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Critical time for acoustic wavesin weakly nonlinear poroelastic materials

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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.

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  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

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Correspondence to K. Wilmanski.

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


62.50, 81.40, 62.65

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

Communicated by K. Hutter

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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

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