Large-deformation poroelasticity

Finite-deformation poroelastic model with a three-field (displacement, solid pressure, fluid pressure) formulation for a saturated porous solid. More...

Description

Large-deformation poroelastic model with volumetric-isochoric split.

Physical model

Three-field mixed formulation \((\mathbf{d}, p_s, p_f)\) for a saturated hyperelastic porous medium undergoing finite deformations.

Kinematics

\[ \mathbf{F} = \mathbf{I} + \nabla_X \mathbf{d}, \quad J = \det\mathbf{F}, \quad \mathbf{C} = \mathbf{F}^\top\mathbf{F}. \]

Governing equations

Momentum (displacement \(\mathbf{d}\)):

\[ -\nabla_X \cdot \mathbf{P} = \mathbf{f}, \qquad \mathbf{P} = \mathbf{P}_\text{iso}(\mathbf{F}) + (p_s - \alpha_B p_f)\, J\, \mathbf{F}^{-\top}, \]

where the isochoric part of the drained skeleton stress \(\mathbf{P}_\text{iso}\) is supplied by the problem via isochoricFirstPiolaKirchhoffStressTensor(F, elemDisc, ipGlobal) and the body force \(\mathbf{f}\) via the problem's source.

Solid pressure ( \(p_s\), algebraic):

\[ p_s^{\mathrm{eq}}(J) - p_s = 0 \]

(volumetric constitutive law; \(p_s^{\mathrm{eq}}\) supplied by the problem via volumetricPressure(J)).

Fluid mass balance ( \(p_f\), transient):

\[ \frac{\partial}{\partial t}\!\left(\alpha_B J + S_p p_f\right) - \nabla_X \cdot \!\left(J\,\frac{\kappa}{\mu_f}\,\mathbf{C}^{-1} \nabla_X p_f\right) = q, \]

with the Biot coefficient \(\alpha_B\), the storage coefficient \(S_p = 1/M\) (inverse Biot modulus, \(S_p = 0\) for incompressible constituents) and the fluid source \(q\) given by the problem's source. In the small-strain limit \(J \approx 1 + \nabla \cdot \mathbf{d}\) this is Biot's storage equation.

The spatial parameters provide biotCoefficient(element, elemDisc, ipGlobal), storageCoefficient(element, elemDisc, ipGlobal), permeability(element, elemDisc, ipGlobal, J) and fluidViscosity(element, elemDisc).

The type tags PoroElasticLargeDefMomentumModel, PoroElasticLargeDefSolidPressureModel and PoroElasticLargeDefFluidPressureModel are coupled via PoroElasticLargeDefCouplingManager and assembled with Experimental::MultiStageMultiDomainAssembler.

Classes
class	Dumux::PoroElasticLargeDefCouplingManager< MDTraits >
	Coupling manager for the large-deformation poroelastic model. More...
class	Dumux::PoroElasticLargeDefMomentumLocalResidual< TypeTag >
	Momentum local residual for the poroelastic large-deformation model. More...
class	Dumux::PoroElasticLargeDefSolidPressureLocalResidual< TypeTag >
	Solid pressure local residual: algebraic constraint \(p_s^{\mathrm{eq}}(J) - p_s = 0\). More...
class	Dumux::PoroElasticLargeDefFluidPressureLocalResidual< TypeTag >
	Fluid pressure local residual for the poroelastic large-deformation model. More...
struct	Dumux::PoroElasticLargeDefMomentumIndices< dim >
	Index set for the momentum subdomain. More...
struct	Dumux::PoroElasticLargeDefMomentumModelTraits< dim >
	Model traits for the momentum subdomain ( \(\dim\) displacement DOFs per node). More...
struct	Dumux::PoroElasticLargeDefSolidPressureIndices
	Index set for the solid pressure subdomain. More...
struct	Dumux::PoroElasticLargeDefSolidPressureModelTraits
	Model traits for the solid pressure subdomain (1 pressure DOF per node). More...
struct	Dumux::PoroElasticLargeDefFluidPressureIndices
	Index set for the fluid pressure subdomain. More...
struct	Dumux::PoroElasticLargeDefFluidPressureModelTraits
	Model traits for the fluid pressure subdomain (1 fluid pressure DOF per node). More...
class	Dumux::PoroElasticLargeDefMomentumVariables< Traits >
	Volume variables for the momentum subdomain (displacement). More...
class	Dumux::PoroElasticLargeDefSolidPressureVariables< Traits >
	Volume variables for the solid pressure subdomain. More...
class	Dumux::PoroElasticLargeDefFluidPressureVariables< Traits >
	Volume variables for the fluid pressure subdomain. More...

Files
file	couplingmanager.hh
	Coupling manager for the large-deformation poroelastic mixed \( \mathbf{d} \)– \( p_s \)– \( p_f \) model.
file	localresidual.hh
	Local residuals for the large-deformation poroelastic mixed \( \mathbf{d} \)– \( p_s \)– \( p_f \) model.
file	model.hh
	Large-deformation poroelastic model with volumetric-isochoric split.
file	variables.hh
	Volume variables for the large-deformation poroelastic mixed \( \mathbf{d} \)– \( p_s \)– \( p_f \) model.