A stabilized mixed-FE scheme for frictional contact and shear failure analyses in deformable fractured media

Luyu Wang*, Cornelis Vuik, Hadi Hajibeygi

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)
26 Downloads (Pure)


Simulation of fracture contact mechanics in deformable fractured media is of paramount important in computational mechanics. Previous studies have revealed that compressive loading may produce mode II fractures, which is quite different from mode I fractures induced by tensile loading. Furthermore, fractures can cross each other. This will increase the complexity of their network deformation under different loading types significantly. In this work, a stabilized mixed-finite element (FE) scheme with Lagrange multipliers is proposed in the framework of variational formulation, which is able to simulate frictional contact, shear failure (mode II) and opening (mode I) of multiple crossing fractures. A novel treatment is devised to guarantee physical solutions at the intersection of crossing fractures. A preconditioner is introduced to re-scale the saddle-point algebraic system and to preserve the numerical robustness. Then, a solution strategy is designed to calculate the unknowns, displacement and Lagrange multipliers, in one algebraic system. Later, numerical tests are conducted to study mechanical behaviors of fractured media. Benchmark study is performed to verify the presented mixed-FE scheme. A deformable medium with crossing fractures is simulated under mixed-mode loading types. The characteristics of fracture contact, surface sliding, opening and variation of stress intensity factor are analyzed. Simulation results show that the curve of slippage induced by compression, as well as the opening induced by internal fluid pressure, along the fracture length holds a parabolic shape. The diagonal contact point, at the intersecting position of the crossing fractures, is studied in detail, specially under different stress states. Finally, the impact of intersecting fractures on frictional contact mechanics is investigated for different loading conditions.

Original languageEnglish
Article number108427
Pages (from-to)1-22
Number of pages22
JournalEngineering Fracture Mechanics
Publication statusPublished - 2022


  • Crossing fractures
  • Fractured media
  • Frictional contact
  • Lagrange multipliers
  • Mixed-finite element method

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