Showing papers on "Extended finite element method published in 2020"

New perspective of fracture mechanics inspired by gap test with crack-parallel compression.

Abstract: The line crack models, including linear elastic fracture mechanics (LEFM), cohesive crack model (CCM), and extended finite element method (XFEM), rest on the century-old hypothesis of constancy of materials' fracture energy. However, the type of fracture test presented here, named the gap test, reveals that, in concrete and probably all quasibrittle materials, including coarse-grained ceramics, rocks, stiff foams, fiber composites, wood, and sea ice, the effective mode I fracture energy depends strongly on the crack-parallel normal stress, in-plane or out-of-plane. This stress can double the fracture energy or reduce it to zero. Why hasn't this been detected earlier? Because the crack-parallel stress in all standard fracture specimens is negligible, and is, anyway, unaccountable by line crack models. To simulate this phenomenon by finite elements (FE), the fracture process zone must have a finite width, and must be characterized by a realistic tensorial softening damage model whose vectorial constitutive law captures oriented mesoscale frictional slip, microcrack opening, and splitting with microbuckling. This is best accomplished by the FE crack band model which, when coupled with microplane model M7, fits the test results satisfactorily. The lattice discrete particle model also works. However, the scalar stress-displacement softening law of CCM and tensorial models with a single-parameter damage law are inadequate. The experiment is proposed as a standard. It represents a simple modification of the three-point-bend test in which both the bending and crack-parallel compression are statically determinate. Finally, a perspective of various far-reaching consequences and limitations of CCM, LEFM, and XFEM is discussed.

Extended finite element method (XFEM) modeling of fracture in additively manufactured polymers

Abstract: The fracture of additively manufactured polymer materials with various layer orientations is studied using the extended finite element method (XFEM) in an anisotropic cohesive zone model (CZM). The single edge notched bending (SENB) specimens made of acrylonitrile-butadiene-styrene (ABS) materials through fused filament fabrications with various crack tip/layer orientations are considered. The XFEM coupled with anisotropic CZM is employed to model the brittle fracture (fracture between layers), ductile fracture (fracture through layers), as well as kinked fracture behaviors of ABS specimens printed with vertical, horizontal, and oblique layer orientations, respectively. Both elastic and elastoplastic fracture models, coupled with linear or exponential traction-separation laws, are developed for the inter-layer and cross-layer fracture, respectively. For mixed inter-/cross- layer fracture, an anisotropic cohesive zone model is developed to predict the kinked crack propagations. Two crack initiation and evolution criteria are defined to include both crack propagation between layers (weak plane failure) and crack penetration through layers (maximum principal stress failure) that jointly determine the zig-zag crack growth paths. The anisotropic cohesive zone model with XFEM developed in this study is able to capture different fracture behaviors of additively manufactured ABS samples with different layer orientations.

Fluid-driven transition from damage to fracture in anisotropic porous media: a multi-scale XFEM approach

Abstract: In this paper, a numerical method is proposed to simulate multi-scale fracture propagation driven by fluid injection in transversely isotropic porous media. Intrinsic anisotropy is accounted for at the continuum scale, by using a damage model in which two equivalent strains are defined to distinguish mechanical behavior in the direction parallel and perpendicular to the layer. Nonlocal equivalent strains are calculated by integration and are directly introduced in the damage evolution law. When the weighted damage exceeds a certain threshold, the transition from continuum damage to cohesive fracture is performed by dynamically inserting cohesive segments. Diffusion equations are used to model fluid flow inside the porous matrix and within the macro-fracture, in which conductivity is obtained by Darcy’s law and the cubic law, respectively. In the fractured elements, the displacement and pore pressure fields are discretized by using the XFEM technique. Interpolation on fracture elements is enriched with jump functions for displacements and with level set-based distance functions for fluid pressure, which ensures that displacements are discontinuous across the fracture, but that the pressure field remains continuous. After spatial and temporal discretization, the model is implemented in a Matlab code. Simulations are carried out in plane strain. The results validate the formulation and implementation of the proposed model and further demonstrate that it can account for material and stress anisotropy.

Numerical analysis of the delamination in CFRP laminates: VCCT and XFEM assessment

Abstract: This document develops a critical analysis of the capabilities offered by well-known numerical approaches such as eXtended Finite Element Method (XFEM) and Virtual Crack Closure Technique (VCCT) to predict delamination in composite materials. Despite several computational analyses having been performed so far, the study of the adequacy of using different modelling approaches in the delamination of composites is still limited. This paper addresses this matter, confronting the advantages and disadvantages offered by VCCT, a well-established numerical approach, and XFEM, a promising and relatively novel modelling technique. For this purpose, the delamination of carbon fibre reinforced polymer (CFRP) laminates is investigated with the simulation of three common tests: Double Cantilever Beam (DCB), End-Notch Flexure (ENF) and Mixed-Mode Bending (MMB). Numerical results are validated with experimental data, taken from other publications, for both modelling approaches analysed. Consistency is maintained for all finite element (FE) simulations carried out in this work to draw meaningful comparisons between XFEM and VCCT. Several interesting conclusions are extracted from this work. For instance, VCCT simulations overall have high accuracy and low computational time, while XFEM shows high capabilities to predict Mode I fracture.

Influence of existing natural fractures and beddings on the formation of fracture network during hydraulic fracturing based on the extended finite element method

Abstract: Numerical simulation of fracture propagation during hydraulic fracturing is performed based on the extended finite element method. The influences of existing natural fractures and beddings on the formation of fracture network are focused. It is shown that the hydraulic fracture network in the case of random distribution for natural fracture is more conducive to form than that in the case of the regular distribution, which indicates that the random arrangement of existing natural fractures is helpful for forming highly communicated and complicated fracture network. However, the randomly distributed natural fractures often cause fracture reorientation and a sudden drop of the fracture aperture of the new branch, which leads to an increasing proportion of ineffective fractures in the formed fracture networks due to that fracture apertures in the new branches may be too narrow to send the proppant inside. For the existing beddings in the stratified rock, the bedding feature and distribution have the important influences upon the hydraulic fracture propagation. Numerical results show that the hydraulic fracture would be more easily to swerve again and form complex network under the condition of the smaller distance and larger bond strength between beddings.

Numerical Investigation of the Effect of Partially Propped Fracture Closure on Gas Production in Fractured Shale Reservoirs

Abstract: Nonuniform proppant distribution is fairly common in hydraulic fractures, and different closure behaviors of the propped and unpropped fractures have been observed in lots of physical experiments. However, the modeling of partially propped fracture closure is rarely performed, and its effect on gas production is not well understood as a result of previous studies. In this paper, a fully coupled fluid flow and geomechanics model is developed to simulate partially propped fracture closure, and to examine its effect on gas production in fractured shale reservoirs. Specifically, an efficient hybrid model, which consists of a single porosity model, a multiple porosity model and the embedded discrete fracture model (EDFM), is adopted to model the hydro-mechanical coupling process in fractured shale reservoirs. In flow equations, the Klinkenberg effect is considered in gas apparent permeability, and adsorption/desorption is treated as an additional source term. In the geomechanical domain, the closure behaviors of propped and unpropped fractures are described through two different constitutive models. Then, a stabilized extended finite element method (XFEM) iterative formulation, which is based on the polynomial pressure projection (PPP) technique, is developed to simulate a partially propped fracture closure with the consideration of displacement discontinuity at the fracture interfaces. After that, the sequential implicit method is applied to solve the coupled problem, in which the finite volume method (FVM) and stabilized XFEM are applied to discretize the flow and geomechanics equations, respectively. Finally, the proposed method is validated through some numerical examples, and then it is further used to study the effect of partially propped fracture closures on gas production in 3D fractured shale reservoir simulation models. This work will contribute to a better understanding of the dynamic behaviors of fractured shale reservoirs during gas production, and will provide more realistic production forecasts.

Simulation of coupled multiphase flow and geomechanics in porous media with embedded discrete fractures

Abstract: In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using uncoupled methods. In recent years, significant research has focused on discretization strategies for these coupled systems, particularly in the presence of complicated fracture network geometries. In this work, we explore a finite-volume discretization for the multiphase flow equations coupled with a finite-element scheme for the mechanical equations. Fractures are treated as lower dimensional surfaces embedded in a background grid. Interactions are captured using the Embedded Discrete Fracture Model (EDFM) and the Embedded Finite Element Method (EFEM) for the flow and the mechanics, respectively. This non-conforming approach significantly alleviates meshing challenges. EDFM considers fractures as lower dimension finiten volumes which exchange fluxes with the rock matrix cells. The EFEM method provides, instead, a local enrichment of the finite-element space inside each matrix cell cut by a fracture element. Both the use of piecewise constant and piecewise linear enrichments are investigated. They are also compared to an Extended Finite Element (XFEM) approach. One key advantage of EFEM is the element-based nature of the enrichment, which reduces the geometric complexity of the implementation and leads to linear systems with advantageous properties. Synthetic numerical tests are presented to study the convergence and accuracy of the proposed method. It is also applied to a realistic scenario, involving a heterogeneous reservoir with a complex fracture distribution, to demonstrate its relevance for field applications.

Coupling XFEM and peridynamics for brittle fracture simulation—part I: feasibility and effectiveness

Abstract: A peridynamics (PD)–extended finite element method (XFEM) coupling strategy for brittle fracture simulation is presented. The proposed methodology combines a small PD patch, restricted near the crack tip area, with the XFEM that captures the crack body geometry outside the domain of the localised PD grid. The feasibility and effectiveness of the proposed method on a Mode I crack opening problem is examined. The study focuses on comparisons of the J integral values between the new coupling strategy, full PD grids and the commercial software Abaqus. It is demonstrated that the proposed approach outperforms full PD grids in terms of computational resources required to obtain a certain degree of accuracy. This finding promises significant computational savings when crack propagation problems are considered, as the efficiency of FEM and XFEM is combined with the inherent ability of PD to simulate fracture.