Abstract: A new class of poroelastic dynamic contact problems stemming from hydraulic fracture theory is introduced and studied. The two-phase medium consists of a solid phase and pores which are saturated with a Newtonian fluid. The porous body contains a fluiddriven crack endowed with non-penetration conditions for the opposite crack surfaces. The poroelastic model is described by a coupled system of hyperbolic–parabolic partial differential equations under the unilateral constraint imposed on displacement. After full discretization using finite-element and Hilber–Hughes–Taylor methods, the well-posedness of the resulting variational inequality is established. Formulation of the complementarity conditions with the help of a minimum-based merit function is used for the semi-smooth. Newton method of solution presented in the form of a primal–dual active set algorithm which is tested numerically.

Cite: Kovtunenko V.A. , Atlasiuk O.M.
Poroelastic medium with non-penetrating crack driven by hydraulic fracture: FEM approximation using HHT-alpha and semi-smooth Newton methods
Algorithms. 2025. V.18. N9. 579 :1-14. DOI: 10.3390/a18090579

Dates:

Submitted:	Aug 9, 2025
Accepted:	Sep 11, 2025
Published print:	Sep 13, 2025

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