Elastodynamic Impact into Piezoelectric Media

: We consider the elastodynamic impact problem involving a one-dimensional (1-D) semi-infinite non-piezoelectric elastic flyer traveling at initial velocity V0 that collides and welds to a finite stationary piezoelectric target backed by a semi-infinite non-piezoelectric elastic half-space. 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 invert the analytical Laplace 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. The final value theorem (FVT) is used to derive an explicit expression for the asymptotic (long-time) displacement current in the target. We also apply a newly derived impact boundary condition to the problem of elastodynamic impact into 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 finite-difference time-domain (FDTD) methods, and the commercial finite element code, COMSOL Multiphysics.