Longitudinal impact into viscoelastic media
- 28 Downloads
We consider several one-dimensional impact problems involving finite or semi-infinite, linear elastic flyers that collide with and adhere to a finite stationary linear viscoelastic target backed by a semi-infinite linear elastic half-space. The impact generates a shock wave in the target which undergoes multiple reflections from the target boundaries. Laplace transforms with respect to time, together with impact boundary conditions derived in our previous work, are used to derive explicit closed-form solutions for the stress and particle velocity in the Laplace transform domain at any point in the target. For several stress relaxation functions of the Wiechert (Prony series) type, a modified Dubner–Abate–Crump algorithm is used to numerically invert those solutions to the time domain. These solutions are compared with numerical solutions obtained using both a finite-difference method and the commercial finite element code, COMSOL Multiphysics. The final value theorem for Laplace transforms is used to derive new explicit analytical expressions for the long-time asymptotes of the stress and velocity in viscoelastic targets; these results are useful for the verification of viscoelastic impact simulations taken to long observation times.
Keywords1-D viscoelastodynamics Numerical inverse Laplace transform Modified Dubner–Abate–Crump Asymptotic impact behavior Mathematica MATLAB COMSOL
We would like to thank our colleague, Dr. Rob Jensen (ARL), for providing the torsional DMA PC data plotted in Fig. 8a.
- 3.Gazonas, G.A., Wildman, R.A., Hopkins, D.A.: Elastodynamic impact into piezoelectric media. U.S. Army Research Laboratory, ARL-TR-7056, Sept (2014)Google Scholar
- 8.Musa, A.B.: Numerical solution of wave propagation in viscoelastic rods (standard linear solid model). In: 4th International Conference on Energy and Environment 2013 (ICEE 2013), IOP Conference Series: Earth and Environmental Science, vol. 16; Putrajaya, Malaysia, pp. 1–6 (2013)Google Scholar
- 9.COMSOL Multiphysics Reference Manual, Version 4.4. COMSOL, Inc., Burlington (2013)Google Scholar
- 11.Christensen, R.M.: Theory of Viscoelasticity: An Introduction. Academic Press, New York (1982)Google Scholar
- 12.Wineman, A.S., Rajagopal, K.R.: Mechanical Response of Polymers: An Introduction. Cambridge University Press, New York (2000)Google Scholar
- 16.Schapery, R.A.: Viscoelastic behavior and analysis of composite materials. In: Sendeckyj, G.P. (ed.) Mechanics of Composite Materials, vol. 2, pp. 85–168. Academic Press, New York (1974)Google Scholar
- 18.Nunziato, J.W., Walsh, E.K., Schuler, K.W., Barker, L.M.: Wave propagation in nonlinear viscoelastic solids. In: Truesdell, C. (ed.) Handbuch Der Physik; Volume VIa/4 Mechanics of Solids IV, pp. 1–108. Springer, New York (1974)Google Scholar
- 26.Mathematica Edition: Version 10.3. Wolfram Research, Champaign (2015)Google Scholar
- 28.MATLAB 9.2.0. The MathWorks, Inc., Natick, Massachusetts, United States (2017)Google Scholar
- 34.Critescu, N., Suliciu, I.: Viscoplasticity. Martinus Nijhoff Publishers, The Hague-Boston-London (1982)Google Scholar