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Wave propagation in strain gradient poroelastic medium with microinertia: closed-form and finite element solutions

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Abstract

This article is about ultrasonic wave propagation in microstructured porous media. The classic Biot’s model is enriched using a strain gradient approach to be able to capture high-order effects when the wavelength approaches the characteristic size of the microstructure. In order to reproduce actual transmission/reflection experiments performed on poroelastic samples, and to validate the choice of the model, the computation of the time domain response is necessary, as it allows for a direct comparison with experimental results. For obtaining the time response, we use two strategies: on the one hand we compute the closed form solution by using the Laplace and Fourier transforms techniques; on the other hand we used a finite element method. The results are presented for a transmission/reflection test performed on a poroelastic sample immersed in water. The effects introduced by the strain gradient terms are visible in the time response and in agreement with experimental observations. The results can be exploited in characterization of mechanical properties of poroelastic media by enhancing the reliability of quantitative ultrasound techniques.

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Authors and Affiliations

  1. Laboratoire Modélisation et Simulation Multi Echelle, MSME UMR 8208 CNRS, Université Paris-Est, 61, Avenue du général de Gaulle, 94010, Créteil Cedex, France

    Giuseppe Rosi, Ilaria Scala, Vu-Hieu Nguyen & Salah Naili

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  1. Giuseppe Rosi
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  2. Ilaria Scala
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  3. Vu-Hieu Nguyen
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  4. Salah Naili
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Correspondence to Giuseppe Rosi.

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Rosi, G., Scala, I., Nguyen, VH. et al. Wave propagation in strain gradient poroelastic medium with microinertia: closed-form and finite element solutions. Z. Angew. Math. Phys. 68, 58 (2017). https://doi.org/10.1007/s00033-017-0802-z

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  • DOI: https://doi.org/10.1007/s00033-017-0802-z

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