LONGITUDINAL IMPACT INTO VISCOELASTIC MEDIA

Abstract eng:
We consider several one-dimensional (1-D) impact problems involving finite or semi-infinite, elastic flyers traveling at initial velocity V0 that collide with, and weld to a finite stationary viscoelastic target backed by a semi-infinite elastic half-space. A Laplace transform method is used to derive numerically-based solutions for this class of transient wave propagation problems that exhibit jump discontinuities due to multiply reflected waves. A Dubner-Abate-Crump (DAC) algorithm [1], modified in [2], is used to invert the analytical Laplace transform domain solutions to the time domain. A newly derived impact boundary condition, used to solve impact problems in elastic [3] and piezoelectric media [4], is extended for use in problems involving viscoelastic impact. We find that the transient impact solutions for targets governed by a hereditary constitutive law (e.g., Maxwell or modified power-law) 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 [5]. The Final Value Theorem is used to derive new explicit analytical expressions for the asymptotic stress and velocity in the targets that are useful for verification of viscoelastic impact simulations taken to long observation times.

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