Enriched Galerkin finite elements for coupled poromechanics with local mass conservation

Large deformation poromechanics with local mass conservation: An enriched Galerkin finite element framework

“…It is noted that, for the same mesh size and polynomial order, the optimal convergence rates of EG, DG, and CG methods are identical . Our recent paper has shown that the mixed EG/CG discretization of the flow/deformation equations in poromechanics provide local mass conservation with the same order of accuracy as the standard CG/CG discretization. Furthermore, the paper has also shown that local mass conservation can lead to marked differences in flow‐induced deformations such as the timing of strain localization.…”

“…We remark that the two governing Equations and in this large strain poromechanical formulation are coupled in additional ways than its infinitesimal strain counterpart . Specifically, here, the permeability, the porosity, and the saturation do depend on u (more precisely, J ), whereas they usually do not depend on u in an infinitesimal deformation formulation.…”

“…This has motivated a number of poromechanical formulations that have combined a locally conservative method for the fluid flow equation with CG discretization of the solid deformation equation. The types of locally conservative methods used for this purpose include the finite volume method, the Raviart‐Thomas mixed finite element method, the discontinuous Galerkin (DG) method, and the enriched Galerkin (EG) method . These studies have shown that the use of a locally conservative method enables more robust solution of the fluid flow equation in a poromechanical problem.…”

“…In this work, we develop a locally mass conservative finite element framework for poromechanical problems undergoing large deformations. The framework builds on our previous work that applies the EG method to discretize the fluid flow equation in small strain poromechanics . The EG method, which has emerged as an efficient way to provide local conservation, augments elementwise constant functions to the finite element space of the CG method and uses the variational form of the DG method .…”

Mohr–Coulomb plasticity for sands incorporating density effects without parameter calibration

“…The Mohr–Coulomb plasticity model is also widely used in research work, since it allows one to capture the pressure‐dependent strength of a geomaterial with a fraction of costs for sophisticated constitutive models. This exceptional efficiency makes the model a common choice for computationally intensive simulations in geomechanics, such as those involve complex domains, soil‐structure interactions, contacts, large deformations, and/or coupled multiphysics …”