A numerical solution of impact between viscoelastic slug of standard linear solid model and elastic rod

Abstract

The study is about impact of a short viscoelastic rod (or slug) on a stationary semi-infinite elastic rod. The viscoelastic materials are modeled as standard linear solid which involve three material parameters and the motion is treated as one-dimensional. We first establish the governing equations pertaining to the impact of viscoelastic materials subject to certain boundary conditions for the case when a viscoelastic slug moving at a speed Vimpacts a semi-infinite stationary elastic rod. The objective is to investigate how the viscosity time constants in the slug gives effect to interface stresses and interface velocities following wave transmission in the slug. If the stress at the interface becomes tensile and the velocity changes its sign, then the slug and the rod part company. If the stress at the interface is compressive after the impact, the slug and the rod remain in contact. After modeling the impact and solve the governing system of partial differential equations in the Laplace transform domain, we inverted the Laplace transformed solution numerically to obtain the stresses and velocities at the interface for several viscosity time constants and ratios of acoustic impedances. In inverting the Laplace transformed equations, we used the complex inversion formula because there is a branch cut and infinitely many poles within the Bromwich contour. Finally, we discussed the relationship between the viscosity time constants, ratios of acoustic impedances and the results of the interface stress and velocities.