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Extended finite element method (XFEM) is one of the strongest numerical methods that its basis is finite element but regardless of mesh location respect to discountinuty solves the problems. In this method, using of enreaching the nodes and increasing of their degrees of freedom (from 2 to 4 or even upto 10) virtually and without verifying the mesh and geometry of discountinuty, one can model and develop the required governing equations of the system. In this paper, fatigue crack growth of repaired aluminum panels containing a crack is studied. The cracked panels were repaired on one side with glass/epoxy composite patches in the mixed mode condition. The extended finite element method is used to study the effects of patch lay-up configuration on crack front displacement and stress intensity factor and the effect of crack angle on stress intensity factor of the repaired panels. The results show that the plate-fiber-fiber-aluminum configuration has best effect and it could reduce the stress intensity factor (k1) by upto seventy percent.

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In this paper, the eXtended Finite Element Method is implemented to model the effect of the mechanical and thermal shocks on a cracked 2D orthotropic media. The uncoupled thermoelasticity equations are considered. Isoparametric four-node and eight-node rectangular elements are used to discrete governing equations. The dynamical stress intensity factors are computed by the interaction integral method. The Newmark and the Crank–Nicolson time integration schemes are used to numerical solve the spatial-discretized elastodynamic and thermal equations, respectively. A MATLAB code is developed to carry out all stages of the calculations from mesh generation to post-processing. Several elastic and thermoelastic numerical examples are implemented, to check the accuracy of the results and to investigate the effect of the orthotropic direction on the stress intensity factors.

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A two-dimensional (2D) eXtended Finite Element Method (XFEM) simulation is presented for propagation of hydraulic fractures from wellbore that the minimum principal in-situ stress is in horizontal plane. One primary role of hydraulic fracturing is to provide a high conductivity pathway along which reservoir fluids can flow to the well. In this study, enriched element has been applied with a maximum principal stress damage criterion, for initiation and propagation of crack in Abaqus 6.12. The properties and input data for rock models were extracted experimentally from Ahwaz reservior- Bangestan wellbore specimens. The specifications of crack were studied by analyzing the rock model without any crack or flaw and under different condition, such as in-situ stresses, pore pressure and elastic modulus. The results show that the critical position of crack initiation is perpendicular to minimum principal in-situ stress and stress condition of borehole and by increasing the pore pressure to the rock models, the pressure of injection fluid decreases. The results show that the pressure of injection fluid decreases at initiation step to constant amplitude after crack propagation. These results are in close agreement with the theoretical data, so that our simple procedure is efficiency and flexible.

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Multiple flaws are frequently occurred in actual components, such as pressure vessels and power plants. These flaws will in some circumstances lead to more severe effects than single flaw alone. Assessment of the interaction behaviour is based on an evaluation of the alignment and combination of these multiple flaws. In the current standards, multiple cracks are treated as an equivalent single crack if the distance between two cracks satisfies a prescribed criterion. First, this study introduces the current alignment and combination rules for through cracks. Following, to investigate the effects of the interaction of cracks, brittle fracture of a plate containig two adjacent cracks is simulated. The effect of cracks distances and crack lengths on stress intensity factors is evaluated. Also, crack growth analysis is simulated based on linear elastic fracture mechanics approach. The extended finite element method has been utilized to model the problem. This method enables the domain to be modeled by finite elements without explicitly meshing the crack surfaces, and hence crack propagation simulations can be carried out without remeshing. Based on the results, a new alignment and combination rule is proposed.

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In the present study, in order to evaluate the elastic displacement field and subsequently the fracture parameters within the isotropic homogeneous elastic solids with the edge or interior cracks, the extended finite element method with level set technique was used to avoid the disadvantages associated with the standard finite element method. An overdeterministic least squares method was utilized to determine the crack stress intensity factors as well as the coefficients of the higher order terms in the Williams' asymptotic series solution for structures containing crack in various modes of failure by fitting the series solution of displacement fields around the crack tip to a large number of nodal displacements obtained from the extended finite element method. For validating the results, several cracked specimens subjected to pure mode I, pure mode II, and mixed modes I/II loading were performed. Comparisons with results available from the literature obtained by the other formulations reveal the efficiency and the simplicity of the proposed method and demonstrate the capability of it to capture accurately the crack stress intensity factors and the coefficients of higher order terms.

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Extended finite element method (X-FEM) has been recently emerged as an approach to implicitly create a discontinuity based on discontinuous partition of unity enrichment (PUM) of the standard finite element approximation spaces. Despite numerous progresses in mesh generating updating of finite element mesh during crack propagation remain extremely heavy and difficult. This problem becomes more complicate, when there are many discontinuities in the finite element domain. However, the extended finite element method (X-FEM) in the combination with level set method (LSM) could overcome this cumbersome issue. In this contribution, predefined cracks and internal boundaries are created using level set functions and also the effects of soft/hard inclusions (interfaces) and voids are considered on crack propagation schemes. In fact, the interaction of crack and heterogeneities are considered. The level set functions are utilized to represent the locations and the evolutions of internal interfaces. In addition, the stress intensity factors for mixed mode crack problems are numerically calculated by using the interaction integral method. Different crack growth paths are simulated automatically for different oriented edge and center cracks and the interactions of internal boundaries on crack propagations are shown. All numerical examples are demonstrated the flexibility and capabilities of X-FEM in the applied fracture mechanics.

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In this paper, the fracture trajectory in blunt V-notched specimens under mixed mode loading is investigated by using two numerical approaches: 1) the extended finite element method (XFEM), 2) the incremental method. The first approach is an extended form of the finite element method in which the fracture takes place and grows according to the cohesive zone model. The second one is also an increment approach which the fracture initiation angle for notched specimen is first determined according to the concept of the maximum tangential stress (MTS) criterion. Afterward, a small crack is added to the notched specimen along the fracture direction and then a new cracked specimen is generated. In the next step, the fracture initiation angle is calculated from MTS criterion and another small crack is again added to the cracked specimen. These steps are continued until the crack reaches to the back boundary. To evaluate these methods, the fracture paths of the rounded-tip V-notched Brazilian disk (RV-BD)specimens under mixed mode loading are predicted by both XFEM and incremental method. It is shown that the incremental method can provide estimates more accurate than XFEM for the fracture initiation angle of the notched samples. It is also demonstrated that both methods can predict the fracture trajectory in good agreements with the experimental results

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In this paper, the strain energy release rate of first mode of failure in the adhesive bonding of two composite plates composed of unidirectional glass fiber is calculated using double cantilever beam specimen. Araldite 2011 adhesive connection which is widely used in the aerospace industry has been employed. Strain energy release rate is calculated by the modified beam method, compliance calibration method and modified compliance calibration method from experimental results. For modeling crack growth in adhesive bonding of two composite plates, the Extended Finite Element Method has been employed. Average value of critical strain energy release rate calculated by the modified compliance calibration method is considered as software input. After comparing force - displacement curve obtained from experimental data and numerical solution that represents good precision of the Extended Finite Element Method in calculating the maximum force and corresponding displacement and also linear part of force-displacement curve, strain energy release rate - force curve, stress intensity factor – force curve, strain energy release rate – displacement of the load effective point and failure stress - stress intensity factor curve are evaluated.

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Damage detection of structures is an important issue for maintaining structural safety and integrity. In order to evaluate the condition of structures, many structural health monitoring (SHM) techniques have been proposed over the last decades. Major approaches of SHM are non-destructive in nature and are widely used for damage detection in engineering structures such as aerospace, civil and marine structures. The existence of damage in a structure may be traced by comparing the response of time-domain wave traveling in the structure at its present state with a base-line response. A difference from the base-line response is correlated to the damage location through estimation of time of arrival of the new peaks (scattered waves). Thus, by employing the wave based methods, presence of damage in a structure is detected by inspecting at the wave parameters affected by the damage. The wave parameters that are commonly used for damage detection are the parameters representing attenuation, reflection and mode conversion of waves due to damage. Although detection of flaws is extremely important for many industrial applications, current approaches are severely restricted to specific flaws, simple geometries and homogeneous materials. In addition, the computational burden is very large due to the inverse nature of the problems where one solves many forward and backward problems. For instance, conventional ultrasonic methods measure the time difference of returning waves reflected from a crack; however, for laminated composite plates, the ultrasonic wave would be partially reflected at the interface of two layers where no crack actually exists, and partially continues to propagate further where it eventually is reflected back by the true crack. Numerical methods employed in crack detection algorithms require the solution of inverse problems in which the spatial problem is often discretized in space using finite elements in association with an optimization scheme. The solution of these problems is not unique, and sometimes the optimization algorithm may converge to local minima which are not the real optimal solution. Moreover, they often require hundreds of iterations to converge considering the algorithm used in the process. On the other hand, an accurate detection of cracks requires the re-meshing of the finite element domain at each iteration of the optimization. This is a severe limitation to any numerical approach when the conventional finite element method is employed for crack modeling, as the re-meshing of a domain is often not a trivial task. This paper investigates crack detection of two-dimensional (2D) structures using the extended finite element method (XFEM) along with particle swarm optimization (PSO) algorithm. The XFEM is utilized to model the cracked structure as a forward problem, while the PSO is employed for finding crack location as an optimization scheme. The XFEM is a robust tool for analysis of structures having discontinuities without re-meshing. Therefore, it is an efficient tool for an iterative process. Also, the PSO is a well-known non-gradient based method which is suitable for this inverse problem. The problem is formulated such that the PSO algorithm searches crack coordinates in order to detect the existing crack by minimizing an error function based upon sensor measurements. This problem is a non-destructive evaluation of a structure. Three benchmark numerical examples are solved to demonstrate capability and accuracy of the XFEM and the PSO for crack detection of 2D domains.

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In the current study, seismic cracking identification of concrete dams is conducted based on extended finite element method (XFEM) and Wavelet (WT) transform. First, the dam is numerically modeled and analyzed using the finite element method (FEM). Then cracking capability to the dam structure is added by applying the XFEM without introducing the initial crack, and the dam is analyzed under the seismic excitation. In fact, the whole dam structure is potentially under damage risk, and any zone reaching the fracture limit, begins to crack, which grows in the structure. This crack is usually unpredictable and is not easy to detect, therefore the structural modal parameters and their variation should be investigated based on structure response by using time-frequency transform. Results show that, investigating time-frequency window of the structure response and model parameters obtained from the numerical model, the history of physical changes occurred in the structure, cracking initiation time and damage localization is performed from comparing the intact and damaged vibration modes. Moreover, investigating the first natural modal indices of the intact and damaged structure, damage initiation and its location on Koyna dam height is easily detected, while for the second indices it is not performable.

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In order to detect damage in a large-scale and complicated structure, there is need to exact nonlinear numerical modeling that its results have been analyzed using a method of system identification. In this way, the extended finite element model (XFEM) based on cohesive crack model (XFEM Based Cohesive Crack Segments) for concrete material as a reliable model is used for investigating real responses of Karun 3 concrete dam against applied loads and damages. In this model, whole of the structure is potentially under damage risk, while there is no initial crack. The dam is numerically modeled and analyzed using the finite element method (FEM) and XFEM Based Cohesive Crack Segments respectively, and the dam is analyzed under the seismic excitation. Then, for specification of crack effects and nonlinear behavior, the structural modal parameters and their variation should be investigated based on structure response for obtaining damage initiation time and its location by using system identification based on continuous Wavelet (CWT) transform. Results show that the dam natural frequencies decrease after the crack is formed, where decrease in longitudinal and vertical responses are more than the transversal response decrease. Moreover, crack width and its exact location are specified precisely from comparing the intact and damaged crest and central cantilever vibration modes. Therefore, the combination of XFEM Based Cohesive Crack Segments and CWT is useful procedure for structural health monitoring of concrete arch dams.

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In this paper, the extended Finite Element Method (XFEM) is implemented to compute the Stress Intensity Factors (SIFs) for rectangular media subjected to a hygrothermal loading. In governing hygrothermoelasticity equations, the cross coupled of temperature and moisture fields and temperature-dependent diffusion in some cases are considered. Furthermore, an interaction integral for hygrothermal loading is developed to compute the stress intensity factors. The non uniform mesh of isoparametric eight-nod rectangular element is used in XFEM to decrease the absolute error in SIFs computations. In order to numerical results validation, the SIF of mode I is obtained analytically. The coupled governing equations are firstly decoupled in terms of new variables and then solved by the separation of variable method. According to the results, the moisture concentration gradient has a significant effect on the SIFs so should be considered in the model. Up to reaching temperature to its steady state, the cross coupled of temperature and moisture synchronies their time variation which affects on the time variation of SIF. At early time of thermal shock, the SIF for shorter cracks is not necessarily lesser than the longer ones. Also, the mode I SIF for longer and inclined cracks is smaller. On the other hand, considering the moisture concentration as a temperature function increases the time required to reach the moisture steady state.

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Studying the behavior of composite materials reveals that various types of failure modes occur when material experiences different loading conditions, which may have a significant impact on performance and properties of a structure. In this research, we study the mechanical response of orthogonal multi-layers by considering different failure modes at micro-scale and their development in macro-scale. For this purpose, the effect of the emergence and growth of fiber separation and subsequent formation of matrix cracks are investigated in the micro-scale. Furthermore, interlayer separation caused by leaving the matrix are studied in macro-scale. To model the separation of fiber matrix which is the first dominant failure mode, the sticky area method is used. The model verification and obtained results are compared with the previous research. Then, XFEM method is used to take into account the failure mode of matrix. Finally, using of the sticky area method, we are able to simulate the separation of matrix layers. The FE-program Abaqus via its user scripting interface (Python) are employed in this research for modeling of fibers embedded into matrix.

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For determination of the fracture parameters of self-compacting lightweight concrete (SCLC) size effect and work of fracture methods were used. For considering the behavior of concrete in different strengths, two mixes with water to cement (W/C) ratios of 0.42 and 0.47 were utilized. At first, the workability of the concrete was investigated and, after ensuring their self-compacting properties, the mechanical properties of the hardened concrete were determined. Then, by using the above-mentioned methods and conducting three-point bending tests on 30 beams, concrete fracture parameters, and crack-tip opening displacement were achieved. The results showed that with increasing W/C ratio from 0.42 to 0.47, the initial and total fracture energies, and fracture toughness decreased by 39.4%, 33.4% and 25.3%, respectively. The effect of the W/C ratio on the fracture parameters of this type of concrete was discussed. Furthermore, several empirical relations have been proposed that by the use of them and only by the determination of the compressive strength, the initial fracture energy, total fracture energy, the ratio of energies to each other, and fracture toughness can be determined. Then, by using the fracture parameters, the mechanical properties of the concrete and the extended finite-element method, the crack propagation was modeled. The results showed that this method has high accuracy in the numerical solution of the fracture problems as well as the efficiency of the obtained parameters for determining the behavior of self-compacting lightweight concrete.

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The present paper investigates and compares the crack propagation in concrete gravity dams using two models of linear fracture mechanics and plasticity damage concrete. The first model is based on linear concrete behavior using the extended finite element method without considering the effect of strain softening on the crack tip while the second model is based on the nonlinear concrete behavior and the strain softening in tension with damage parameter. According to two different algorithms and based on two models, several benchmark examples are reviewed and the results compared with those reported in the literature. Then, path of the crack growth in Koyna gravity dam due to a seismic excitation of Koyna earthquake in 1962 has been performed by considering the dam-reservoir interaction.
The results show that due to low compressive stresses during analysis of concrete gravity dams, consideration of compressive nonlinear behavior has no effect on crack initiation and almost is the same for two models. However because of crack opening and closing with tapping the crack faces together in extended finite element model, the compressive stress will be more than the allowable stress of concrete. Crack initiation at downstream and upstream face occurred at angle of 90 and zero degrees respectively, which in both models, the numerical results are in agreement with the experimental model.
The crack in the extended finite element model grows faster such that the crest block of dam in this model is separated from the dam body, earlier than the concrete plastic damage model. Also the values of dam crest displacement and hydrodynamic pressure in the reservoir in extended finite element model with linear elastic fracture mechanic are more than the other model, which can be attributed to the linear and nonlinear behavior of concrete in extended finite element and concrete plastic damage model respectively. In the extended finite element model, due to using linear fracture mechanic, the maximum principal stress in the cracked elements reaches the values greater than the maximum tensile strength, but in the concrete plastic damage model as soon as the stress reaches a tension limit value, elements are damaged and the stress is reduced. In both models, the crack located at the slope change area, propagates with the downward slope from downstream dam face and connects to the crack at upstream face which is growth horizontally.
Because of laboratory sample dimension and boundary condition of dam-reservoir compared with actual manner, neither of two crack profiles covered the experimental model, accurately. But it is shown that the crack profiles in the extended finite element model are more consistent with experimental results. Finally, the results show that the crack profile are slightly different in the two models because of quasi brittle behavior of the dam concrete, which can be attributed to the small fracture process zone of the crack tip in comparison with the dimension of the concrete gravity dams such that by removing strain softness part, the error in the amount of additional computation can be neglected.  
 

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