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In this paper, a coupled hydro-mechanical formulation is developed for deformable porous media subjected to crack interfaces in the framework of extended finite element method. Governing equations of the porous medium consist of the momentum balance of the bulk together with the momentum balance and continuity equations of the fluid phase, known as [InlineEquation not available: see fulltext.] formulation. The discontinuity in fractured porous medium is modeled for both opening and closing modes that results in the fluid flow within the fracture, and/or contact behavior at the crack edges. The fluid flow through the fracture is assumed to be viscous and is modeled by employing the Darcy law... 

In this paper, the interaction between the fluid-driven fracture and frictional natural fault is modeled using an enriched-FEM technique based on the partition of unity method. The intersection between two discontinuities is modeled by introducing a junction enrichment function. In order to model the fluid effect within the fracture, the fluid pressure is assumed to be constant throughout the propagation process. The frictional contact behavior along the fault faces is modeled using an X-FEM penalty method within the context of the plasticity theory of friction. Finally, several numerical examples are solved to illustrate the accuracy and robustness of proposed computational algorithm as... 

In this paper, an extended finite element method is presented for simulation of interaction between hydraulic fracturing and natural fractures in saturated porous media. The well-known u−p formulation is employed in order to obtain the fully coupled set of governing equations. Natural faults are modeled for both opening and closure modes where the fluid inflow and contact conditions are considered at the interface, respectively. The Darcy law is employed in conjunction with an aperture dependent permeability for the fracture channel to describe the interfacial inflow. The contact constraints of both the solid and fluid phases are imposed using the Penalty method. The Heaviside and modified... 

In this paper, the crack growth simulation is presented in saturated porous media using the extended finite element method. The mass balance equation of fluid phase and the momentum balance of bulk and fluid phases are employed to obtain the fully coupled set of equations in the framework of u - p formulation. The fluid flow within the fracture is modeled using the Darcy law, in which the fracture permeability is assumed according to the well-known cubic law. The spatial discritization is performed using the extended finite element method, the time domain discritization is performed based on the generalized Newmark scheme, and the non-linear system of equations is solved using the... 

In this paper, an Uzawa-type augmented Lagrangian contact formulation is presented for modeling frictional discontinuities in the framework of the X-FEM technique. The kinematically nonlinear contact problem is resolved based on an active set strategy to fulfill the Kuhn-Tucker inequalities in the normal direction of contact. The Coulomb's friction rule is employed to address the stick-slip behavior on the contact interface through a return mapping algorithm in conjunction with a symmetrized (nested) augmented Lagrangian approach. A stabilization algorithm is proposed for the robust imposition of the frictional contact constraints within the proposed augmented Lagrangian framework. Several... 

In the extended finite element method (FEM), the transition elements between the enriched and standard elements, which are generally referred as the blending, or partially enriched elements, are often crucial for a good performance of the local partition of unity enrichments. In these elements, the enrichment function cannot be reproduced exactly due to the lack of a partition of unity, and blending elements produce unwanted terms into the approximation that cannot be compensated by the standard final element part of the approximation. In this paper, some optimal X-FEM-type methods reported in literature are employed to study the performance of blending elements in large plastic deformation... 

In this paper, an enriched finite element technique is presented to simulate the mechanism of interaction between the hydraulic fracturing and frictional natural fault in impermeable media. The technique allows modeling the discontinuities independent of the finite element mesh by introducing additional DOFs. The coupled equilibrium and flow continuity equations are solved using a staggered Newton solution strategy, and an algorithm is proposed on the basis of fixed-point iteration concept to impose the flow condition at the hydro-fracture mouth. The cohesive crack model is employed to introduce the nonlinear fracturing process occurring ahead of the hydro-fracture tip. Frictional contact is... 

Mechanical characterization of fractures, i.e., identifying their characteristic parameters such as energy release rate, is crucial to assess the safety and stability of structural members. This is generally achieved using a combination of finite element analysis and optimization. Machine learning models are increasingly used to characterize engineering problems. While such models have shown impressive performance on smooth data, their performance diminishes significantly on data with discontinuities and sharp gradients. For fractures, this issue is more severe due to the singular solutions in the vicinity of the fracture tips. To resolve this difficulty, leveraging classical fracture...