A rate‐dependent constitutive model for the dynamic deformation of ductile materials is developed. The model introduces a physical length scale into the equations governing the progressive failure of materials due to void growth. Consequently, mesh sensitivity or localization problems inherent to rate‐independent models are precluded. The model is implemented into an explicit, finite‐difference computer code. The insensitivity of the model to changes in the mesh size is demonstrated. Comparisons are provided between numerical simulations and data for uniaxial impact experiments. Excellent agreement is established between the final porosity levels and the width of the damage zone. Also, excellent agreement is provided for the stress histories, including the peak stress values and the spall signal.