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Simulation of frictional contact and shear failure of fractures in fracturedmedia is of paramount important in computational mechanics. In this work, apreconditioned mixed-finite element (FE) scheme with Lagrange multipliers isproposed in the framework of constrained variational principle, which has thecapability to handle frictional contact and slip of the multiple crossingfractures. The slippage, opening and contact traction on fractures arecalculated by the resulted saddle-point algebraic system. A novel treatment isdevised to guarantee physical solutions at the intersected position of crossingfractures. A preconditioning technique is introduced to re-scale the resultingsaddle-point algebraic system, to preserve the robustness of the system. Aniteration strategy, namely monolithic-updated contact algorithm, is thendesigned to update the two primary unknowns (displacement and Lagrangemultiplier) in one algebraic block. Then, a series of numerical tests isconducted to study the frictional contact and shear failure of single- andmulti-crossing fractures. Benchmark study is performed to verify the presentedmixed-FE scheme. Two tests with crossing fractures are studied, in which theslippage and opening can be calculated. The effects of crossing fractures onthe deformation field are observed in the simulation, in which the variation ofslippage, opening and stress intensity factor are analyzed under differentloading conditions.

A stabilized mixed finite element scheme for frictional contact mechanics and shear failure analyses in deformable media with crossing fractures