Springer Nature is making SARS-CoV-2 and COVID-19 research free. View research | View latest news | Sign up for updates

Critical time for acoustic wavesin weakly nonlinear poroelastic materials

  • 56 Accesses

  • 3 Citations

Abstract.

The final time of existence (critical time) of acoustic waves is a characteristic feature of nonlinear hyperbolic models. We consider such a problem for poroelastic saurated materials of which the material properties are described by Signorini-type constitutitve relations for stresses in the skeleton, and whose material parameters depend on the current porosity. In the one-dimensional case under consideration, the governing set of equations describes changes of extension of the skeleton, a mass density of the fluid, partial velocities of the skeleton and of the fluid and a porosity. We rely on a second order approximation. Relations of the critical time to an initial porosity and to an initial amplitude are discussed. The connection to the threshold of liquefaction is indicated.

This is a preview of subscription content, log in to check access.

References

  1. 1

    Albers, B., Wilmanski K.: An axisymmetric steady-state flow through a poroelastic medium under large deformations. Arch. Appl. Mech. 69, 121-132 (1999)

  2. 2

    Albers, B., Wilmanski, K.: On modeling acoustic waves in saturated poroelastic media. ASCE, Jour. Engn. Mech. 5, 131 (2005)

  3. 3

    Albers, B., Wilmanski, K.: Monochromatic surface waves on impermeable boundaries in two-component poroelastic media. Cont. Mech. Thermodyn. (to appear, 2005)

  4. 4

    Biot, M.A., Willis, D.G.: The elastic coefficients of the theory of consolidation. J. Appl. Mech. 24, 594-601 (1957)

  5. 5

    Lax, P.D.: Development of singularities of solutions of nonlinear hyperbolic partial differential equations. J. Math. Phys. 5, 611-613 (1964)

  6. 6

    Osinov, V.A.: On the formation of discontinuities of wave fronts in a saturated granular body. Cont. Mech. Thermodyn. 10, 253-268 (1998)

  7. 7

    Tolstoy, I.: Acoustics, Elasticity and Thermodynamics of Porous Media: Twenty-One Papers by M. A. Biot. Acous. Soc. of America 1991

  8. 8

    White, J.E.: Underground Sound. Application of Seismic Waves. Elsevier, Amsterdam 1983

  9. 9

    Wilhelm, T., Wilmanski, K.: On the onset of flow instabilities in granular media due to porosity inhomogeneities. Int. J. Multiphase Flow 28, 1929-1944 (2002)

  10. 10

    Wilmanski, K.: Thermomechanics of Continua, Springer, Berlin 1998

  11. 11

    Wilmanski, K.: On the time of existence of weak discontinuity waves. Arch. Mech. 50, 657-669 (1998)

  12. 12

    Wilmanski, K.: Waves in porous and granular materials. In: Hutter, K., Wilmanski, K. (eds.) Kinetic and Continuum Theories of Granular and Porous Media, CISM 400, Springer, Wien NY, 1999, pp. 131-186

  13. 13

    Wilmanski, K.: Thermodynamical admissibility of Biot’s model of poroelastic saturated materials. Arch. Mech. 54, 709-736 (2002)

  14. 14

    Wilmanski, K.: On a micro-macro transition for poroelastic Biot’s model and corresponding gassmann-type relations. Geotechnique 54, 9, 593-604 (2004)

  15. 15

    Wilmanski, K., Albers, B.: Acoustic Waves in Porous Solid-Fluid Mixtures. In: Hutter, K., Kirchner, N. (eds.) Dynamic Response of Granular and Porous Materials under Large and Catastrophic Deformations. Springer, Berlin, 2003, pp. 285-314

Download references

Author information

Correspondence to K. Wilmanski.

Additional information

Received: 10 August 2004, Accepted: 3 December 2004, Published online: 4 March 2005

PACS:

62.50, 81.40, 62.65

Dedicated to Prof J. L. Ericksen on the occasion of his 80th birthday

Communicated by K. Hutter

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Wilmanski, K. Critical time for acoustic wavesin weakly nonlinear poroelastic materials. Continuum Mech. Thermodyn. 17, 171–181 (2005). https://doi.org/10.1007/s00161-004-0196-y

Download citation

Keywords:

  • shock waves in porous materials
  • flow instability in granular materials
  • fluidization