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

Simulation of frictional contact and shear failure of fractures in fractured media is of paramount important in computational mechanics. In this work, a preconditioned mixed-finite element (FE) scheme with Lagrange multipliers is proposed in the framework of constrained variational principle, which has the capability to handle frictional contact and slip of the multiple crossing fractures. The slippage, opening and contact traction on fractures are calculated by the resulted saddle-point algebraic system. A novel treatment is devised to guarantee physical solutions at the intersected position of crossing fractures. A preconditioning technique is introduced to re-scale the resulting saddle-point algebraic system, to preserve the robustness of the system. An iteration strategy, namely monolithic-updated contact algorithm, is then designed to update the two primary unknowns (displacement and Lagrange multiplier) in one algebraic block. Then, a series of numerical tests is conducted to study the frictional contact and shear failure of single- and multi-crossing fractures. Benchmark study is performed to verify the presented mixed-FE scheme. Two tests with crossing fractures are studied, in which the slippage and opening can be calculated. The effects of crossing fractures on the deformation field are observed in the simulation, in which the variation of slippage, opening and stress intensity factor are analyzed under different loading conditions.