption landscape addresses an entrenched misconception in the field by revealing that specific energy absorption inherently inflates the performance of thinner targets due to geometric normalization, rather than reflecting genuine material enhancement.