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Poromechanical Models

  • Michal PakulaEmail author
  • Mariusz Kaczmarek
  • Frederic Padilla
Chapter
  • 1.7k Downloads

Abstract

This chapter reviews the Biot’s model for predicting propagation of ultrasonic waves in cancellous bone. A presentation of the general theory, including recent developments in the field of poroelastic modelling is proposed. These include micro-inhomogeneity in the fluid flow, thermal conduction effects, macroscopic viscous stresses and micro-poromechanical models such as the multi-layer model. Studies comparing empirical results with predictions from different versions of the Biot’s model are reviewed, and the relevance of these models is discussed. A parametric analysis is performed to illustrate the strong sensitivity of the theoretical predictions to the input parameters.

Keywords

Attenuation coefficient Biot-Allard model Biot’s theory Biot-Willis elastic constants Characteristic size of pore space Darcy flow Dynamic coupling Fast wave Interaction force Johnson-Koplik-Dashen model Modified Biot-Attenborough model Multi-layer model Permeability Phase velocity Poro-elasticity Poromechanical modelling Porosity Schoenberg model Slip effect Slow wave Squirt flow Tortuosity Two-phase model Velocity dispersion Viscous characteristic length Viscous coupling 

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Copyright information

© Springer Netherlands 2011

Authors and Affiliations

  • Michal Pakula
    • 1
    Email author
  • Mariusz Kaczmarek
    • 1
  • Frederic Padilla
    • 2
    • 3
  1. 1.Institute of Mechanics and Applied Computer ScienceKazimierz Wielki University in BydgoszczBydgoszczPoland
  2. 2.Laboratoire d’Imagerie Parametrique, UMR 7623Université Pierre et Marie Curie, CNRSParisFrance
  3. 3.Department of RadiologyUniversity of Michigan Medical CenterAnn ArborUSA

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