Sharif Digital Repository

The standard finite element models, i.e. the finite element methods that use the classical continuum models, suffer from the excessive mesh dependence when a strain-softening model is used. It cannot converge to a meaningful solution and the governing differential equation loses the ellipticity. This paper presents an enriched finite element algorithm for simulation of localization phenomenon using a higher order continuum model based on the Cosserat continuum theory. The governing equations are regularized by adding the rotational degrees-of-freedom to the conventional degrees-of-freedom and including the internal length parameter in the model. The extended finite element method (X-FEM) is... 

In this paper, an enriched finite element method is presented for numerical simulation of saturated porous media. The arbitrary discontinuities, such as material interfaces, are encountered via the extended finite element method (X-FEM) by enhancing the standard FEM displacements. The X-FEM technique is applied to the governing equations of porous media for the spatial discretization, followed by a generalized Newmark scheme used for the time domain discretization. In X-FEM, the material interfaces are represented independently of element boundaries and the process is accomplished by partitioning the domain with some triangular sub-elements whose Gauss points are used for integration of the... 

In this paper, a new computational technique is presented based on the eXtended Finite Element Method (X-FEM) in pressure-sensitive plasticity of powder compaction considering frictional contact. In X-FEM, the need for mesh adaption to discontinuity interface is neglected and the process is accomplished by partitioning the domain with some triangular sub-elements whose Gauss points are used for integration of the domain of the elements. The technique is applied by employing additional functions, which are added to approximate the displacement field of the elements located on the interface. The double-surface cap plasticity model is employed within the X-FEM framework in numerical simulation... 

In this paper, the extended finite element method (X-FEM) is developed for modeling of frictional contact problems. In order to model the frictional contact behavior within the standard finite element framework, the special functions are included in standard FE method to simulate discontinuity without considering the boundary conditions in meshing the domain. The classical finite element approximation is therefore enriched by applying additional terms to simulate the frictional behavior of contact between two bodies. These terms, which are included for enrichment of nodal displacements, depend on the contact condition between two surfaces. The partition of unity method is applied to... 

In this paper, the eXtended Finite Element Method (X-FEM) is developed in pressure-sensitive plasticity of powder compaction process. In X-FEM, the need for mesh adaption to discontinuity interface is neglected and the process is accomplished by employing additional functions, which are added to approximate the displacement field of the elements located on the interface. The double-surface cap plasticity model is employed within the X-FEM framework in numerical simulation of powder material. The plasticity model includes a failure surface and an elliptical cap, which closes the open space between the failure surface and hydrostatic axis. The moving cap expands in the stress space according... 

In this paper, a computational technique is presented for the isothermal and non-isothermal water injection into naturally fractured oil reservoirs. A remarkable number of naturally fractured reservoirs contain relatively heavy oils that could not be extracted economically; hence, the thermal recovery methods are extensively used for such reservoirs. In this study, the effectiveness of hot water injection over cold (isothermal) water injection in oil production is quantified. The influence of long and short fractures and their alignments on oil recovery are discussed. To this end, a 2D model for two-phase fluid flow and heat transfer is presented. The medium is assumed to be partially... 

In this paper, the extended finite element method is presented for thermo-hydro-mechanical (THM) modeling of impermeable discontinuities in saturated porous media. The X-FEM technique is applied to the THM governing equations for the spatial discretization, followed by a generalized Newmark scheme for the time domain discretization. The displacement field is enriched by the Heaviside and crack tip asymptotic functions, and the pressure and temperature fields are enriched by the Heaviside and appropriate asymptotic functions. The process is accomplished by partitioning the domain with triangular sub-elements. Numerical examples are presented to demonstrate the capability of proposed technique... 

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... 

In this paper, a numerical model is developed based on the X-FEM technique to simulate the proppant transport and tip screen-out in hydraulic fracturing. The governing equations are based on the momentum balance and mass conservation of the fluid. The hydro-mechanical coupling between the fracture and surrounding porous medium is fulfilled through the weak form of the governing equations. The fluid inflow within the fracture is modeled using the one-dimensional mass conservation of the injected slurry and proppant along the fracture, in which the viscosity of the slurry is dependent on the proppant concentration. The transition from the Poiseuille to Darcy flow regime is incorporated into... 

In this paper, a numerical model is developed based on the X-FEM technique to simulate the transport of dense solute in a single fluid phase through the fractured porous media. The governing equation is based on the mass conservation law which is applied to the fluid phase and the solute in both matrix and fracture domain. The integral governing equations of the mass exchange between the fracture and the surrounding matrix is derived. The extended finite element method (X-FEM) is applied by employing appropriate enrichment functions to model the fractured porous domain. The superiority of the X-FEM is that the FE mesh is not necessary to be conformed to the fracture geometry, so the regular... 

This paper presents new achievements in the extended finite element modeling of large elasto-plastic deformation in solid problems. The computational technique is presented based on the extended finite element method (X-FEM) coupled with the Lagrangian formulation in order to model arbitrary interfaces in large deformations. In X-FEM, the material interfaces are represented independently of element boundaries, and the process is accomplished by partitioning the domain with some triangular sub-elements whose Gauss points are used for integration of the domain of elements. The large elasto-plastic deformation formulation is employed within the X-FEM framework to simulate the non-linear... 

In this paper, a computational technique is presented for the isothermal and non-isothermal water injection into naturally fractured oil reservoirs. A remarkable number of naturally fractured reservoirs contain relatively heavy oils that could not be extracted economically; hence, the thermal recovery methods are extensively used for such reservoirs. In this study, the effectiveness of hot water injection over cold (isothermal) water injection in oil production is quantified. The influence of long and short fractures and their alignments on oil recovery are discussed. To this end, a 2D model for two-phase fluid flow and heat transfer is presented. The medium is assumed to be partially... 

In this paper, a numerical model is developed for the assessment of carbon dioxide transport through naturally fractured cap-rocks during CO2 sequestration in underground aquifers. The cap-rock contains two types of fracture with different length scales: micro-cracks (fissures) and macro-cracks (faults). The effect of micro-cracks is incorporated implicitly by modifying the intrinsic permeability tensor of porous matrix, while the macro-cracks are modeled explicitly using the extended finite element method (X-FEM). The fractured porous medium is decomposed into the porous matrix and fracture domain, which are occupied with two immiscible fluid phases, water and CO2. The flow inside the...