7.6.15.13.3. Coussy

Syntax

Porosity [{of} SpeciesName] = Coussy (M_Inv = m_inv | Biot = biot | [Ref_Porosity = ref_porosity] | [Ref_Pressure = ref_pressure] | [K_D = K_d] | [Thermal_Expansion = thermal_expansion] | [Ref_Temperature = ref_temperature] | [Alpha_S = alpha_s] | [Alpha_F = alpha_f] | [K_T = k_t])

Scope

Aria Material

Summary

Coussy’s model of porosity for deforming media (based on pore pressure and div(u), fixed-stress formulation

Description

$\phi = \phi_0 + M_{INV}\left(p_{k+1} - p_{0}\right) + b\epsilon_{v, k} - \alpha_m\left(T_{k+1} - T_{0}\right) + \frac{b^2}{K_{d}}\left(p_{k+1} - p_{k}\right) + b\alpha_s\left(T_{k+1} - T_{k}\right)$

where $\phi_0$ is the reference porosity, $p$ is pressure, $p_0$ is reference pressure $\epsilon_{v, k} = \nabla \cdot \bf{u}$ ( $\bf{u}$ is displacement), $T$ is temperature, $T_{0}$ is reference temperature, and $b$ is the biot coefficient.

The last two terms are stabilization terms for doing fixed stress iterations (where the mesh motion equation and porosity equations are segregated). In this case, the stabilization parameter $K_d$ must be provided. Additionally, the subscript $k+1$ and $k$ represent the current and old solution, respectively.

When thermal expansion is included, $\alpha_m = \phi_{0}\alpha_f + (b-\phi_{0})\alpha_s$ and is the bulk thermal expansion coefficient, where $\alpha_f$ and $\alpha_s$ are thermal expansion coefficients for the fluid and solid, respectively.

Parameter	Value	Default
{of}	{of \| species \| subindex}	–
SpeciesName	string	–
m_inv	real	–
biot	real	–
ref_porosity	real	0
ref_pressure	real	0
K_d	real	0
thermal_expansion	integer	0
ref_temperature	real	0
alpha_s	real	0
alpha_f	real	0
k_t	real	0