Thermoelastic analysis of multiple defects with the extended finite element method

In this paper, the extended finite element method (XFEM) is adopted to analyze the interaction between a single macroscopic inclusion and a single macroscopic crack as well as that between multiple macroscopic or microscopic defects under thermal/mechanical load. The effects of different shapes of multiple inclusions on the material thermomechanical response are investigated, and the level set method is coupled with XFEM to analyze the interaction of multiple defects. Further, the discretized extended finite element approximations in relation to thermoelastic problems of multiple defects under displacement or temperature field are given. Also, the interfaces of cracks or materials are represented by level set functions, which allow the mesh assignment not to conform to crack or material interfaces. Moreover, stress intensity factors of cracks are obtained by the interaction integral method or the M-integral method, and the stress/strain/stiffness fields are simulated in the case of multiple cracks or multiple inclusions. Finally, some numerical examples are provided to demonstrate the accuracy of our proposed method.

Cracking Propagation of Hardening Concrete Based on the Extended Finite Element Method

Self-deformation cracking is the cracking caused by thermal deformation, autogenous volume deformation or shrinkage deformation. In this paper, an extended finite element calculation method was deduced for concrete crack propagation under a constant hydration and hardening condition during the construction period, and a corresponding programming code was developed. The experimental investigation shows that initial crack propagation caused by self-deformation loads can be analyzed by this program. This improved algorithm was a preliminary application of the XFEM to the problem of the concrete self-deformation cracking during the hydration and hardening period. However, room for improvement exists for this algorithm in terms of matching calculation programs with mass concrete temperature fields containing cooling pipes and the influence of creep or damage on crack propagation.

Mesoscopic characterization and modeling of microcracking in cementitious materials by the extended finite element method

This study develops a mesoscopic framework and methodology for the modeling of microcracks in concrete. A new algorithm is first proposed for the generation of random concrete meso-structure including microcracks and then coupled with the extended finite element method to simulate the heterogeneities and discontinuities present in the meso-structure of concrete. The proposed procedure is verified and exemplified by a series of numerical simulations. The simulation results show that microcracks can exert considerable impact on the fracture performance of concrete. More broadly, this work provides valuable insight into the initiation and propagation mechanism of microcracks in concrete and helps to foster a better understanding of the micro-mechanical behavior of cementitious materials.

Extended finite element-based cohesive zone method for modeling simultaneous hydraulic fracture height growth in layered reservoirs

In this study,a fully coupled hydromechanical model within the extended finite element method(XFEM)-based cohesive zone method(CZM)is employed to investigate the simultaneous height growth behavior of multi-cluster hydraulic fractures in layered porous reservoirs with modulus contrast.The coupled hydromechanical model is first verified against an analytical solution and a laboratory experiment.Then,the fracture geometry(e.g.height,aperture,and area)and fluid pressure evolutions of multiple hydraulic fractures placed in a porous reservoir interbedded with alternating stiff and soft layers are investigated using the model.The stress and pore pressure distributions within the layered reservoir during fluid injection are also presented.The simulation results reveal that stress umbrellas are easily to form among multiple hydraulic fractures’tips when propagating in soft layers,which impedes the simultaneous height growth.It is also observed that the impediment effect of soft layer is much more significant in the fractures suppressed by the preferential growth of adjoining fractures.After that,the combined effect of in situ stress ratio and fracturing spacing on the multi-fracture height growth is presented,and the results elucidate the influence of in situ stress ratio on the height growth behavior depending on the fracture spacing.Finally,it is found that the inclusion of soft layers changes the aperture distribution of outmost and interior hydraulic fractures.The results obtained from this study may provide some insights on the understanding of hydraulic fracture height containment observed in filed.

OPTIMAL QUADRATIC NITSCHE EXTENDED FINITE ELEMENT METHOD FOR INTERFACE PROBLEM OF DIFFUSION EQUATION

In this paper, we study Nitsche extended finite element method （XFEM） for the inter- face problem of a two dimensional diffusion equation. Specifically, we study the quadratic XFEM scheme on some shape-regular family of grids and prove the optimal convergence rate of the scheme with respect to the mesh size. Main efforts are devoted onto classifying the cases of intersection between the elements and the interface and prove a weighted trace inequality for the extended finite element functions needed, and the general framework of analysing XFEM c^n be implemented then.

Extended finite element methods for optimal control problems governed by Poisson equation in non-convex domains

This paper analyzes two extended finite element methods(XFEMs)for linear quadratic optimal control problems governed by Poisson equation in non-convex domains.We follow the variational discretization concept to discretize the continuous problems,and apply an XFEM with a cut-off function and a classic XFEM with a fixed enrichment area to discretize the state and co-state equations.Optimal error estimates are derived for the state,co-state and control.Numerical results confirm our theoretical results.

Numerical Study of Quasi-Static Crack Growth Problems Based on Extended Finite Element Method

The extended finite element method(XFEM) is a numerical method for modeling discontinuities within a classical finite element framework. Based on the algorithm of XFEM, the major factors such as integral domain factor and mesh density which all influence the calculation accuracy of stress intensity factor(SIF) are discussed,and the proper parameters to calculate the SIF are given. The results from the case analysis demonstrate that the crack path is the most sensitive to the crack growth increment size, and the crack path is not mesh-sensitive. A reanalysis method for the XFEM has been introduced. The example presented shows that there is a significantly reduced computational cost for each iteration of crack growth achieved by using the reanalysis method and the reanalysis approach has increasing benefits as the mesh density increases or the value of crack growth increments size decreases.

Recent advances in the extended finite element method (XFEM) and isogeometric analysis (IGA)

The finite element method (FEM) is one of the most popular and efficient methods for computational modeling in scientific research and engineering [1-3]. To expand its application to more complex problems, lots of new FEM-based methods have been developed in recent decades. One major achievement is the significantly improvement on the flexibility

Numerical simulation of loading edge cracks by edge impact using the extended finite element method

The extended finite element method is used to analyze a plate with two parallel edge cracks impacted by a cylindrical projectile. The influence of the impact speed, crack length, plate thickness and notch tip radius on the crack initiation and propagation is studied. Dynamics equations are solved by an implicit time integration scheme which is unconditionally stable. Very good agreement is achieved between numerical predictions and experimental results. The critical velocity of the crack initiation under different conditions is examined. The influence of the crack length is greater than that of the impact speed, plate thickness and notch tip radius.

Concurrent fatigue crack growth simulation using extended finite element method

In this paper,a concurrent simulation framework for fatigue crack growth analysis is proposed using a novel small time scale model for fatigue mechanism analysis and the extended finite element method(X-FEM)for fatigue crack growth simulation.The proposed small time scale fatigue model does not require the cycle counting as those using the classical fatigue analysis methods and can be performed concurrently with structural/mechanical analysis.The X-FEM greatly facilitates crack growth simulation without remeshing requirements ahead of the crack tip as in the classical finite element method.The basic concept and theory of X-FEM was briefly introduced and numerical predictions of stress intensity factors are verified with reference solutions under both uniaxial and multiaxial loadings.The small time scale fatigue model is integrated into the numerical simulation algorithm for concurrent fatigue crack growth analysis.Model predictions are compared with available experimental observations for model validation.

Extended multiscale finite element method for mechanical analysis of heterogeneous materials

An extended multiscale finite element method （EMsFEM） is developed for solving the mechanical problems of heterogeneous materials in elasticity.The underlying idea of the method is to construct numerically the multiscale base functions to capture the small-scale features of the coarse elements in the multiscale finite element analysis.On the basis of our existing work for periodic truss materials, the construction methods of the base functions for continuum heterogeneous materials are systematically introduced. Numerical experiments show that the choice of boundary conditions for the construction of the base functions has a big influence on the accuracy of the multiscale solutions, thus,different kinds of boundary conditions are proposed. The efficiency and accuracy of the developed method are validated and the results with different boundary conditions are verified through extensive numerical examples with both periodic and random heterogeneous micro-structures.Also, a consistency test of the method is performed numerically. The results show that the EMsFEM can effectively obtain the macro response of the heterogeneous structures as well as the response in micro-scale,especially under the periodic boundary conditions.

Fixed-length roof cutting with vertical hydraulic fracture based on the stress shadow effect:A case study

Pre-driven longwall retracement roadway(PLRR)is commonly used in large mine shaft.The support crushing disasters occur frequently during the retracement,and roof management is necessary.Taking the 31107 panel as research background,the roof breaking structure of PLRR is analyzed.It is concluded that the roof cutting with vertical hydraulic fracture(HF)at a specified position,that is,fixed-length roof cutting,can reduce support load and keep immediate roof intact.The extended finite element method(XFEM)is applied to simulate hydraulic fracturing.The results show that both the axial and transverse hydraulic fracturing cannot effectively create vertical HFs.Therefore,a novel construction method of vertical HF based on the stress shadow effect(SSE)is proposed.The stress reversal region and HF orientation caused by the prefabricated hydraulic fracture(PF)are verified in simulation.The sub-vertical HFs are obtained between two PFs,the vertical extension range of which is much larger than that of directional hydraulic fracturing.The new construction method was used to determine the field plan for fixed-length roof cutting.The roof formed a stable suspended structure and deformation of the main PLRR was improved after hydraulic fracturing.

Simulation of PFZ on intergranular fracture based on XFEM and CPFEM

A unit cell including the matrix, precipitation free zone(PFZ) and grain boundary was prepared, and the crystal plasticity finite element method(CPFEM) and extended finite element method(XFEM) were used to simulate the propagation of cracks at grain boundary. Simulation results show that the crystallographic orientation of PFZ has significant influence on crack propagation, which includes the crack growth direction and crack growth velocity. The fracture strain of soft orientation is larger than that of hard orientation due to the role of reducing the stress intensity at grain boundary in intergranular brittle fracture. But in intergranular ductile fracture, the fracture strain of soft orientation may be smaller than that of hard orientation due to the roles of deformation localization.

Numerical computation of central crack growth in an active particle of electrodes influenced by multiple factors

Mechanical degradation, especially fractures in active particles in an electrode, is a major reason why the capacity of lithiumion batteries fades. This paper proposes a model that couples Li-ion diffusion, stress evolution, and damage mechanics to simulate the growth of central cracks in cathode particles（Li Mn_2 O_4） by an extended finite element method by considering the influence of multiple factors. The simulation shows that particles are likely to crack at a high discharge rate, when the particle radius is large, or when the initial central crack is longer. It also shows that the maximum principal tensile stress decreases and cracking becomes more difficult when the influence of crack surface diffusion is considered. The fracturing process occurs according to the following stages： no crack growth, stable crack growth, and unstable crack growth. Changing the charge/discharge strategy before unstable crack growth sets in is beneficial to prevent further capacity fading during electrochemical cycling.

Numerical simulation of fracture propagation in Russia carbonate reservoirs during refracturing

Refracturing treatment is often performed on Russian carbonate reservoirs because of the quick production decline of reservoirs.The traditional refracturing model assumes that a refracture initiates in the normal direction relative to the initial hydro-fracture.This assumption is inconsistent with oilfield measurements of refracture propagation trajectories.Indeed,the existing model is not based on an indepth understanding of initiation and propagation mechanisms of the second hydraulic fractures during refracturing.In this study,we use the extended finite element method to investigate refracture propagation paths at different initiation angles.Both the enriched function approach and phantom mode technique are incorporated into the refracturing model,thereby ensuring that the refracture can freely extend on the structured mesh without any refinement near the crack tips.Key factors including production time,stress anisotropy and initiation angle,and the propped mechanical effect are analyzed in detail.This study provides new insight into the mechanism of refracture propagation in unconventional reservoirs.

考虑焊接效应的T型对接接头裂缝中的应力集中因子异常现象的数值研究

Industry design standards such as BS 7910 deployed some empirical formulas for the prediction of stress intensity factor(SIF) based on simulation results from traditional finite element method(FEM).However,such FEM simulation occasionally failed to convince people due to the large discrepancies compared with engineering practice.As a consequence,inaccuracy predictions via such formulas in engineering standards inevitably occur,which will compromise the safety of structures.In our previous research work,an abnormal phenomenon of SIF in a cracked T-butt joint accounting for welding effect has been observed.Compared with BS 7910,the calculation results of SIF at the surface points of welded specimens cannot be well predicted,with a large discrepancy appearing.In order to explore such problem with an abnormal increase at the surface points of cracked welded specimens,a numerical investigation in terms of SIF among BS 7910,XFEM,and FEM is performed in this paper.Numerical models on both a simple cracked plate without welding effect and a cracked T-butt joint with welding effect are developed through ABAQUS.Parametric studies in terms of the effects of varied crack depth to thickness ratio(a/T) and the effects of crack depth to crack half-length ratio(a/c) are carried out.Empirical solutions from BS 7910 are used for comparison.It is found that the XFEM can provide predictions of SIF at both the crack deepest point and crack surface point of a simple cracked plate as accurate as FEM.For a T-butt joint with a transverse stiffener,a large discrepancy in terms of the weld magnification factors(Mk) occurs at the crack surface point compared with empirical predictions.An exceptional increase of von Mises stress gradient in regions close to the weld-toe is found through the simulation of FEM,whereas a constant stress gradient is obtained through XFEM.The comparison results indicate an inappropriate prediction of SIF by the utilization of the empirical formulas in BS 7910.A more reasonable prediction of the SIF at the surface point of a crack is obtained by the XFEM.Therefore,further updating of the empirical solutions in BS7910 for SIF accounting for welding effect is recommended.

Crack Propagation Path in Two-Directionally Graded Composites Subjected to Mixed-Mode Ⅰ+Ⅱ Loading

Crack propagation path in two-directionally graded composites was investigated by the finite element method.A graded extended finite element method(XFEM)was employed to calculate displacement and stress fields in cracked graded structures.And a post-processing subroutine of interaction energy integral was implemented to extract the mixed-mode stress intensity factors(SIFs).The maximum hoop stress(MHS)criterion was adopted to predict crack growth direction based on the assumption of local homogenization of asymptotic crack-tip fields in graded materials.Effects of material nonhomogeneous parameters on crack propagation paths were also discussed in detail.It is shown that the present method can provide relatively accurate predictions of crack paths in two-directionally graded composites.Crack propagates in the decreasing direction of effective Young′s modulus.The shape and steepness of property gradient perpendicular to the crack surface have great influences on crack paths.Through redesigning material property reasonably,crack growth in graded material can be changed to improve mechanical behaviours of cracked structures.

Stable Fatigue Crack Propagation of 16MnR Steel

A research on the stable fatigue crack propagation of 16MnR steel is investigated systematically in this paper.First,control experiments of 16MnR with compact tension specimen is conducted to study the effect of R-ratios,specimen thickness and notch sizes.The experiments show that the fatigue crack growth(FCG)rate in stable propagation was insensitive to these factors.Then,the stress intensity factor(SIF)is computed and compared by displacement interpolation method,J integral and interaction integral method respectively.The simulation shows that optimization on the mesh density and the angle of singular element improved the computational efficiency and accuracy of SIF and the interaction integral method has an obvious advantage on stability.Finally,the FCG rate is modeled by the Jiang fatigue damage criterion and the extended finite element method(XFEM)respectively.The simulation results of FCG rate are in line with experiments data and indicate that XFEM method is more accurate than Jiang fatigue damage method.

Numerical modeling of thermally-induced fractures in a large rock salt mass

Numerical modeling of thermally-induced fractures is a concern for many geo-structures including deep underground energy storage caverns. In this paper, we present the numerical simulation of a large-scale cooling experiment performed in an underground rock salt mine. The theory of fracture mechanics was embedded in the extended finite element code used. The results provide reliable information on fracture location and fracture geometry. Moreover, the timing of the fracture onset, as well as the stress redis- tribution due to fracture propagation, is highlighted. The conclusions of this numerical approach can be used to improve the design of rock salt caverns in order to guarantee their integrity in terms of both their tightness and stability.

Interface failure of segmental tunnel lining strengthened with steel plates based on fracture mechanics

Segmental tunnel lining strengthened with steel plates is widely used worldwide to provide a permanent strengthening method.Most existing studies assume an ideal steel-concrete interface,ignoring discontinuous deformation characteristics,making it difficult to accurately analyze the strengthened structure’s failure mechanism.In this study,interfacial fracture mechanics of composite material was applied to the segmental tunnel lining strengthened with steel plates,and a numerical three-dimensional solid nonlinear model of the lining structure was established,combining the extended finite element method with a cohesive-zone model to account for the discontinuous deformation characteristics of the interface.The results accurately describe the crack propagation process,and are verified by full-scale testing.Next,dynamic simulations based on the calibrated model were conducted to analyze the sliding failure and cracking of the steel-concrete interface.Lastly,detailed location of the interface bonding failure are further verified by model test.The results show that,the cracking failure and bond failure of the interface are the decisive factors determining the instability and failure of the strengthened structure.The proposed numerical analysis is a major step forward in revealing the interface failure mechanism of strengthened composite material structures.