Solid mechanics with fluid pressure

Models linear elastic deformation of a solid taking into account fluid pressure. More...

Description

A poroelastic geomechanical model.

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.

Files
file	geomechanics/poroelastic/couplingmanager.hh
	Coupling manager for porous medium flow problems coupled to a poro-mechanical problem.
file	geomechanics/poroelastic/iofields.hh
	Adds I/O fields specific to the poro-elastic model.
file	geomechanics/poroelastic/localresidual.hh
	Element-wise calculation of the local residual for problems using the poroelastic model.
file	geomechanics/poroelastic/model.hh
	A poroelastic geomechanical model.
file	geomechanics/poroelastic/volumevariables.hh
	Quantities required by the poroelastic model defined on a sub-control volume.
file	poromechanics/poroelastic/couplingmanager.hh
	Coupling manager for porous medium flow problems coupled to a poro-mechanical problem.
file	poromechanics/poroelastic/fvspatialparams.hh
	The base class for spatial parameters of poro-elastic geomechanical problems.
file	poromechanics/poroelastic/iofields.hh
	Adds I/O fields specific to the poro-elastic model.
file	poromechanics/poroelastic/localresidual.hh
	Element-wise calculation of the local residual for problems using the poroelastic model.
file	poromechanics/poroelastic/model.hh
	A poroelastic geomechanical model.
file	poromechanics/poroelastic/volumevariables.hh
	Quantities required by the poroelastic model defined on a sub-control volume.

Classes
class	Dumux::PoroMechanicsCouplingManager< MDTraits, PMFlowId, PoroMechId >
	Coupling manager for porous medium flow problems coupled to a poro-mechanical problem. More...
class	Dumux::FVPoroElasticSpatialParams< GridGeometry, Scalar, Implementation >
	The base class for spatial parameters of poro-elastic geomechanical problems. More...
class	Dumux::PoroElasticIOFields
	Adds I/O fields specific to the poro-elastic model. More...
class	Dumux::PoroElasticLocalResidual< TypeTag >
	Element-wise calculation of the local residual for problems using the poroelastic model. More...
struct	Dumux::PoroElasticModelTraits< dim, numSC, numFP, numFC >
	Specifies a number properties of the poroelastic model. More...
class	Dumux::PoroElasticVolumeVariables< Traits >
	Contains the quantities which are constant within a finite volume in the poroelastic model. More...