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Dynamic stress concentration of a smooth moving punch influenced by a shear wave in an initially stressed dry sandy layer

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Abstract

In the present model, we have analyzed the dynamic stress concentration of a semi-infinite smooth moving punch on the shear wave propagation in an initially stressed dry sandy strip. For the analytical solution of the problem, the Wiener–Hopf technique and two-sided Fourier integral transforms have been used. The expression of dynamic stress concentration for the force of a constant intensity has been determined in closed-form. Noticeable effects of the speed of the moving punch, horizontal initial stress, vertical initial stress, and sandiness parameter on the dynamic stress concentration in an initially stressed dry sandy strip have been unraveled and depicted by numerical computations and graphical demonstrations. Further, the expression of dynamic stress concentration for the case of constant load has been deduced from the obtained expression of dynamic stress concentration. Comparison of dynamic stress concentration performed for different cases of initial stresses and differently configured strips serve as one of the major highlights of the present problem. Moreover, for the sake of validation, the obtained results for constant load have been matched with the pre-established results as a particular case of the problem.

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References

  1. Abrahams, I.D.: On the application of the Wiener-Hopf technique to problems in dynamic elasticity. Wav. Mot. 36, 311–333 (2002)

    Article  MathSciNet  Google Scholar 

  2. Koiter, W.T.: Approximate solutions of Wiener-Hopf type equations with applications. Proc. Kon. Ned. Acad. Wet. 2, 57 (1954)

    Google Scholar 

  3. Büyükaksoy, A., Çınar, G.: Solution of a matrix Wiener-Hopf equation connected with the plane wave diffraction by impedance loaded parallel plate waveguide. Math. Meth. Appl. Sci. 28, 1633–1645 (2005). https://doi.org/10.1002/mma.625

    Article  MathSciNet  MATH  Google Scholar 

  4. Miklowitz, J.: Plane-stress unloading waves emanating from a suddenly punched hole in a stretched elastic plate. J. Appl. Mech. 27, 165–171 (1960). https://doi.org/10.1115/1.3643892

    Article  MathSciNet  MATH  Google Scholar 

  5. Dhaliwal, R.S.: Punch problem for an elastic layer overlying an elastic foundation. Int. J. Eng. Sci. 8, 273–288 (1970). https://doi.org/10.1016/0020-7225(70)90058-3

    Article  MATH  Google Scholar 

  6. Achenbach, J.D.: Wave Propagation in Elastic Solids. North Holland Publ. Comp, New York (1975)

    MATH  Google Scholar 

  7. Keer, L.M., Pariha, K.S.: A note on the singularity at the corner of a wedge-shaped punch or crack. SIAM J. Appl. Math. 34, 297–302 (1978). https://doi.org/10.1137/0134024

    Article  MathSciNet  MATH  Google Scholar 

  8. Georgiadis, H.G.: Moving punch on a highly orthotropic elastic layer. Act. Mech. 68, 193–202 (1987). https://doi.org/10.1007/BF01190883

    Article  MATH  Google Scholar 

  9. Hasebe, N., Okumura, M., Nakamura, T.: Frictional punch and crack in plane elasticity. J. Eng. Mech. 115, 1137–1149 (1989). https://doi.org/10.1061/(ASCE)0733-9399(1989)115:6(1137)

    Article  Google Scholar 

  10. Jin, B., Liu, H.: Exact solution for horizontal displacement at center of the surface of an elastic half space under horizontal impulsive punch loading. Soil Dyn. Earthq. Eng. 18, 495–498 (1999). https://doi.org/10.1016/S0267-7261(99)00020-2

    Article  Google Scholar 

  11. Comez, I., Guler, M.A.: The contact problem of a rigid punch sliding over a functionally graded bilayer. Act. Mech. 228, 2237 (2017). https://doi.org/10.1007/s00707-017-1827-2

    Article  MathSciNet  MATH  Google Scholar 

  12. Çömez, İ: Moving contact problem of an unbonded layer in the presence of body force. Iran. J. Sci. Tech. Transact. Mech. Eng. 1, 1–16 (2021). https://doi.org/10.1007/s40997-021-00464-y

    Article  Google Scholar 

  13. Dey, S., Gupta, A.K., Gupta, S.: Propagation of torsional surface waves in dry sandy medium under gravity. Math. Mech. Sol. 3, 229–235 (1998). https://doi.org/10.1177/108128659800300207

    Article  MATH  Google Scholar 

  14. Dey, S., Gupta, A.K., Gupta, S.: Effect of gravity and initial stress on torsional surface waves in dry sandy medium. J. Eng. Mech. 128, 1115–1118 (2002). https://doi.org/10.1061/(ASCE)0733-9399(2002)128:10(1116)

    Article  Google Scholar 

  15. Naeini, S.A., Baziar, M.H.: Effect of fines content on steady-state strength of mixed and layered samples of a sand. Soil Dyn. Earth. Eng. 24, 181–187 (2004). https://doi.org/10.1016/j.soildyn.2003.11.003

    Article  Google Scholar 

  16. Singh, A.K., Singh, A.K., Yadav, R.P.: Stress intensity factor of dynamic crack in double-layered dry sandy elastic medium due to shear wave under different loading conditions. Int. J. Geomech. 20, 04020215 (2020). https://doi.org/10.1061/(ASCE)GM.1943-5622.0001827

    Article  Google Scholar 

  17. Du, J., Jin, X., Wang, J.: Love wave propagation in layered magneto-electro-elastic structures with initial stress. Acta. Mech. 192, 169–189 (2007). https://doi.org/10.1007/s00707-006-0435-3

    Article  MATH  Google Scholar 

  18. Yu, J., Zhang, C.: Influences of initial stresses on guided waves in functionally graded hollow cylinders. Acta. Mech. 224, 745–757 (2013). https://doi.org/10.1007/s00707-012-0748-3

    Article  MATH  Google Scholar 

  19. Yu, J., Zhang, C.: Effects of initial stress on guided waves in orthotropic functionally graded plates. Appl. Math. Mod. 38, 464–478 (2014). https://doi.org/10.1016/j.apm.2013.06.029

    Article  MathSciNet  MATH  Google Scholar 

  20. Singh, A.K., Das, A., Chattopadhyay, A., Dhua, S.: Dispersion of shear wave propagating in vertically heterogeneous double layers overlying an initially stressed isotropic half-space. Soil Dyn. Earth. Eng. 69, 16–27 (2015). https://doi.org/10.1016/j.soildyn.2014.10.021

    Article  Google Scholar 

  21. Mahanty, M., Chattopadhyay, A., Kumar, P., Singh, A.K.: Effect of initial stress, heterogeneity and anisotropy on the propagation of seismic surface waves. Mech. Adv. Mat. Str. 27, 177–188 (2020). https://doi.org/10.1080/15376494.2018.1472329

    Article  Google Scholar 

  22. Ejaz, K., Shams, M.: Propagation of Rayleigh wave in initially-stressed compressible hyper elastic materials. Wav. Mot. 100, 102675 (2021). https://doi.org/10.1016/j.wavemoti.2020.102675

    Article  MATH  Google Scholar 

  23. Guha, S., Singh, A.K.: Plane wave reflection/transmission in imperfectly bonded initially stressed rotating piezothermoelastic fiber-reinforced composite half-spaces. Eur J Mech-A/Solids 88, 104242 (2021). https://doi.org/10.1016/j.euromechsol.2021.104242

    Article  MathSciNet  MATH  Google Scholar 

  24. Mandi, A., Kundu, S., Pal, P.C., Pati, P.: An analytic study on the dispersion of Love wave propagation in double layers lying over inhomogeneous half-space. J. Sol. Mech. 11, 570–580 (2019). https://doi.org/10.22034/JSM.2019.666690

    Article  Google Scholar 

  25. Biot, M.A.: The influence of initial stress on elastic waves. J. Appl. Phys. 11, 522–530 (1940). https://doi.org/10.1063/1.1712807

    Article  MathSciNet  MATH  Google Scholar 

  26. Titchmarsh, E.C.: Theory of Fourier Integrals. Oxford University Press, London (1939)

    Google Scholar 

  27. Noble, B.: Methods Based on Wiener-Hopf Technique for the Solution of Partial Differential Equations. Pergamon Press, London (1958). https://doi.org/10.1063/1.3060973

    Book  MATH  Google Scholar 

  28. Chattopadhyay, A.: Effect of punch on the propagation of shear waves in a self-reinforced medium. Proc.-Indian Natl. Sci. Acad. Part A 61, 37–46 (1995)

    MATH  Google Scholar 

  29. Singh, A.K., Parween, Z., Chatterjee, M., Chattopadhyay, A.: Love-type wave propagation in a pre-stressed viscoelastic medium influenced by smooth moving punch. Wav. Rand. Compl. Med. 25, 268–285 (2015). https://doi.org/10.1080/17455030.2015.1015182

    Article  MathSciNet  MATH  Google Scholar 

  30. Gubbins, D.: Seismology and Plate Tectonics. Cambridge University Press (1990)

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Acknowledgements

The authors convey their sincere thanks to University Grants Commission, New Delhi for providing Senior Research Fellowship to Mr. Ajeet Kumar Singh. The authors are also indebted to the Department of Science and Technology, Science and Engineering Research Board (DST-SERB) (Grant No.: EMR/2017/000263/MS) for providing the necessary facilities to carry out this research work.

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  1. Department of Mathematics and Computing, Indian Institute of Technology (Indian School of Mines), Dhanbad, Jharkhand, 826004, India

    Abhishek Kumar Singh & Ajeet Kumar Singh

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Correspondence to Ajeet Kumar Singh.

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Singh, A.K., Singh, A.K. Dynamic stress concentration of a smooth moving punch influenced by a shear wave in an initially stressed dry sandy layer. Acta Mech 233, 1757–1768 (2022). https://doi.org/10.1007/s00707-022-03197-4

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