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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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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