Studying the Interaction of Waves to Determine the Impact Response of a Layered Elastic Medium

Abstract

When an impactor strikes a layered target, both the impactor and the target experience waves. The waves produced travel and engage in interactions with other waves as well as the interfaces in the impactor-target system. For the impact problems on a layered medium with periodic properties and layered elastic media of Goupillaud-type (each layer has the same wave travel time), researchers have presented an analytical solution for stress variation with position and time within the target. However, the solution for an elastic media not satisfying the above conditions is not available in the literature. The present study fills this gap and finds the behaviour of a generalized layered medium to an impact problem. The response of the material at any position inside the layered medium is found by solving the interaction between waves, interfaces, and boundaries. The mass, momentum balance and constitutive relationship are solved to get the exact analytical expressions for particle velocity and stress for each possible wave interaction happening in the impactor and the layered medium. The expressions are utilized in a computer program to study the impact behaviour of a layered media. The code tracks each wave as it travels through the system and identifies those interactions that occur in the shortest time, uses the stress and velocity expression for that interaction, and updates the state of the material. When stress produced at the impact surface is tensile in nature, the impactor and target can be separated. The work can be applied to both finite and semi-infinite impactors and targets, and the layered medium does not necessarily have to be a periodic layered media or a Goupillaud-type medium.