Poroelasticity with Deformation Dependent Permeability
The poroelasticity theory that was originally developed in the context of geophysical applications has been successfully used to model the mechanical behavior of fluid-saturated living bone tissue. In this paper we focus on the numerical solution of the coupled fluid flow and mechanics in Biot’s consolidation model of poroelasticity. The method combines mixed finite elements for Darcy flow and Galerkin finite elements for elasticity. The permeability tensor in the model is allowed to be a nonlinear function on the deformation, since this influence has relevance in the case of biological tissues like bone. We deal with the nonlinear term by considering a semi-implicit in time scheme. We provide the a priori error estimates for the numerical solution of the fully discretized model. For efficiency, we also explore an operator splitting strategy where the flow problem is solved before the mechanical problem, in an iterative process.
This work was partially supported by the Centre for Mathematics of the University of Coimbra—UID/MAT/00324/2019, funded by the Portuguese Government through FCT/MEC and co-funded by the European Regional Development Fund through the Partnership Agreement PT2020.
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