Penetration of a rigid body into a viscoplastic compressible fluid

In this paper, a model for describing steady-state penetration into a cemen-titious or geological material is proposed. A compressible viscoplastic fluid constitutive equation that captures the combined effects of high-strain rate and high-pressure (confinement) on yielding was developed. To account for the experimentally observed characteristics of the response at high-pressures, the hypothesis of a locking medium was adopted (i.e. the density cannot exceed a critical limit). To simulate steady-state penetration, a mixed finite-element and finite-volume strategy is developed. Specifically, the variational inequality for the velocity field is discretized using the finite element method and a finite volume method is adopted for the density equation. An added numerical difficulty is related to the fact that the two incompressible zones within the deformed region of the impacted medium, namely the fully compacted zone and the unloading zone are in contact. Thus, to solve the velocity, problem Uzawa algorithm coupled with a Newton method is used. The ability of the proposed model to accurately describe the density changes in the impacted medium as well as the distribution of fracture zones is demonstrated. The fact that fracture occurs ahead of the penetrator and along planes which are not symmetric with respect to the penetrator centerline, may contribute to trajectory deviations.