Deformation of a solid body using the theory of linear elasticity (small deformations) More...

#include <dune/common/fvector.hh>
#include <dumux/common/properties.hh>
#include <dumux/common/properties/model.hh>
#include <dumux/geomechanics/properties.hh>
#include <dumux/flux/hookeslaw.hh>
#include "indices.hh"
#include "localresidual.hh"
#include "volumevariables.hh"

Description

This model describes the deformation of a solid body using the theory of linear elasticity. The momentum balance equation of the solid body can be expressed by

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

where \( \boldsymbol{\sigma} \) is the stress tensor, \( \rho \) is the density of the solid, \( \mathbf{f} \) 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 \( \rho\ddot{\mathbf{u}} \approx 0\).

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.

Classes
struct	Dumux::ElasticModelTraits< dim, numSolidComp >
	Specifies a number properties of the elastic model. More...

struct	Dumux::ElasticVolumeVariablesTraits< PV, DV, MT, SST, SSY >
	Traits class for the volume variables of the elastic model. More...

struct	Dumux::Properties::TTag::Elastic

struct	Dumux::Properties::LocalResidual< TypeTag, TTag::Elastic >
	Use the local residual of the elastic model. More...

struct	Dumux::Properties::ModelTraits< TypeTag, TTag::Elastic >
	The model traits of the elastic model. More...

struct	Dumux::Properties::VolumeVariables< TypeTag, TTag::Elastic >
	Set the volume variables property. More...

struct	Dumux::Properties::StressType< TypeTag, TTag::Elastic >
	By default, we use hooke's law for stress evaluations. More...

Namespaces
namespace	Dumux

namespace	Dumux::Properties
	The energy balance equation for a porous solid.

namespace	Dumux::Properties::TTag
	Type tag for numeric models.

Include dependency graph for geomechanics/elastic/model.hh:

Description

Classes

Namespaces