Propagation of Acoustic Waves in Porous Media and their Reflection and Transmission at a Pure Fluid/Porous Medium Permeable Interface

International audienceWe find a sufficient condition of hyperbolicity for a differential system governing the motion of a onedimensional porous medium, so ensuring the existence of a solution for the associated Cauchy problem. We study propagation of linear waves impacting at a pure-fluid/porous-medium interface and we deduce novel expressions for the reflection and transmission coefficients in terms of the spectral properties of the governing differential system. We show three dimensional plots drawing reflection and transmission coefficients as functions of Biot's parameters. In such a way we propose an indirect method for measuring Biot's parameters when the measurement of the reflection and transmission coefficients associated to the traveling waves is possible

One-parameter family of equations of state for isotropic compressible solids

Applying the theorem proved by the authors in [10], we established the hyperbolicity of non-stationary equations of hyperelastic isotropic solids for a one-parameter family of equations of state containing, in particular, generalized neo-hookean solids. The hyperbolicity is equivalent to the rank-one convexity of the corresponding stored energy. The influence of the parameter on the solution properties is shown in the case of a strong shear test