poromechanics/poroelastic/model.hh File Reference

A poroelastic geomechanical model. More...

#include <dune/common/fvector.hh>
#include <dumux/common/properties.hh>
#include <dumux/solidmechanics/elastic/indices.hh>
#include <dumux/solidmechanics/elastic/model.hh>
#include <dumux/flux/hookeslaw.hh>
#include <dumux/flux/effectivestresslaw.hh>
#include "localresidual.hh"
#include "volumevariables.hh"
#include "iofields.hh"

Go to the source code of this file.

Description

This model describes the deformation of a porous medium using the theory of linear poroelasticity. The momentum balance equation of a porous medium can be expressed by

$$\mathrm{\nabla }\cdot {\mathit{\sigma }}_{\mathbf{eff}}+\rho \mathbf{g}+\mathbf{f}=\rho \ddot{\mathbf{u}},$$

where ${\mathit{\sigma }}_{\mathbf{eff}}$ is the effective stress tensor, $\rho =(1-\varphi ){\rho }_s+\varphi {\rho }_f$ is the average density of solids and fluids within the porous medium, $\mathbf{f}$ in $\mathrm{N}/{\mathrm{m}}^3$ is the external force acting on the body per unit volume (e.g. magnetism), and $\mathbf{u}=\mathbf{x}-{\mathbf{x}}_{\mathrm{initial}}$ is the displacement, defined as the difference in material points $\mathbf{x}$ and ${\mathbf{x}}_{\mathrm{initial}}$ in the deformed and undeformed (initial) state, respectively. The model assumes quasi-static conditions, that is, the above momentum balance equation is solved under the assumption that the acceleration term $\rho \ddot{\mathbf{u}}\approx 0$.

Using the concept of the effective stress, the effective stress tensor ${\mathit{\sigma }}_{\mathbf{eff}}$ is determined by the stress tensor $\mathit{\sigma }$ , the effective pore pressure $p_{\mathrm{eff}}$ and the Biot's coefficient $\alpha$ :

$${\mathit{\sigma }}_{\mathbf{eff}}=\mathit{\sigma }-\alpha p_{\mathrm{eff}}\mathbf{I}$$

Per default, Hookes' Law is used for expressing the stress tensor $\mathit{\sigma }$ as a function of the displacement:

$$\mathit{\sigma }=\lambda \mathrm{tr}(\mathit{\epsilon })\mathbf{I}+2G\mathit{\epsilon },$$

with

$$\mathit{\epsilon }=\frac{1}{2}[\mathrm{\nabla }\mathbf{u}+(\mathrm{\nabla }\mathbf{u}{)}^{\mathrm{T}}].$$

Primary variables are the displacements in each direction $\mathbf{u}$. Gravity can be enabled or disabled via a runtime parameter.

Classes
struct	Dumux::PoroElasticModelTraits< dim, numSC, numFP, numFC >
	Specifies a number properties of the poroelastic model. More...
struct	Dumux::Properties::TTag::PoroElastic
struct	Dumux::Properties::LocalResidual< TypeTag, TTag::PoroElastic >
	Use the local residual of the poro-elastic model. More...
struct	Dumux::Properties::IOFields< TypeTag, TTag::PoroElastic >
	default vtk output fields specific to this model More...
struct	Dumux::Properties::ModelTraits< TypeTag, TTag::PoroElastic >
	The default model traits of the poro-elastic model. More...
struct	Dumux::Properties::VolumeVariables< TypeTag, TTag::PoroElastic >
	Set the volume variables property. More...
struct	Dumux::Properties::StressType< TypeTag, TTag::PoroElastic >
	Per default, we use effective stresses on the basis of Hooke's Law. More...

Namespaces
namespace	Dumux
namespace	Dumux::Properties
	The energy balance equation for a porous solid.
namespace	Dumux::Properties::TTag
	Type tag for numeric models.

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