A generalized model for one dimensional impact response of a heterogeneous layered medium

Abstract

In this paper, we study the response of a heterogeneous layered medium subjected to a one-dimensional normal impact, with low, intermediate, and high velocity of impact, by studying the interactions between the waves generated in the target. We consider a multi-linear stress–strain relation approximating the nonlinear stress–strain behavior. The mass and momentum balance jump equations, along with maximally dissipative kinetic relation, are used to get the solution to the wave propagation problem. A program has been developed that tracks and solves the interaction of each propagating wave in the flyer–target system to obtain the response of the medium. The new interactions and the associated Riemann problems due to variation in parameters of the multi-linear stress–strain behavior of the target layers are identified and solved. The effect of parameters of the multi-linear stress–strain behavior on the impact response of the target is studied. The flyer impacting the target results in the formation of the waves in the flyer and target depending on the velocity of impact and properties of the flyer and target. The possible outcomes are the formation of elastic waves, elastic and shock waves, and only shock waves in the target. The impact response of the target for all three cases is found by studying the interactions happening in the flyer–target system. The impact response obtained from the developed numerical code is verified by performing a finite element study for the same problem. The results obtained from the developed code and the finite element analysis (FEA) are in good agreement for all three cases of low, intermediate, and high-velocity impact.