diff --git a/dumux/geomechanics/elastic/model.hh b/dumux/geomechanics/elastic/model.hh index 82614c943f8ff39a015ecf7e49dd6a2987a83f91..bce39074e947616beab3cf9311ea9d424b43ebf2 100644 --- a/dumux/geomechanics/elastic/model.hh +++ b/dumux/geomechanics/elastic/model.hh @@ -19,7 +19,34 @@ /*! * \file * \ingroup Elastic - * \brief Defines a type tag and some properties for the elastic geomechanical model + * \brief A geomechanical model. + * + * 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 + \f[ + \nabla\cdot\boldsymbol{\sigma} + \rho \mathbf{g} + \mathbf{f} = \rho\ddot{\mathbf{u}}, + \f] + * where \f$\boldsymbol{\sigma} \f$ is the stress tensor, \f$\rho \f$ is the density of + * the solid, \f$\mathbf{f} \f$ in \f$\mathrm{N/m^3} \f$ is the external force acting on the body per unit volume (e.g. magnetism), + * and \f$\mathbf{u} = \mathbf{x} - \mathbf{x}_{\mathrm{initial}} \f$ is the displacement, + * defined as the difference in material points \f$\mathbf{x} \f$ and \f$\mathbf{x}_{\mathrm{initial}} \f$ + * 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 + * \f$\rho\ddot{\mathbf{u}} \approx 0\f$. + * + * Per default, Hookes' Law is used for expressing the stress tensor \f$\boldsymbol{\sigma} \f$ as a function of the + * displacement: + \f[ + \boldsymbol{\sigma} = \lambda\mathrm{tr}(\boldsymbol{\varepsilon}) \mathbf{I} + 2G \boldsymbol{\varepsilon}, + \f] + * with + \f[ + \boldsymbol{\varepsilon} = \frac{1}{2} \left[ \nabla\mathbf{u} + (\nabla\mathbf{u})^{\mathrm{T}} \right]. + \f] + * + * Primary variables are the displacements in each direction \f$\mathbf{u} \f$. + * Gravity can be enabled or disabled via a runtime parameter. + * */ #ifndef DUMUX_GEOMECHANICS_ELASTIC_MODEL_HH #define DUMUX_GEOMECHANICS_ELASTIC_MODEL_HH diff --git a/dumux/geomechanics/poroelastic/model.hh b/dumux/geomechanics/poroelastic/model.hh index 68334dd6e781e40eababcfa2ef37bc3483dec67d..98d590e4f4133e4b17e2c1d22a340a4e0a614e95 100644 --- a/dumux/geomechanics/poroelastic/model.hh +++ b/dumux/geomechanics/poroelastic/model.hh @@ -19,7 +19,41 @@ /*! * \file * \ingroup PoroElastic - * \brief Defines a type tag and some properties for the poroelastic geomechanical model + * \brief 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 + \f[ + \nabla\cdot\boldsymbol{\sigma_{\mathrm{eff}}} + \rho \mathbf{g} + \mathbf{f} = \rho\ddot{\mathbf{u}}, + \f] + * where \f$\boldsymbol{\sigma_{\mathrm{eff}}} \f$ is the effective stress tensor, + * \f$\rho = (1 - \phi) \rho_s + \phi \rho_f \f$ is the average density of solids and fluids within the porous medium, + * \f$\mathbf{f} \f$ in \f$\mathrm{N/m^3} \f$ is the external force acting on the body per unit volume (e.g. magnetism), + * and \f$\mathbf{u} = \mathbf{x} - \mathbf{x}_{\mathrm{initial}} \f$ is the displacement, + * defined as the difference in material points \f$\mathbf{x} \f$ and \f$\mathbf{x}_{\mathrm{initial}} \f$ + * 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 + * \f$\rho\ddot{\mathbf{u}} \approx 0\f$. + * + * Using the concept of the effective stress, the effective stress tensor \f$\boldsymbol{\sigma_{\mathrm{eff}}} \f$ is + * determined by the stress tensor \f$\boldsymbol{\sigma} \f$ , the effective pore pressure \f$p_{\mathrm{eff}} \f$ and the Biot's coefficient \f$\alpha \f$ : + \f[ + \boldsymbol{\sigma_{\mathrm{eff}}} = \boldsymbol{\sigma} - \alpha p_{\mathrm{eff}} \mathbf{I} + \f] + * + * Per default, Hookes' Law is used for expressing the stress tensor \f$\boldsymbol{\sigma} \f$ as a function of the + * displacement: + \f[ + \boldsymbol{\sigma} = \lambda\mathrm{tr}(\boldsymbol{\varepsilon}) \mathbf{I} + 2G \boldsymbol{\varepsilon}, + \f] + * with + \f[ + \boldsymbol{\varepsilon} = \frac{1}{2} \left[ \nabla\mathbf{u} + (\nabla\mathbf{u})^{\mathrm{T}} \right]. + \f] + * + * Primary variables are the displacements in each direction \f$\mathbf{u} \f$. + * Gravity can be enabled or disabled via a runtime parameter. + * */ #ifndef DUMUX_GEOMECHANICS_POROELASTIC_MODEL_HH #define DUMUX_GEOMECHANICS_POROELASTIC_MODEL_HH