Solid mechanics with fluid pressure

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

\[ \nabla\cdot\boldsymbol{\sigma_{\mathrm{eff}}} + \rho \mathbf{g} + \mathbf{f} = \rho\ddot{\mathbf{u}}, \]

where \( \boldsymbol{\sigma_{\mathrm{eff}}} \) is the effective stress tensor, \( \rho = (1 - \phi) \rho_s + \phi \rho_f \) is the average density of solids and fluids within the porous medium, \( \mathbf{f} \) in \( \mathrm{N/m^3} \) 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 \( \boldsymbol{\sigma_{\mathrm{eff}}} \) is determined by the stress tensor \( \boldsymbol{\sigma} \) , the effective pore pressure \( p_{\mathrm{eff}} \) and the Biot's coefficient \( \alpha \) :

\[ \boldsymbol{\sigma_{\mathrm{eff}}} = \boldsymbol{\sigma} - \alpha p_{\mathrm{eff}} \mathbf{I} \]

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

\[ \boldsymbol{\sigma} = \lambda\mathrm{tr}(\boldsymbol{\varepsilon}) \mathbf{I} + 2G \boldsymbol{\varepsilon}, \]

with

\[ \boldsymbol{\varepsilon} = \frac{1}{2} \left[ \nabla\mathbf{u} + (\nabla\mathbf{u})^{\mathrm{T}} \right]. \]

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.

Classes
class	Dumux::PoroMechanicsCouplingManager< MDTraits, PMFlowId, PoroMechId >
	Coupling manager for porous medium flow problems coupled to a poro-mechanical problem. 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...