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Materials 2016, 9(5), 377; doi:10.3390/ma9050377

Stress Wave Propagation in Viscoelastic-Plastic Rock-Like Materials

Energy School, Xi’an University of Science and Technology, Xi’an 710054, China
Key Laboratory of Western Mines and Hazards Prevention, Ministry of Education of China, Xi’an 710054, China
Department of Civil Engineering, Inha University, Incheon 402-751, Korea
School of Geology Engineering and Geomatics, Changan University, Xi’an 710054, China
School of Civil & Resource Engineering, University of Western Australia, Perth 6009, Australia
Author to whom correspondence should be addressed.
Academic Editor: Nicola Pugno
Received: 19 October 2015 / Revised: 25 April 2016 / Accepted: 3 May 2016 / Published: 17 May 2016
(This article belongs to the Section Structure Analysis and Characterization)
View Full-Text   |   Download PDF [2938 KB, uploaded 17 May 2016]   |  


Rock-like materials are composites that can be regarded as a mixture composed of elastic, plastic, and viscous components. They exhibit viscoelastic-plastic behavior under a high-strain-rate loading according to element model theory. This paper presents an analytical solution for stress wave propagation in viscoelastic-plastic rock-like materials under a high-strain-rate loading and verifies the solution through an experimental test. A constitutive equation of viscoelastic-plastic rock-like materials was first established, and then kinematic and kinetic equations were then solved to derive the analytic solution for stress wave propagation in viscoelastic-plastic rock-like materials. An experimental test using the SHPB (Split Hopkinson Pressure Bar) for a concrete specimen was conducted to obtain a stress-strain curve under a high-strain-rate loading. Inverse analysis based on differential evolution was conducted to estimate undetermined variables for constitutive equations. Finally, the relationship between the attenuation factor and the strain rate in viscoelastic-plastic rock-like materials was investigated. According to the results, the frequency of the stress wave, viscosity coefficient, modulus of elasticity, and density play dominant roles in the attenuation of the stress wave. The attenuation decreases with increasing strain rate, demonstrating strongly strain-dependent attenuation in viscoelastic-plastic rock-like materials. View Full-Text
Keywords: viscoelastic-plastic rock-like materials; constitutive equation; stress wave equation; strain rate; attenuation; SHPB apparatus viscoelastic-plastic rock-like materials; constitutive equation; stress wave equation; strain rate; attenuation; SHPB apparatus

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Lang, L.; Song, K.-I.; Zhai, Y.; Lao, D.; Lee, H.-L. Stress Wave Propagation in Viscoelastic-Plastic Rock-Like Materials. Materials 2016, 9, 377.

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