Solid mechanics w/o fluid pressure

Models linear elastic deformation of a solid. Disregards fluid pressure. More...

Description

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

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.

Files
file	geomechanics/elastic/indices.hh
	Defines the indices for the elastic model.
file	geomechanics/elastic/localresidual.hh
	Element-wise calculation of the local residual for problems using the elastic model considering linear elasticity.
file	geomechanics/elastic/model.hh
	Deformation of a solid body using the theory of linear elasticity (small deformations)
file	geomechanics/elastic/volumevariables.hh
	Quantities required by the elastic model defined on a sub-control volume.

Classes
struct	Dumux::ElasticIndices
	The indices for the linear elasticity model. More...
class	Dumux::ElasticLocalResidual< TypeTag >
	Element-wise calculation of the local residual for problems using the elastic model considering linear elasticity. More...
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...
class	Dumux::ElasticVolumeVariables< Traits >
	Contains the quantities which are constant within a finite volume in the elastic model. More...