Anisotropic Poroelastic Material

Use the node to define the poroelastic material and fluid properties of an anisotropic porous material. Anisotropic properties can here be defined for the elastic matrix material properties as well as the relevant poroacoustic properties (flow resistivity, tortuosity factor, and viscous characteristic length).

The is selected by default. The list contains all applicable coordinate systems in the component. The coordinate system is used for interpreting directions of orthotropic and anisotropic material data and when stresses, strains, and porous properties are presented in a local system.

	Coordinate systems with directions which change with time should not be used.

Select the Model as either or (the default). See the Poroelastic Material for details on the options.

Select a : ; ; or . Then enter or select the settings as described.

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Porous Drained Matrix, Isotropic

If is selected (the default) from the list, select a pair of elastic properties to describe an isotropic drained porous material. The drained parameters are also sometimes referred to as the in-vacuo elastic parameters; they are in principle measured without the presence of the saturating fluid.

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to specify drained Young’s modulus (elastic modulus) Ed (SI unit: Pa) and Poisson’s ratio νd (dimensionless). For an isotropic material, Young’s modulus is the spring stiffness in Hooke’s law, which in 1D form is σ = Edε, where σ is the stress and ε is the strain. Poisson’s ratio defines the normal strain in the perpendicular direction, generated from a normal strain in the other direction and follows the equation ε⊥ = −υε||

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(the default for the Biot–Allard model) to specify drained shear modulus Gd (SI unit: Pa) and Poisson’s ratio νd (dimensionless).

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to specify drained Young’s modulus (elastic modulus) Ed (SI unit: Pa) and drained shear modulus Gd (SI unit: Pa).

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(the default for the Biot model) to specify the drained bulk modulus Kd (SI unit: Pa) and the drained shear modulus Gd (SI unit: Pa). The bulk drained modulus is a measure of the solid porous matrix’s resistance to volume changes. The shear modulus is a measure of the solid porous matrix’s resistance to shear deformations.

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to specify the drained Lamé parameters λd (SI unit: Pa) and μd (SI unit: Pa).

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to specify the drained pressure-wave speed cp (SI unit: m/s) and the shear-wave speed cs (SI unit: m/s).

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to specify the drained density of the porous material in vacuum ρd (SI unit: kg/m3). The drained density ρd is equal to (1 − εp) ρs where ρs is the density of the solid material from which the matrix is made and εp is the porosity.

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(only for the Biot-Allard model) to specify the loss factor of the porous matrix ηs (dimensionless). This value introduces the damping due to losses in the porous structure by transform the elastic moduli into complex valued quantities. This quantity can be frequency dependent if necessary.

For each pair of properties, select from the applicable list to use the value or enter a value or expression. Each of these pairs define the drained elastic properties and it is possible to convert from one set of properties to another.

When is selected from the list, the material properties of the solid porous matrix vary in orthogonal directions only.

The default properties take values . For , enter values or expressions for the drained E (SI unit: Pa), the drained ν (dimensionless), and the drained G (SI unit: Pa).

When is selected from the list, the material properties of the solid porous matrix vary in all directions, and the stiffness comes from the symmetric , D (SI unit: Pa). The default uses values . For enter values in the 6-by-6 symmetric matrix that displays.

In the model the [κp]ijand the [τ∞]ij can have anisotropic properties. The remaining (isotropic) parameters are described in the Porous Parameters for Biot (viscous losses) section.

For the two inputs select either (the default) or . For the option, select if the material property is entered as or (the properties only have non-zero components in the diagonal for i = j). When taken the properties can now be defined as diagonal tensor data, when defining a material in the node.

In the model the [Rf]ij, the [τ∞]ij, and the [Lv]ij can have anisotropic properties. The remaining (isotropic) parameters are described in the Porous Parameters for Biot–Allard (thermal and viscous losses) section.

For the three inputs select either (the default) or . For the option, select if the material property is entered as or (the properties only have non-zero components in the diagonal for i = j). When taken , the properties can now be defined as diagonal tensor data, when defining a material in the node.