### 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 language | English |
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Title of host publication | International Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014 |

Editors | Mohammad Fadzli Ramli, Nurshazneem Roslan, Ahmad Kadri Junoh, Maz Jamilah Masnan, Mohammad Huskhazrin Kharuddin |

Publisher | American Institute of Physics Inc. |

ISBN (Electronic) | 9780735413047 |

DOIs | |

Publication status | Published - 15 May 2015 |

Event | International Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014 - Penang, Malaysia Duration: 28 May 2014 → 30 May 2014 |

### Publication series

Name | AIP Conference Proceedings |
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Volume | 1660 |

ISSN (Print) | 0094-243X |

ISSN (Electronic) | 1551-7616 |

### Other

Other | International Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014 |
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Country | Malaysia |

City | Penang |

Period | 28/05/14 → 30/05/14 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Physics and Astronomy(all)

### Cite this

*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

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*International Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014.*, 070127, AIP Conference Proceedings, vol. 1660, American Institute of Physics Inc., International Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014, Penang, Malaysia, 28/05/14. https://doi.org/10.1063/1.4915844

**Validation of numerical results of impact of viscoelastic slug and elastic rod through viscoelastic discontinuity analysis : Standard linear solid model.** / Musa, A. B.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

TY - GEN

T1 - Validation of numerical results of impact of viscoelastic slug and elastic rod through viscoelastic discontinuity analysis

T2 - Standard linear solid model

AU - Musa, A. B.

PY - 2015/5/15

Y1 - 2015/5/15

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85006219365&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85006219365&partnerID=8YFLogxK

U2 - 10.1063/1.4915844

DO - 10.1063/1.4915844

M3 - Conference contribution

AN - SCOPUS:85006219365

T3 - AIP Conference Proceedings

BT - International Conference on Mathematics, Engineering and Industrial Applications, ICoMEIA 2014

A2 - Ramli, Mohammad Fadzli

A2 - Roslan, Nurshazneem

A2 - Junoh, Ahmad Kadri

A2 - Masnan, Maz Jamilah

A2 - Kharuddin, Mohammad Huskhazrin

PB - American Institute of Physics Inc.

ER -