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Transversal inertial effect on relaxation/retardation time of cement mortar under harmonic wave

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Abstract

Under dynamic loading, the constitutive relation of the cement mortar will be significantly affected by the transversal inertial effect of specimens with large diameters. In this paper, one-dimensional theoretical analysis is carried out to determine the transversal inertial effect on the relaxation/retardation time of the cement mortar under the harmonic wave. Relaxation time or retardation time is obtained by means of the wave velocity, attenuation coefficient and the frequency of the harmonic wave. Thus, the transversal inertial effect on the relaxation time from Maxwell model, as well as on retardation time from Voigt model is analyzed. The results show that the transversal inertial effect may lead to the increase of the relaxation time, but induce the decrease of the retardation time. Those should be taken into account when eliminating the transversal inertial effect in applications.

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References

  1. Wilby, C.B., Concrete Materials and Structures. Cambridge University Press, 1991.

  2. Wei, P.J. and Gu, L.L., Influences of interphase on dynamic effective properties of composites reinforced by dispersed spherical particles. Journal of University of Science and Technology Beijing, Mineral, Metallurgy, Material, 2006, 13(3): 256–262.

    Article  Google Scholar 

  3. Wei, P.J. and Chen, J.K., A viscoelastic constitutive model with nonlinear evolutionary internal variables. Acta Mechanica, 2003, 164(3–4): 217–225.

    Article  Google Scholar 

  4. Chang, L.H., Chen, J.K., Experimental study on constitutive relation of cement mortar. Journal of Hydraulic Engineering, 2007, 38(2): 217–220.(in Chinese).

    MathSciNet  Google Scholar 

  5. Yang, T.Q., Luo, W.B., Xu, P., Wei, Y, T. and Gang, Q.G., Theory and Application of Viscoelasticity. Beijing: Science Press, 2004 (in Chinese).

    Google Scholar 

  6. Wang, L.L., Shi, S.Q., Chen, J.Y., Huang, D.J. and Shen, L.J., Influences of strain-rate and stress-state on dynamic response of cement mortar. International Journal of Structural Stability and Dynamics, 2003, 3(3): 419–433.

    Article  Google Scholar 

  7. Inoue, H., Harrigan, J.J. and Reid, S.R., Review of inverse analysis of indirect measurement of impact force. Applied Mechanics Review, 2001, 54(6): 503–524.

    Article  Google Scholar 

  8. Pochhammer, L., The Mathematical Theory of Elasticity. New York: Dover Publishing Co Inc, 1944, 289.

    Google Scholar 

  9. Chree, C., The equations of an isotropic elastic solid in polar and cylindrical coordinates, their solutions and applications. Transactions of the Cambridge Philosophical Sociaty, 1889, 14: 250–309.

    Google Scholar 

  10. Bancroft, D., The velocity of longitudinal waves in cylindrical bars. Physics Review, 1941, 59: 588–93.

    Article  Google Scholar 

  11. Wang, C.Y. and Xia, Y.M., Dispersion analysis for elastic wave in the cylindrical bar by Fourier transform. Explosion and Shock Waves, 1998, 18(1): 1–7.(in Chinese).

    MathSciNet  Google Scholar 

  12. Wang, C.Y., Xia, Y.M., Application of Fourier analysis of the dispersion effect to split Hopkinson pressure testing system and bar tensile impact testing system. Explosion and Shock Waves, 1998, 18(3): 213–219.(in Chinese).

    MathSciNet  Google Scholar 

  13. Zhao, H., Material behavior characterization using SHPB techniques, tests and simulations. Computers and Structures, 2003, 81: 1301–1310.

    Article  Google Scholar 

  14. Lu, J.H., Shen, J.H. and Zhao, L.M., Application of the inverse analysis to the dynamic response test of structures subjected to intense dynamic loading. Explosion and Shock Waves, 2004, 24(2): 140–144.(in Chinese).

    Google Scholar 

  15. Wu E.B., Tsai, C.Z. and Tseng, L.H., A deconvolution method for force reconstruction in rods under axial impact. Journal of the Acoustical Sociaty of America, 1998, 104(3): 1418–1426.

    Article  Google Scholar 

  16. Zhu, J., Hu, S.S. and Wang, L.L., The wave propagation and inverse analyses on ϕ37mm split Hopkinson pressure bar. Proceedings of the 3rd National Symposium on Experimental Techniques in Mechanics of Explosion, Huangshan, 2004, 260–266 (in Chinese).

  17. Zhao, H. and Gary, G., A three-dimensional analytical solution of longitudinal wave propagation in an infinite linear viscoelastic cylindrical bar. Application to experimental techniques. Journal of the Mechanics and Physics, 1995, 43: 1335–1348.

    Article  MathSciNet  Google Scholar 

  18. Christensen, R.M., Theory of Viscoelasticity: An Introduction. New York: Academic Press Inc., 1982, 15–76.

    Google Scholar 

  19. Wang, L.L., Foundations of Stress Waves. Beijing: National Defense Industry Press, 1985; Amstadam: Elsevier, 2007.

    Google Scholar 

  20. Timoshenko, S.P. and Goodier, J.N., Theory of Elasticity. New York: McGraw-Hill Book Company, 1970, 6–16.

    MATH  Google Scholar 

  21. Hibbeler, R.C., Engineering Mechanics (Dynamics, tenth edition), Beijing: Pearson Education North Limited and Higher Education Press, 2004, 377–461.

    Google Scholar 

  22. Chen, J.K., Cao, Y.H., Wang, H.R. and Zhu, J., Experimental on the Viscous Attenuation of Ultrasonic Waves in Cement Mortar. In: Piezoelectricity, Acoustic Waves and Device Applications, Proceedings of the 2006 Symposium, World Scientific Publishing Co. Pte. Ltd., 2007, 250–254.

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Correspondence to Jiankang Chen.

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Project supported by the National Natural Science Foundation of China (No. 10572064), K.C. Wong Magna Fund in Ningbo University, and the Natural Science Foundation of Zhejiang Province (No. Y107780) and Ningbo University (No. XK0609017).

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Zhu, J., Cao, Y. & Chen, J. Transversal inertial effect on relaxation/retardation time of cement mortar under harmonic wave. Acta Mech. Solida Sin. 21, 44–50 (2008). https://doi.org/10.1007/s10338-008-0807-4

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  • DOI: https://doi.org/10.1007/s10338-008-0807-4

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