Showing papers on "Extended finite element method published in 2018"

A microstructure-sensitive driving force for crack growth

Abstract: A stored energy based methodology for calculating the driving force for crack growth is introduced which can capture the highly local microstructural sensitivity. This has been implemented in the context of crystal plasticity finite element simulations with explicit representation of the crack with the eXtended Finite Element Method (XFEM), with non-local approaches for both stored energy and J-integral calculation. The model is shown to have good agreement with discrete dislocation plasticity (DDP) models in terms of the crack-tip dislocation configurational energy, and with experimental observations of long and very short (microstructurally-sensitive) cracks for both fracture toughness and crack growth rate data. The method is shown to capture the microstructural sensitivity, in contrast with the widely used J-Integral method. By modelling different crack lengths, the diminution of the microstructural sensitivity with increasing crack length is quantified and a critical length defined above which the microstructural sensitivity is insignificant.

Analysis of a High-Order Trace Finite Element Method for PDEs on Level Set Surfaces

Abstract: We present a new high-order finite element method for the discretization of partial differential equations on stationary smooth surfaces which are implicitly described as the zero level of a level set function. The discretization is based on a trace finite element technique. The higher discretization accuracy is obtained by using an isoparametric mapping of the volume mesh, based on the level set function, as introduced in [C. Lehrenfeld, Comp. Meth. Appl. Mech. Engrg., 300 (2016), pp. 716--733]. The resulting trace finite element method is easy to implement. We present an error analysis of this method and derive optimal order $H^1(\Gamma)$-norm error bounds. A second topic of this paper is a unified analysis of several stabilization methods for trace finite element methods. Only a stabilization method which is based on adding an anisotropic diffusion in the volume mesh is able to control the condition number of the stiffness matrix also for the case of higher-order discretizations. Results of numerical e...

Multiple crack detection in 3D using a stable XFEM and global optimization

Abstract: A numerical scheme is proposed for the detection of multiple cracks in three dimensional (3D) structures. The scheme is based on a variant of the extended finite element method (XFEM) and a hybrid optimizer solution. The proposed XFEM variant is particularly well-suited for the simulation of 3D fracture problems, and as such serves as an efficient solution to the so-called forward problem. A set of heuristic optimization algorithms are recombined into a multiscale optimization scheme. The introduced approach proves effective in tackling the complex inverse problem involved, where identification of multiple flaws is sought on the basis of sparse measurements collected near the structural boundary. The potential of the scheme is demonstrated through a set of numerical case studies of varying complexity.

An Efficient Numerical Hybrid Model for Multiphase Flow in Deformable Fractured-Shale Reservoirs

Abstract: After hydraulic fracturing, a shale reservoir usually has multiscale fractures and becomes more stress-sensitive. In this work, an adaptive hybrid model is proposed to simulate hydromechanical coupling processes in such fractured-shale reservoirs during the production period (i.e., the hydraulic-fracturing process is not considered and cannot be simulated). In our hybrid model, the single-porosity model is applied in the region outside the stimulated reservoir volume (SRV), and the matrix and natural/induced fractures in the SRV region are modeled using a double-porosity model that can accurately simulate the matrix/fracture fluid exchange during the entire transient period. Meanwhile, the fluid flow in hydraulic fractures is modeled explicitly with the embedded-discrete-fracture model (EDFM), and a stabilized extended-finite-element-method (XFEM) formulation using the polynomial-pressure-projection (PPP) technique is applied to simulate mechanical processes. The developed stabilized XFEM formulation can avoid the displacement oscillation on hydraulic-fracture interfaces. Then a modified fixed-stress sequential-implicit method is applied to solve the hybrid model, in which mixed-space discretization [i.e., finite-volume method (FVM) for flow process and stabilized XFEM for geomechanics] is used. The robustness of the proposed model is demonstrated through several numerical examples. In conclusion, several key factors for gas exploitation are investigated, such as adsorption, Klinkenberg effect, capillary pressure, and fracture deformation. In this study, all the numerical examples are 2D, and the gravity effect is neglected in these simulations. In addition, we assume there is no oil phase in the shale reservoirs, thus the gas/water two-phase model is used to simulate the flow in these reservoirs.

Coupled hydromechanical-fracture simulations of nonplanar three-dimensional hydraulic fracture propagation

Abstract: Summary This paper presents an algorithm and a fully coupled hydromechanical-fracture formulation for the simulation of three-dimensional nonplanar hydraulic fracture propagation. The propagation algorithm automatically estimates the magnitude of time steps such that a regularized form of Irwin's criterion is satisfied along the predicted 3-D fracture front at every fracture propagation step. A generalized finite element method is used for the discretization of elasticity equations governing the deformation of the rock, and a finite element method is adopted for the solution of the fluid flow equation on the basis of Poiseuille's cubic law. Adaptive mesh refinement is used for discretization error control, leading to significantly fewer degrees of freedom than available nonadaptive methods. An efficient computational scheme to handle nonlinear time-dependent problems with adaptive mesh refinement is presented. Explicit fracture surface representations are used to avoid mapping of 3-D solutions between generalized finite element method meshes. Examples demonstrating the accuracy, robustness, and computational efficiency of the proposed formulation, regularized Irwin's criterion, and propagation algorithm are presented.

Stress-based topology optimization using spatial gradient stabilized XFEM

Abstract: This paper presents an immersed boundary approach for level set topology optimization considering stress constraints. A constraint agglomeration technique is used to combine the local stress constraints into one global constraint. The structural response is predicted by the eXtended Finite Element Method. A Heaviside enrichment strategy is used to model strong and weak discontinuities with great ease of implementation. This work focuses on low-order finite elements, which given their simplicity are the most popular choice of interpolation for topology optimization problems. The predicted stresses strongly depend on the intersection configuration of the elements and are prone to significant errors. Robust computation of stresses, regardless of the interface position, is essential for reliable stress constraint prediction and sensitivities. This study adopts a recently proposed fictitious domain approach for penalization of displacement gradients across element faces surrounding the material interface. In addition, a novel XFEM informed stabilization scheme is proposed for robust computation of stresses. Through numerical studies the penalized spatial gradients combined with the stabilization scheme is shown to improve prediction of stresses along the material interface. The proposed approach is applied to the benchmark topology optimization problem of an L-shaped beam in two and three dimensions using material-void and material-material problem setups. Linear and hyperelastic materials are considered. The stress constraints are shown to be efficient in eliminating regions with high stress concentration in all scenarios considered.

Heat transfer model and finite element formulation for simulation of selective laser melting

Abstract: A novel approach and finite element formulation for modeling the melting, consolidation, and re-solidification process that occurs in selective laser melting additive manufacturing is presented. Two state variables are introduced to track the phase (melt/solid) and the degree of consolidation (powder/fully dense). The effect of the consolidation on the absorption of the laser energy into the material as it transforms from a porous powder to a dense melt is considered. A Lagrangian finite element formulation, which solves the governing equations on the unconsolidated reference configuration is derived, which naturally considers the effect of the changing geometry as the powder melts without needing to update the simulation domain. The finite element model is implemented into a general-purpose parallel finite element solver. Results are presented comparing to experimental results in the literature for a single laser track with good agreement. Predictions for a spiral laser pattern are also shown.

Fully coupled simulation of multiple hydraulic fractures to propagate simultaneously from a perforated horizontal wellbore

Abstract: In hydraulic fracturing process in shale rock, multiple fractures perpendicular to a horizontal wellbore are usually driven to propagate simultaneously by the pumping operation. In this paper, a numerical method is developed for the propagation of multiple hydraulic fractures (HFs) by fully coupling the deformation and fracturing of solid formation, fluid flow in fractures, fluid partitioning through a horizontal wellbore and perforation entry loss effect. The extended finite element method (XFEM) is adopted to model arbitrary growth of the fractures. Newton’s iteration is proposed to solve these fully coupled nonlinear equations, which is more efficient comparing to the widely adopted fixed-point iteration in the literatures and avoids the need to impose fluid pressure boundary condition when solving flow equations. A secant iterative method based on the stress intensity factor (SIF) is proposed to capture different propagation velocities of multiple fractures. The numerical results are compared with theoretical solutions in literatures to verify the accuracy of the method. The simultaneous propagation of multiple HFs is simulated by the newly proposed algorithm. The coupled influences of propagation regime, stress interaction, wellbore pressure loss and perforation entry loss on simultaneous propagation of multiple HFs are investigated.

The Numerical Analysis of Fault-Induced Mine Water Inrush Using the Extended Finite Element Method and Fracture Mechanics

Abstract: Fault activation caused by construction, earthquakes, or mining can produce disastrous water-inrush episodes in underground mines. Fault activation is generally caused by stress concentration at the fault tip, so in this study, a computational model of a typical underground stope with a hidden fault was established to quantitatively assess the magnitude of the stress concentration of the stress fields of the fault-tip. Numerical simulation was performed using the extended finite element method and fracture mechanics. Stress intensity factors, which represent the magnitude of the stress concentration, were obtained using the interaction integral method to quantitatively evaluate the tip fields and assess the possibility of fault activation. The mining depth, fluid pressure, fault dip, and fault length were analyzed and the advance of a working face was simulated to determine whether underground mining would cause fault activation.

Investigating the effect of retained austenite and residual stress on rolling contact fatigue of carburized steel with XFEM and experimental approaches

Abstract: In this study, the effects of retained austenite (RA) and residual stress on rolling contact fatigue (RCF) of carburized AISI 8620 steel were investigated through modeling and experiments. In modeling, a two-dimensional finite element RCF model was developed to examine the crack propagation and fatigue life of carburized AISI 8620 steel. An extended finite element method (XFEM) was used to initiate and propagate the cracks in the model. A Voronoi Tessellation was randomly generated to simulate the randomness of the microstructures in steel. The cracks were initiated on the grain boundaries of a Voronoi cell prior to the simulations at different locations in the RCF model. The RCF life of the samples was determined by rolling contact fatigue tests. The results in both simulations and experiments showed that the higher level of RA and compressive residual stress achieved improved RCF life through mitigation of crack propagation. The effect of increased RA led to significant improvement on RCF life as compared to increased in compressive residual stress.

A parallel two-grid linearized method for the coupled Navier-Stokes-Darcy problem

Abstract: In this paper, based on a two-grid method and a recent local and parallel finite element method, a parallel two-grid linearized method for the coupled Navier-Stokes-Darcy problem is proposed and analyzed. This method ensures that all the local subproblems on the fine grid can be solved in parallel. Optimal error bounds of the approximate solution are obtained. Finally, numerical experiments are presented to demonstrate the accuracy and effectiveness of the proposed method.