This contribution presents a generalized conceptual model for the finite element
solution of quasi-static isothermal hydro-mechanical processes in (fractured) porous
media at large strains. A frequently used averaging procedure, known as Theory of
Porous Media, serves as background for the complex multifield approach presented here.
Within this context, a consistent representation of the weak formulation of the governing
equations (i.e., overall balance equations for mass and momentum) in the reference configuration
of the solid skeleton is preferred. The time discretization and the linearization are
performed for the individual variables and nonlinear functions representing the integrands
of the weak formulation instead of applying these conceptual steps to the overall nonlinear
system of weighted residuals. Constitutive equations for the solid phase deformation
are based on the multiplicative split of the deformation gradient allowing the adaptation
of existing approaches for technical materials and biological tissues to rock materials in
order to describe various inelastic effects, growth and remodeling in a thermodynamically
consistent manner. The presented models will be a feature of the next version of
the scientific open-source finite element code OpenGeoSys developed by an international
developer and user group, and coordinated by the authors.
