A new theory, inspired by analogy with turbulence, was recently proposed to model the apparent dynamic overstress due to the energy that is dissipated by material comminution during penetration of missiles into concrete walls. The high-rate interface fracture comminuting the material to small particles was considered to be driven by the release of kinetic energy of high-rate shear of the forming particles, and the corresponding energy dissipation rate was characterized in the damage constitutive law by additional viscosity. However, in spite of greatly improved predictions for missile impact and penetration, the calculation of viscosity involved two simplifications—one crude simplification in the calculation of viscosity from the shear strain rate, and another debatable simplification in treating the comminution as an instantaneous event, as in the classical rate-independent fracture mechanics. Presented is a refined theory in which both simplifications are avoided without making the theory significantly more complicated. The interface fracture is considered to be progressive and advance according to Evans' power law extended to the fast growth of interface crack area. The growth rate of interface cracks naturally leads to an additional viscosity, which allows close matching of the published test data. In combination with the microplane damage constitutive model M7 for concrete, the refined theory gives a close match of the exit velocities of missiles penetrating concrete walls of different thicknesses and of the penetration depths of missiles of different velocities into a massive block.