Lagrangian methods for ballistic impact simulations

This thesis explores various Lagrangian methods for simulating ballistic impact with the ultimate goal of finding a universal, robust and scalable computational framework to assist in the design of armor systems. An overview is provided of existing Lagrangian strategies including particle methods, meshless methods, and the peridynamic approach. We review the continuum formulation of mechanics and its discretization using finite elements. A rigid body contact algorithm for explicit dynamic finite elements is presented and used to model a rigid sphere impacting a confined alumina tile. The constitutive model for the alumina is provided by the Deshpande-Evans ceramic damage model. These simulations were shown to capture experimentally observed radial crack patterns. An adaptive remeshing strategy using finite elements is then explored and applied, with limited success, to the problem of predicting the transition from dwell to penetration for long-rod penetrators impacting confined ceramic targets at high velocities. Motivated by the difficulties of mesh-based Lagrangian approaches for modeling impact, an alternative Lagrangian approach is investigated which uses established constitutive relations within a particle-based computational framework. The resulting algorithm is based on a discretization of the peridynamic formulation of continuum mechanics. A validating benchmark example using a Taylor impact test is shown and compared to previous results from the literature. Further numerical examples involving ballistic impact and the crushing of an aluminum sandwich structures provide further demonstration of the method's potential for armor applications. Thesis Supervisor: Radl A. Radovitzky Title: Associate Professor of Aeronautics and Astronautics Thesis Reader: Tomasz Wierzbicki Title: Professor of Mechanical Engineering