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Crack initiation and propagation analysis in brittle two-dimensional isotropic materials are conducted using the damage Phase Field Method (PFM) following the variational approach. Here, we study two-dimensional (2D) structures that contain material heterogeneities (e.g., interfaces and inclusions) as well as geometric ones (e.g., cracks and voids) when subjected to quasi-static uniaxial tensile loading. The adopted methodology combines Extended Finite Element Method (XFEM) and Level-Set couple with PFM in order to investigate both the case of heterogeneous materials (composite or porous) as well as the case of interfacial cracks between two different materials for their interest and relevance as practical examples. Among many others, one can, for example, argue that: (a) the regular hexagonal arrangement of heterogeneities leads to a significantly higher strength than any random arrangement, for both the composite material (containing fibers) and the porous material (containing voids), (b) the effects of contrasting stiffness and toughness between two materials along with their respective impacts on the interfacial crack trajectory, on energy balance and on reaction force are in favor of toughness.

We introduce a coupled system of partial differential equations for the modeling of the fluid–fluid and fluid–solid interactions in a poroelastic material with a single static fracture. The fluid flow in the fracture is modeled by a lower-dimensional Darcy equation, which interacts with the surrounding rock matrix and the fluid it contains. We explicitly allow the fracture to end within the domain, and the fracture width is an unknown of the problem. The resulting weak problem is nonlinear, elliptic and symmetric, and can be given the structure of a fixed-point problem. We show that the coupled fluid–fluid problem has a solution in a specially crafted Sobolev space, even though the fracture width cannot be bounded away from zero near the crack tip. For numerical simulations, we combine XFEM discretizations for the rock matrix deformation and pore pressure with a standard lower-dimensional finite element method for the fracture flow problem. The resulting coupled discrete system consists of linear subdomain problems coupled by nonlinear coupling conditions. We solve the coupled system with a substructuring solver and observe very fast convergence. We also observe optimal mesh dependence of the discretization errors even in the presence of crack tips.

In this work, stochastic perturbation-based vibration characteristics of cracked bi-material and functionally graded material (FGM) domain with uncertain material properties are investigated using the extended finite element method. The level set function is implemented to track the geometrical discontinuities. The partition of unity-based extrinsic enrichment technique is employed to model the crack and material interface. The exponential law is used to model the graded material properties of FGM. The First-order perturbation technique (FOPT) is implemented to predict the standard deviation of natural frequency for the given uncertainties in the material properties. The numerical results are presented to show the effect of geometrical discontinuities and material randomness on vibration characteristics.

Cracks in transport pipelines significantly impact their structural safety, making pipeline fracture damage a major concern. While experimental tests can study crack growth, their setup and costs are substantial. To address this, our work involves parametric analyses to investigate the effects of initial crack length, load types and sizes, and pipe wall thickness on the crack tip stress field. The finite element model is established according to the actual operation, and the crack defects of the pipe are established by the extended finite element method (XFEM). The crack tip variation is studied by extracting the von Mises stress and strain at the crack tip. When the crack propagates, the stress field at the crack tip will fluctuate in a certain range. The relationship between stress field fluctuation and crack propagation was studied by changing the XFEM crack growth for comparative analysis. Utilizing 429 numerical results obtained from a parametric numerical model implemented with Python and Abaqus, we establish a back propagation (BP) neural network prediction model to forecast the stress field at the crack tip. The relative errors between the numerical results and the predictions by our model remain below 5%. In conclusion, our proposed approach for analyzing pipeline fracture under multiple loads proves valuable for pipeline safety assessment, and it offers useful insights for evaluating the suitability of transportation pipelines.

The present work investigates the fatigue life of a functionally graded material (FGM) made of aluminum alloy and alumina (ceramic) under cyclic mixed mode loading. Both element free Galerkin method (EFGM) and extended finite element method (XFEM) are employed to simulate and compare the fatigue crack growth. Partition of unity is used to track the crack path in XFEM while a new enrichment criterion is proposed to track the crack path in EFGM. The fatigue lives of aluminum alloy, FGM and an equivalent composite (having the same composition as of FGM) are compared for a major edge crack and center crack in a rectangular domain. The proposed enrichment criterion not only simulates the crack propagation but it also extends the applicability and robustness of EFGM for accurate estimation of fatigue life of component.

Macroscale mesh sensitivity and RVE size dependence are the two major issues that make the conventional homogenization techniques incapable of modeling the softening behavior of quasi-brittle materials. In this paper, a new continuous–discontinuous multiscale modeling approach to failure is presented. Inspired by the classical crack band model of Bazant and Oh (1983), this approach is built upon an extended computational homogenization (CH) scheme for representing the macroscale crack behavior. During the multiscale computation, once a macroscale material point loses its stability with the XFEM, a new crack segment represented is inserted for which cohesive RVE models using the extended CH and with copied initial states are coupled to crack integration points. In the extended CH, the macroscale strain applied to the boundary of the cohesive RVE model is enriched with a macroscale discontinuity related term regularized with the effective length of the microscale localization band. This helps alleviate the RVE size dependency of the homogenized cohesive response. The weakly periodic BCs that are aligned with the localization direction are employed to minimize spurious boundary effects. Several numerical examples are provided to demonstrate the effectiveness of this framework, with a comparison against direct numerical simulations.

In the framework of the extended finite element method, a two-dimensional four-node quadrilateral element enriched with only the Heaviside step function is formulated for stationary and propagating crack analyses. In the proposed method, two types of signed distance functions are used to implicitly express crack geometry, and finite elements, which interact with the crack, are appropriately partitioned according to the level set values and are then integrated numerically for derivation of the stiffness matrix and internal force vectors. The proposed method was verified by evaluating stress intensity factors, performing crack propagation analyses and comparing the obtained results with reference solutions.

This paper presents a stochastic fracture response and crack growth analysis of mixed-mode stress intensity factors (MSIFs) for edge cracked laminated composite beams subjected to uniaxial, uniform tensile, shear and combined stresses with random system properties. The randomness in material properties of the composite material, lamination angle, laminate thickness, the crack length and the crack angle are modeled as both input uncorrelated and correlated random variables. An extended finite element method (XFEM) through the so-called M-interaction approach combined with the second-order perturbation technique (SOPT) and Monte Carlo simulation (MCS) is used to obtain the statistics in terms of the mean and coefficient of variation (COV) of MSIFs for edge cracked laminated composite beams. The effect of crack propagation on the MSIFs in the presence of tensile, shear and combined stresses using a global tracking algorithm is also investigated. The results using the present approach are compared with the available published results. A good agreement is seen whenever alternative results are available.

Piezoelectric materials possess special characteristics of electromechanical coupling behavior and thus have found numerous applications such as transducers, sensors, actuators. Fracture of piezoelectric materials has drawn substantial attention of the research community and is being widely investigated for predicting their failure. Most of the research on piezoelectric materials is based on impermeable crack conditions. In the present study semi-permeable crack boundary conditions has been analyzed using the extended finite element method (XFEM). Combined Mechanical and Electrical loading with quasi-static crack growth has been considered on a pre-cracked rectangular plate with crack at its edge and center. Stress intensity factors have been evaluated by interaction integral approach using the asymptotic crack tip fields. Effect of presence of minor cracks and holes have been analyzed on the intensity factors of semi-permeable major crack.

This work is focused to investigate the effect of various discontinuities like cracks, inclusions and voids for an orthotropic plate, to evaluate the normalized mixed-mode stress intensity factors (NMMSIFs) by implementing the extended finite element method (XFEM) under uniaxial tensile loading though considering the various numerical examples. The NMMSIFs are investigated with the interaction of crack, single- and multi-inclusions/voids for an orthotropic plate. The effect of NMMSIFs is analyzed for an orthotropic plate with several orthotropy axis orientations by changing the position of single- and multi-inclusions/voids while aligned, above and away with respect to an edge crack of the plate and for the both side inclusions/voids aligned the center crack. It is also investigated for the effect of various shapes of inclusions/voids for an edge crack orthotropic plate under uniaxial tensile loading using XFEM.

Engineering components are susceptible to numerous fatigue fracture issues in the context of long-term service. The failure of a large number of components is often accompanied by the propagation process of fatigue cracks. The elastic-plastic finite element simulation analysis method was employed to deeply investigate the crack propagation mechanism of aluminum alloy materials under fatigue loading in this paper. First, a finite element model of the CT specimen was constructed based on the constitutive relationship of elastic-plastic materials. Additionally, the crack propagation rule was defined using the extended finite element method (XFEM). Subsequently, the validity and accuracy of the simulation model were verified through fatigue crack propagation experiments using a 6005A aluminum alloy CT specimen. Finally, the simulation model was further utilized to investigate the effects of different stress ratios and specimen thicknesses on the crack propagation behavior. The research findings demonstrated that the crack propagation simulation model established by the elastic-plastic material constitutive and the XFEM is capable of accurately simulating the crack propagation behavior of aluminum alloys under fatigue loading. In the validation CT model, the crack of the simulation model expanded from 13mm to 30mm after 160,000 cycles, and the expansion rate ranged from $2.5\times 10^{-5}$ to $3\times 10^{-3}$. The height and width of the plastic zone at a crack length of 16 mm were 3.1mm and 2.0mm, respectively, which are very close to the experimental results. Furthermore, the simulation model also reveals the significant role of plastic flow at the crack tip in the fatigue crack propagation process.

Piezoelectric materials due to their electromechanical coupling characteristics are being widely used in actuators, sensor, transducers, etc. Considering wide application it is essential to accurately predict their fatigue and fracture under applied loading conditions. The present study deals with analysis of fatigue crack growth in piezoelectric material using the extended finite element method (XFEM). A pre-cracked rectangular plate with crack at its edge and center impermeable crack-face boundary conditions is considered for simulation. Fatigue crack growth is simulated using extended finite element method under plane strain condition and mechanical, combined (mechanical and electrical) cyclic loading. Stress intensity factors for mechanical and combined (mechanical and electrical cyclic loadings) have been evaluated by interaction integral approach using the asymptotic crack tip fields. Crack propagation criteria have been applied to predict propagation and finally the failure.

Extended finite element method (XFEM) and second-order perturbation technique (SOPT) were combinedly utilized using interaction integral (M-integral) through partition of unity method to find out the mean and variance of mixed mode stress intensity factor (MMSIF). Uncertain system parameters are considered in material properties, crack length, crack orientation, gradient coefficients in the present study. MMSIF in a numerical example with center crack is computed to validate the accuracy of the presented model. Finally, typical numerical results are presented to examine the different modulus ratios, crack angle, crack length, position of crack and tensile, shear and combined loadings with uncertain system properties on the MMSIF.