Asymptotic impact behavior of Goupillaud-type layered elastic media

In this paper, we use the method of Riemann invariants to develop a system of recurrence relations for the one-dimensional elastic impact problem in which a semi-infinite flyer collides with (and adheres to) a stationary Goupillaud-type layered elastic target plate of finite thickness that is bonded to a semi-infinite half-space. We derive explicit expressions for the long-time asymptotes of stress and particle velocity that are independent of the layered target’s elastic properties. This result is verified by numerical simulations of impact into layered targets with periodic or randomly distributed elastic properties, and holds when the half-space backing the target is replaced by either free or fixed boundary conditions. Our discrete recurrence relation solutions for impact into layered media, generalize our recent analytical results concerning impact into homogeneous, single-layer targets, as well as prior discrete recurrence relation solutions for stress wave propagation in Goupillaud-type layered elastic media.