Acta Mechanica Solida Sinica

, Volume 32, Issue 1, pp 69–80 | Cite as

Rate-Dependent Characteristic of Relaxation Time of Concrete

  • Hui Song
  • Jiankang ChenEmail author
  • Cheng Qian
  • Yunfeng Lv
  • Yonghui Cao


This study focused on the rate-dependent relaxation time of concrete using the split Hopkinson pressure bar test and the ultrasonic technique. Based on the experimental results, and considering the viscous effect in concrete, the viscoelastic stress–strain relationship was established in terms of the principles of irreversible thermodynamics and the generalized Onsager’s principle, providing the convergence of an iterative scheme in terms of the Lipschitz’s condition. It was found that the relaxation time of concrete depends on the strain rate. Furthermore, considering the state equations and damage evolution, a nonlinear viscoelastic constitutive model of concrete coupling damage was proposed. Compared with the experimental results, this model could better characterize the strengthening and softening characteristics of concrete prior to and beyond the strength limit. Further analysis indicated that the viscous effect is dominantly caused by the C–S–H in concrete.


Concrete Constitutive relation Viscoelasticity Relaxation time Damage evolution 



The authors would like to acknowledge the financial support from the National Natural Science Foundation of China (NSFC #11832013, #11772164, #11572163), the National Basic Research Program of China (973 Program, 2009CB623203), the Key Research Program of Society Development of Ningbo (2013C51007) and the K.C. Wong Magna Fund in Ningbo University.


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics 2018

Authors and Affiliations

  • Hui Song
    • 1
    • 3
  • Jiankang Chen
    • 1
    • 2
    Email author
  • Cheng Qian
    • 1
  • Yunfeng Lv
    • 1
  • Yonghui Cao
    • 1
  1. 1.The Faculty of Mechanical Engineering and MechanicsNingbo UniversityNingboChina
  2. 2.State Key Laboratory of Turbulence and Complex SystemsPeking UniversityBeijingChina
  3. 3.The Faculty of Civil Engineering and ArchitectureNanchang Institute of TechnologyNanchangChina

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