Poroelastic medium with non-penetrating crack driven by hydraulic fracture: Variational inequality and its semidiscretization

A new class of unilateral variational models appearing in the theory of poroelasticity is introduced and studied. A poroelastic medium consists of solid phase and pores saturated with a Newtonian fluid. The medium contains a fluid-driven crack, which is subjected to non-penetration between the opposite crack faces. The fully coupled poroelastic system includes elliptic-parabolic governing equations under the unilateral constraint. Well-posedness of the corresponding variational inequality is established based on the Rothe semi-discretization in time, after subsequent passing time step to zero. The NLCP-formulation of non-penetration conditions is given which is useful for a semi-smooth Newton solution strategy. (c) 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Automated summary

A new class of unilateral variational models is introduced and studied in the field of poroelasticity. The fully coupled poroelastic system under the unilateral constraint is analyzed, and the well-posedness of the corresponding variational inequality is established. A non-linear complementarity problem formulation is given for solving the non-penetration conditions, which provides an effective numerical solution strategy.