Model of Biot

The model of Biot is a physical model of which the goal is to model the mechanical behavior of porous materials or poro-rubber bands. It is named according to its inventor, the Belgian physicist Maurice Anthony Biot. It is called also " model of Biot-Allard"

Porous materials

These materials consist of a solid skeleton comprising of the pores filled of the surrounding fluid (of the air for acoustics, of water in geology…) The porous materials are foams, the glass wools, the felts, the porous rocks…

Parameters of Biot

In this model, a material is characterized by a certain number of parameters:

Traditional mechanical parameters

the Density of the skeleton (noted in general $\ rho$ )
the Modulus Young of the skeleton in the vacuum (noted $E$ in general)
the Poisson's ratio of the skeleton in the vacuum (noted $\ nu$ in general)
structural damping (noted $\ eta$ in general)

Specific parameters known as parameters of Biot

the porosity (noted in general $\ Phi_P$ ), equal to the voluminal fraction occupied by the air in the porous
the resistivity (noted in general $\ sigma_R$ ), expressed in general in $N.s.m^ {- 4}$ , which represents the intensity with which the porous one is opposed in the passing air
the tortuosity (noted in general $\ alpha$ ), higher than 1, which represents the relationship between the distance between two points while following the ways defined by the pores, and outdistances it between the two points " with flight of oiseau"
the viscous characteristic length (noted in general $\ Lambda$ ), representing the scale where the phenomena of viscous dissipation occur.
the thermal length characteristic (noted in general $\ Lambda'$ ), representing the scale where the phenomena of thermal dissipation occur, always higher than the preceding one.

Uses

It is used in particular in acoustics, to calculate the insulation and the acoustic absorption offered by foams and glass wools, treès frequently used for the soundproofing in the building and the industry of transport (automobile, railway, aeronautical).

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