NONTRIVIAL POWER-LAW SCALING OF PEAK FORCES DURING GRANULAR IMPACT

Abstract

Ballistic impact into a soil target has broad military relevance. Understanding the forces during impact is crucial to predicting damage and survivability. This process involves several nonlinear physical mechanisms, making it difficult to describe. While some existing models of ballistic impact characterize the average response during penetration well, these models fail during the initial stages of impact when forces are the largest. There currently is no theoretical framework for understanding the forces and dynamics during these crucial early stages. In this thesis, we use numerical simulations of intruders impacting granular media, coupled with existing experimental data, to understand the forces during the initial stages of impact. For slow impacts, forces are independent of speed and set by the weight of the intruder. For fast impacts, the impact forces grow as a non-linear power law in the impact velocity with exponent 4/3. This scaling depends on the size of the intruder and stiffness of the grains, and it is insensitive to gravity, friction, the nonlinear force law between grains, and the density of the intruder. We use dimensional analysis to collapse all data onto a single curve, providing a first step toward a comprehensive theoretical description of this process.