Longitudinal impact of piezoelectric media

We consider the elastodynamic impact problem involving a one-dimensional finite-thickness piezoelectric flyer traveling at initial velocity $$V_0$$ that collides with (and adheres to) a stationary piezoelectric target of finite thickness backed by a semi-infinite non-piezoelectric elastic half-space. We derive expressions for the stress, velocity, and electric displacement in the target at all times after impact. A combined d’Alembert and Laplace transform method is used to derive new numerically based solutions for this class of transient wave propagation problems. A modified Dubner–Abate–Crump (DAC) algorithm is used to invert the analytical Laplace transform domain solutions to the time domain. Unlike many authors who neglect electromechanical coupling in the initially unstressed region ahead of the shock, we consider this effect, which gives rise to the development of a tensile stress wave within the piezoelectric target ahead of the shock. To solve the problem, we derive a new piezoelectric impact boundary condition and apply it to the problem of a finite quartz (Si $$\text {O}_2$$ ) flyer impacting a lead zirconate titanate (PZT-4) target and find that the solutions obtained using the modified DAC algorithm compare well with those obtained using both a finite-difference time-domain method, and the commercial finite element code, COMSOL multiphysics.