An alternative Biot's displacement formulation for porous materials.
This paper proposes an alternative displacement formulation of Biot's linear model for poroelastic materials. Its advantage is a simplification of the formalism without making any additional assumptions. The main difference between the method proposed in this paper and the original one is the choice of the generalized coordinates. In the present approach, the generalized coordinates are chosen in order to simplify the expression of the strain energy, which is expressed as the sum of two decoupled terms. Hence, new equations of motion are obtained whose elastic forces are decoupled. The simplification of the formalism is extended to Biot and Willis thought experiments, and simpler expressions of the parameters of the three Biot waves are also provided. A rigorous derivation of equivalent and limp models is then proposed. It is finally shown that, for the particular case of sound-absorbing materials, additional simplifications of the formalism can be obtained.
Dazel
Olivier
O
Laboratoire d'Acoustique de l'Université du Maine-UMR CNRS 6613, Avenue Olivier Messiaen, F-72 085 Le Mans Cedex France. olivier.dazel@univ-lemans.fr
Brouard
Bruno
B
Depollier
Claude
C
Griffiths
Stéphane
S
D000162:Acoustics; D004548:Elasticity; D007700:Kinetics; D008433:Mathematics; D008962:Models, Theoretical; D016062:Porosity; D013016:Sound