Validation of numerical results of impact of viscoelastic slug and elastic rod through viscoelastic discontinuity analysis: Standard linear solid model

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Abstract

The study is about impact of a short elastic rod (or slug) on a stationary semi-infinite viscoelastic 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 an elastic slug moving at a speed V impacts a semi-infinite stationary viscoelastic rod. The objective is to validate the numerical results of stresses and velocities at the interface following wave transmissions and reflections in the slug after the impact using viscoelastic discontinuity. 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 modelling the impact and solve the governing system of partial differential equations in the Laplace transform domain, we invert 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. In the viscoelastic discontinuity analysis, we look at the moving discontinuities in stress and velocity using the impulse-momentum relation and kinematical condition of compatibility. Finally, we discussed the relationship of the stresses and velocities using numeric and the validated stresses and velocities using viscoelastic discontinuity analysis.

Original languageEnglish
Title of host publicationInternational Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014
EditorsMohammad Fadzli Ramli, Nurshazneem Roslan, Ahmad Kadri Junoh, Maz Jamilah Masnan, Mohammad Huskhazrin Kharuddin
PublisherAmerican Institute of Physics Inc.
ISBN (Electronic)9780735413047
DOIs
Publication statusPublished - 15 May 2015
EventInternational Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014 - Penang, Malaysia
Duration: 28 May 201430 May 2014

Publication series

NameAIP Conference Proceedings
Volume1660
ISSN (Print)0094-243X
ISSN (Electronic)1551-7616

Other

OtherInternational Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014
CountryMalaysia
CityPenang
Period28/05/1430/05/14

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All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

Musa, A. B. (2015). Validation of numerical results of impact of viscoelastic slug and elastic rod through viscoelastic discontinuity analysis: Standard linear solid model. In M. F. Ramli, N. Roslan, A. K. Junoh, M. J. Masnan, & M. H. Kharuddin (Eds.), International Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014 [070127] (AIP Conference Proceedings; Vol. 1660). American Institute of Physics Inc.. https://doi.org/10.1063/1.4915844