XFEM Research Articles

Effect of random variation in input parameter on cracked orthotropic plate using extended isogeometric analysis (XIGA) under thermomechanical loading

Abstract This research introduces the Stochastic Extended Isogeometric Analysis (XIGA) method to investigate fracture behavior of isotropic and orthotropic materials under mechanical, thermal, and thermomechanical loads. Employing knot spans from Isogeometric Analysis (IGA) for domain discretization, the study utilizes identical basis functions for geometry construction and solution discretization. Utilizing Extended Finite Element Method (XFEM) enrichment functions, accurate crack face displacement discontinuity and tip singularity within the stress field are characterized. Additionally, employing a second-order perturbation technique within XIGA framework, the research derives mean and coefficient of variance values for mixed-mode Stress Intensity Factors (SIF). Stochastic variations in material elastic properties, crack length, and crack angle are considered in this computation. Credibility and robustness of the study are confirmed through comparative analyses against available literatures and Monte Carlo Simulations (MCS). The observed exceptional agreement validates the precision and reliability of the proposed stochastic XIGA method for fracture analysis in orthotropic material systems under thermomechanical loading conditions.

Sprain energy consequences for damage localization and fracture mechanics

The 2023 smooth Lagrangian Crack-Band Model (slCBM), inspired by the 2020 invention of the gap test, prevented spurious damage localization during fracture growth by introducing the second gradient of the displacement field vector, named the "sprain," as the localization limiter. The key idea was that, in the finite element implementation, the displacement vector and its gradient should be treated as independent fields with the lowest ([Formula: see text]) continuity, constrained by a second-order Lagrange multiplier tensor. Coupled with a realistic constitutive law for triaxial softening damage, such as microplane model M7, the known limitations of the classical Crack Band Model were eliminated. Here, we show that the slCBM closely reproduces the size effect revealed by the gap test at various crack-parallel stresses. To describe it, we present an approximate corrective formula, although a strong loading-path dependence limits its applicability. Except for the rare case of zero crack-parallel stresses, the fracture predictions of the line crack models (linear elastic fracture mechanics, phase-field, extended finite element method (XFEM), cohesive crack models) can be as much as 100% in error. We argue that the localization limiter concept must be extended by including the resistance to material rotation gradients. We also show that, without this resistance, the existing strain-gradient damage theories may predict a wrong fracture pattern and have, for Mode II and III fractures, a load capacity error as much as 55%. Finally, we argue that the crack-parallel stress effect must occur in all materials, ranging from concrete to atomistically sharp cracks in crystals.

Use of Extended Finite Element Method to Characterize Stress Interference Caused by Nonuniform Stress Distribution during Hydraulic Fracturing

Use of Extended Finite Element Method to Characterize Stress Interference Caused by Nonuniform Stress Distribution during Hydraulic Fracturing

Fatigue Characteristics Analysis of Carbon Fiber Laminates with Multiple Initial Cracks

In the entire wind turbine system, the blade acts as the central load-bearing element, with its stability and reliability being essential for the safe and effective operation of the wind power unit. Carbon fiber, known for its high strength-to-weight ratio, high modulus, and lightweight characteristics, is extensively utilized in blade manufacturing due to its superior attributes. Despite these advantages, carbon fiber composites are frequently subjected to cyclic loading, which often results in fatigue issues. The presence of internal manufacturing defects further intensifies these fatigue challenges. Considering this, the current study focuses on carbon fiber composites with multiple pre-existing cracks, conducting both static and fatigue experiments by varying the crack length, the angle between cracks, and the distance among them to understand their influence on the fatigue life under various conditions. Furthermore, this study leverages the advantages of Paris theory combined with the Extended Finite Element Method (XFEM) to simulate cracks of arbitrary shapes, introducing a fatigue simulation method for carbon fiber composite laminates with multiple cracks to analyze their fatigue characteristics. Concurrently, the Particle Swarm Optimization (PSO) algorithm is employed to determine the optimal weight configuration, and the Backpropagation neural network (BP) is used to train and adjust the weights and thresholds to minimize network errors. Building on this foundation, a surrogate model for predicting the fatigue life of carbon fiber composite laminates with multiple cracks under conditions of physical parameter uncertainty has been constructed, achieving modeling and assessment of fatigue reliability. This research offers theoretical insights and methodological guidance for the utilization of carbon fiber-reinforced composites in wind turbine blade applications.

Numerical Fatigue Crack Growth on Compact Tension Specimens under Mode I and Mixed-Mode (I+II) Loading.

This study focused on standard Compact Tension (CT) specimens and two loading modes during the numerical analyses carried out, namely: pure mode I and mixed-mode loading (Modes I+II). Numerical stress intensity factors, KI, were calculated using Abaqus® 2022 and compared with those given analytically under pure mode I loading, showing very good agreement. Additionally, KI, KII, and KIII results obtained from Abaqus® were presented for mixed-mode loading, analyzing crack growth and variation through the thickness of the CT specimen. Moreover, fatigue crack growth simulations under mode I loading were conducted on standard CT specimens using the Extended Finite Element Method (XFEM) and the Paris Law parameters of an AISI 316L stainless steel. It was shown that XFEM effectively determines crack propagation direction and growth, provided that an appropriate mesh is implemented.

Tensile performance prediction of CFRPs with voids using multiscale analysis and neural networks

The overall work provides a novel multiscale modeling strategy applicable to the mechanical response prediction of arbitrarily laid porous laminates under uniaxial tension by establishing representative defective volumes (RDVs) for the inter-ply and intra-ply regions. A representative defective volume modeling method based on void characterization results using X-ray computed tomography for the interlaminar region was proposed. Elastic properties, tensile strength, and fracture energies of porous and poreless microscale models were obtained and used in the macroscale model. Defective properties were assigned to partial elements in the macroscale model according to the preset distribution mode. The Extended Finite Element Method was taken to simulate the failure process. Tensile properties of porous laminates with stacking sequences of [90]8, [90/0/90/0]2S, and [45/90/-45/0]2S were experimentally tested and numerically simulated. The predicted tensile properties and crack propagation behavior coincide well with the test results. Besides, the effects of micro-voids and macroscopic void distribution were discussed in detail. Further, a back-propagation neural network was used to achieve a fast prediction of the tensile properties and save computational costs. The computation time (<1 s) greatly improved compared with multiscale modeling (>38 h). This work provides an efficient tool for composite performance prediction, design, and optimization.

Numerical simulation of hydraulic fracture propagation from recompletion in refracturing with dynamic stress modeling

Owing to the rapid decline of oil production from tight oil reservoirs after primary hydraulic fracturing treatment on the horizontal well, a refracturing stimulation is proposed for tight oil recovery. In this study, a fully coupled dynamic stress computational method with a finite-element method is presented, and depletion-induced dynamic stress is simulated by coupled numerical modeling. In addition, the extended finite-element method (XFEM) approach is used to investigate the effect of different parameters on fracture dynamic propagation in recompletion from refracturing. The results highlight the effects of production-induced stress changes following hydraulic fracture propagation. When multiple fractures are stimulated simultaneously from recompletion during refracturing, curved fractures are commonly observed, and the deflected fractures generally divert toward the primary stimulated area with low pore pressure. The results indicate that comprehensive factors can affect the hydraulic fractures propagation from recompletion. The optimal refracturing time window can be determined using the dynamic stress condition and stimulated area. The initial completion spacing, initial fracture length, and recompletion perforation cluster spacing can also affect the fracture geometry from the recompletion. A larger initial fracture length can induce a larger stress change area, whereas a larger distance between the new perforations in recompletion and the old perforations can decrease the depletion-induced stress effect. A high horizontal stress contrast can increase the depletion-induced stress effect because a long fracture extends the area. Owing to the nonuniform pressure and stress distributions, more nonuniform fractures are commonly generated in the refracturing treatment. Thus, temporary plugging injection and proppant inertia must be designed while reducing the number of perforations near the initial perforation positions. This can help decrease the possibility of strong curved fractures and screen out problems.

Sequential thermomechanical stress and cracking analysis of photovoltaic modules with full and half-cut cells

The transition from conventional full-cell patterns to half-cell modules in the photovoltaic (PV) industry promises enhanced stability and efficiency. This study investigates the thermomechanical behaviour and stress distribution within half-cell and full-cell PV modules during the manufacturing and operational phases. Using finite element modeling, the research simulates sequentially the manufacturing and operating processes such as laser cutting, soldering, lamination, mechanical loading and thermal cycling. The Extended Finite Element Method (XFEM) predicts crack initiation and propagation in the crack-sensitive regions in PV modules during their entire life. Key findings highlight stress concentrations during manufacturing, influenced by parameters like laser power, scribing length and Silicon wafer size. Mechanical loading (ML) and thermal cycling (TC) induce additional stresses, impacting module reliability. The results are useful for the optimization of material properties and the development of advanced design strategies contributing to the durability and efficiency of PV systems.

A novel approach to crack modeling using extended finite element and substructures methods

In the present work, a combination of Extended Finite Element Method (XFEM) and substructures methods has been utilized for crack modeling. Structures are divided into several substructures, and XFEM is employed to model the presence of cracks within each substructure. In another method, crack modeling has been carried out without using the Extended Finite Element Method. Instead, cracks are modeled by eliminating boundary constraints from two substructures. The Krylov-Schur algorithm is utilized to accelerate the computation of structural modes by preparing stiffness and mass matrices for eigenvalue and eigenvector calculations related to the superstructure. For evaluating this method, four examples have been considered: In the first example, an experimental L-shaped steel structure comprising a beam and a column was examined. The second example involved an experimental steel beam with a box-shaped cross-section. In the third example, a steel beam with simple supports at both ends and a rectangular cross-section was proposed. In the fourth example, a real two-span bridge (Turtle Mountain Bridge) is also presented to evaluate the proposed method. The method was applied for modeling, and the obtained results were validated using experimental and analytical results. In this work, the Structural Similarity Index Method (SSIM) for mode shape similarity assessment has been employed for crack identification. Based on the results obtained from the modeling and crack identification evaluations, it can be concluded that the current method can model multiple cracks in structures with variable cross-sections, real concrete bridges, frame-shaped structures, and diverse structures by assembling substructures. Despite simplifying the problems, it maintains an acceptable level of accuracy in validation. This advantage enables the identification of cracks through a straightforward comparison of mode shapes.

Evaluation of retrofitting effect of concrete filling in hollow RC columns using XFEM

Hollow RC columns are widely utilized in the construction of high piers in mountainous regions. Recently, precast hollow RC columns have been increasingly used to enhance transportability and ease of handling, aiding Accelerated Bridge Construction. This paper evaluated the effectiveness of concrete-filling retrofitting measures for hollow RC columns using eXtended Finite Element Method (X-FEM). Our focus was particularly on instances where original hollow sections and post-filled concrete sections don't behave as unified structures. The proposed X-FEM model's reliability was validated through simulations replicating compressive strength tests on molded concrete specimens and previous static loading tests on hollow RC columns conducted to evaluate the efficacy of concrete-filling retrofitting for hollow RC columns. The proposed X-FEM model successfully represents the compressive softening and fracture behavior of concrete under uniaxial compression. It also successfully replicated the lateral load capacity and the crack patterns of hollow RC columns observed in the previous experiments. When comparing the component ratios of bending and shear deformation of the columns, the shear deformation component of the hollow RC column retrofitted with the concrete filling was about 1.5 times larger than that of the solid RC column at each displacement. This result indicates that concrete-filling retrofitting might not enhance the shear capacity of hollow RC columns to the anticipated level in scenarios where the pre-existing hollow portion and the post-filled concrete portion fail to function as unified structures. Based on these findings, this study investigated the efficacy of anchor reinforcement in hollow RC columns filled with concrete to enhance the structural unity of existing and filled portions. The results indicate that anchor reinforcement improved the shear resistance properties by enhancing the structural unity between the pre-existing hollow portion and the post-filled concrete portion.

Estimating equivalent elastic properties of frozen clay soils using an XFEM-based computational homogenization

This study addresses the challenge of estimating the elastic properties of heterogeneous frozen clay soils by introducing a comprehensive approach that combines analytical and numerical models. The frozen clay soil is treated as a mixture composed of frozen clay-water composites and nonclay mineral inclusions. An inversion algorithm is employed to deduce the elastic properties of the matrix (clay-water composites) of two artificially frozen sandy clay samples with known temperature-dependent elastic properties. Subsequently, a two-dimensional numerical simulation using the eXtended Finite Element Method (XFEM) is conducted to carry out numerical homogenization by considering the imperfect bond among frozen clay-water composites and nonclay minerals. The numerical homogenization model offers insights into the temperature-dependent behavior of the interface stiffness parameter. The numerical homogenization results are compared with conventional numerical homogenization approaches like the FEM, which rigidly defines the bonding between inclusions and the matrix. The comparison indicates that the neglect of imperfect bonds among clay-water composites and nonclay minerals will lead to unrealistic outcomes in cases with a high fraction of inclusions. This integrated approach advances the understanding and prediction of elastic properties of frozen clay soils by considering their heterogeneous nature.

Novel FGM-USDFLD approach in Graded Cohesive Zone Modeling (GCZM): Predicting debonding and crack propagation in composite-patched notched plates

This study uses a graded adhesive approach to investigate the efficacy of composite patch reinforcement on a notched aluminum plate. The methodology employs the volumetric fraction concept of Functionally Graded Materials (FGM) to develop a Graded Cohesive Zone Model (GCZM). A variable field, introduced through a Fortran-based USDFLD subroutine, adapts the formulation of this GCZM. Patch debonding is simulated via adhesive damage using the Cohesive Zone Model (CZM). At the same time, crack initiation and propagation within the plate are modeled using the Extended Finite Element Method (XFEM) implemented in ABAQUS finite element software. The adhesive behavior is characterized by a triangular traction-separation law, with the GCZM incorporating gradation in both shear and normal separation modes relative to the notch radius. The GCZM concept is compared against two non-graded cases, Araldite 420 and AV138 adhesives, with one case replicating a previous study. Three gradation concepts are explored: C-1, where the more resistant Araldite 420 is located at the notch; C-2, at the extremity; and C-3, where it is at both the notch and extremity. These configurations aim to homogenize load transfer to the composite reinforcement and elucidate how different GCZM concepts influence debonding between the plate and composite reinforcement. By implementing USDFLD, this work effectively demonstrates the impact of gradation concepts and volumetric fraction indices on the competition between debonding and crack initiation in the plate. The results provide valuable insights into optimizing adhesive properties for enhanced structural integrity in composite-reinforced metallic structures.

Advanced damage prediction in notched plates reinforced with Graded composite patches: Integrating XFEM-CZM and fiber-matrix coupling laws using Functionally Graded Materials

This study introduces a novel approach to reinforcing notched aluminum plates using functionally graded composites (FGCs). By integrating volume fraction principles of Functionally Graded Materials (FGMs) into fiber-matrix mixture laws, we propose an advanced patch reinforcement strategy. The research employs the Cohesive Zone Model (CZM) and Extended Finite Element Method (XFEM) in ABAQUS to simulate patch debonding, crack initiation, and propagation. We compare linearly graded and FGM patches against non-graded counterparts, demonstrating superior load distribution and damage tolerance of graded composites. Three gradation concepts are explored: C-1 (peak fiber density at mid-thickness), C-2 (increased fiber density near patch edge), and C-3 (highest fiber density adjacent to the adhesive joint). Results reveal a critical interplay between adhesive debonding and crack propagation in the aluminum substrate. The study highlights the efficacy of graded composite patches in mitigating damage and offers significant insights into advanced reinforcement techniques for enhanced structural durability and reliability in engineering applications.

Numerical Investigation of Fatigue Behavior in Ti-6Al-4V Orthopedic Hip Implants Subjected to Different Environments.

In this paper, hip implants made of Ti-6Al-4V titanium alloy are analyzed numerically using Extended Finite Element Method XFEM. The combined effect of corrosion and fatigue was considered here since this is a common cause of failure of hip implants. Experimental testing of Ti-6Al-4V alloy was performed to determine its mechanical properties under different working environments, including normal, salty, and humid conditions. The integrity and life of the hip implant were assessed using the Linear Elastic Fracture Mechanics (LEFM) approach. For this purpose, the conditional fracture toughness Kq using CT specimens from all three groups (normal, humid, salty conditions) were determined. This provided insight into how different aggressive environments affect the behavior of Ti-6Al-4V alloy; i.e., how much its resistance to crack growth would degrade depending on conditions corresponding to the real exploitation of hip implants. Next, analytical and XFEM analyses of fatigue behavior in terms of the number of cycles were performed for all three groups, and the obtained results showed good agreement, confirming the validity of the integrity assessment approach shown in this work, which also represented a novel approach since fatigue and corrosion effects were investigated simultaneously.

Damage analysis in welded steel pipe elbow under strong cyclic loading

According to cyclic loading modes, highly pressurized tubular elements, such as those in elbows, differ from other straight tubular structures in their modes of stress and damage. This work aims to perform a numerical prediction of a tubular structure. It consists of an X52 steel elbow welded to X65 grade ends by straight tubular sections. This pressurized structure is subjected to strong cyclic loading in bending moment applied until damage occurs. The bending moment is combined with different orientations between the closing or opening moment and the out-of-plane moment, presenting a possible but rarely analyzed situation. This cyclic loading mode is taken as an evaluative parameter in its various amplitudes, orientations, and patterns. The cyclic hardening of the elbow and straight tubular sections, including those of the welded joints, are all formulated by the combined isotropic and kinematic model introduced in the ABAQUS calculation code with parameters calibrated according to the Voce model and experimental results, using plasticity by the Von Mises equivalent stress flow theory. The appropriate XFEM (Extended Finite Element Method) technique is used in conjunction with the hardening model to overcome numerical calculation difficulties and predict damage in traction laws, separation by crack initiation and propagation. The results, in the form of hysteresis curves in cyclic bending moment and angular displacement, have shown a strong dependency that conditions the structure’s response as well as the level of its damage.

Novel cell-based smoothed extended finite element method for simulating the interactions of ultrasonic waves with randomly distributed cracks in solid structures

The conventional extended finite element method (XFEM) is a powerful tool for simulating crack-related problems in materials; however, several limitations exist, such as numerical instabilities and convergence issues. These problems arise because enriched elements have higher stiffness than standard elements, and this difference can cause computational difficulties. To overcome these limitations, we developed the cell-based smoothed extended finite element method (CS-XFEM), an advanced computational technique designed to simulate the intricate interactions between ultrasonic waves and randomly distributed cracks within solid materials. This innovative approach integrates a cell-based smoothing technique into the XFEM, effectively softening the stiffness of the enriched elements around crack tips. Therefore, the CS-XFEM eliminates numerical instability, providing a more stable and reliable computational framework. In this study, numerical experiments were conducted in which plasticity properties were assigned to both the crack bodies and tips to reflect crack yielding. Further, frictional contact in the crack body elements was formulated using the Heaviside function, and deformation around the crack tips was approximated using a singular function. Through comprehensive numerical investigations, we demonstrated that the conventional XFEM fails to converge and, instead, diverges when ultrasonic waves interact with randomly distributed cracks. By contrast, our proposed CS-XFEM method demonstrates strong convergence capabilities, rendering it well-suited for exploring the interactions between ultrasonic waves and randomly distributed cracks under varying crack quantities, lengths, and friction coefficients. Overall, the proposed CS-XFEM is an efficient, accurate, and robust method for investigating the acoustic nonlinearity induced by randomly distributed cracks with frictional contact in solid structures.

A three-dimensional finite strain volumetric cohesive XFEM-based model for ductile fracture

The verification/prediction by numerical simulation of the resistance of large-scale metal structures subjected to extreme loading (e.g. accidental mechanical overload) that can lead to failure constitutes a major issue in the transport, energy, and defense sectors. This work aims to develop a three-dimensional numerical methodology (i) capable of macroscopically accounting for the various dissipative mechanisms of plasticity and damage until failure, (ii) formulated within the framework of large deformation, (iii) implemented in a commercial computation code, and (iv) mesh-objective. The commercial computational code is ABAQUS-std, and the methodology is implemented as a user finite element (UEL). Geometric non-linearities are treated within the framework of an updated Lagrangian formulation (ULF). The more or less diffuse damage phase is described by the Gurson–Tvergaard–Needleman (GTN) microporous plasticity model with standard finite element (FE). The micro-void coalescence phase-induced dilation/shear band is described using an original volumetric cohesive extended finite element method approach (VCZM-XFEM). The progressive loss of cohesion leading to ultimate cracking is treated with extended finite element method (XFEM). Particular attention is paid to transition criteria (damage to localization, localization to cracking), to the orientation of the localization plane (especially in Mode II), to the cohesive zone model and to techniques for overcoming numerical difficulties (volumetric locking, numerical integration). The so-built 3D-FS-GTN-VCZM-XFEM unified methodology is capable of reproducing the degradation mechanisms, and, the failure surface shape and orientation in large elasto-plastic deformation of structures typical of laboratory tests, even for fairly coarse meshes.

Predicting Damage in Notched Functionally Graded Materials Plates through extended Finite Element Method based on computational simulations

Presently, Functionally Graded Materials (FGMs) are extensively utilised in several industrial sectors, and the modelling of their mechanical behaviour is consistently advancing. Most studies investigate the impact of layers on the mechanical characteristics, resulting in a discontinuity in the material. In the present study, the extended Finite Element Method (XFEM) technique is used to analyse the damage in a Metal/Ceramic plate (FGM-Al/SiC) with a circular central notch. The plate is subjected to a uniaxial tensile force. The maximum stress criterion was employed for fracture initiation and the energy criterion for its propagation and evolution. The FGM (Al/SiC) structure is graded based on its thickness using a modified power law. The plastic characteristics of the structure were estimated using the Tamura-Tomota-Ozawa (TTO) model in a user-defined field variables (USDFLD) subroutine. Validation of the numerical model in the form of a stress-strain curve with the findings of the experimental tests was established following a mesh sensitivity investigation and demonstrated good convergence. The influence of the notch dimensions and gradation exponent on the structural response and damage development was also explored. Additionally, force-displacement curves were employed to display the data, highlighting the fracture propagation pattern within the FGM structure.

Numerical method for predicting the nucleation and propagation of multiple cracks based on the modified extended finite element method

In practical engineering, structures will inevitably suffer from multiple cracks and require accurate numerical methods to calculate the structural behavior. Regarding the multi-crack problems, the nucleation of new cracks and the development of existing cracks will affect the subsequent structural responses. Therefore, the criterion for calculating crack nucleation and development is a critical factor influencing the numerical results. This paper presents a modified Extended Finite Element Method (XFEM) to predict the nucleation and development of multiple cracks in plane members focusing on the interaction of multiple cracks. In the proposed method, the crack competition criterion is based on the minimum total energy principle, which can ensure that the nucleation and development of cracks can achieve a maximum energy dissipation per unit length. The effectiveness and robustness of the presented method are verified by comparing the numerical results with experimental and/or other numerical simulations. The result shows that the proposed competition criterion can accurately judge the sequence of new-crack nucleation and existing-crack propagation.

Extended finite element analysis for the 2nd and 3rd metatarsals stress fracture during push-off

Metatarsal stress fractures (MSF), particularly the 2nd and 3rd MSF, are common injuries among athletes. Although there are several practices to reduce foot and ankle injuries, there is no injury prevention program specifically designed to minimize MSF. This is mainly due to the lack of information about the loadings/postures that cause MSF. Therefore, this study aimed to investigate dangerous loadings/postures potentially causing MSF during push-off (PO). The analysis was conducted with Finite Element Modelling (FEM), calibrated with the three-point bending test, and validated with peak plantar pressure (PPP) and fracture force measurement. Extended Finite Element Method was used for MSF simulation such that ten different foot and ankle configurations were designed, with five for each of the 2nd and 3rd MSF under pure vertical loadings. A more complex loading, ankle eversion/inversion during PO, was also examined for the MSF. The average error percentage for the calibration of the model with the three-point bending test was 3.05%. The average error percentages for the validation of the model with PPP and fracture force measurements were 18% and 30%, respectively. The outcomes of pure vertical loadings indicated the higher potential for the 2nd and 3rd MSF at 30% PO and 70% PO, respectively. The results of ankle eversion/inversion loadings represented that the most dangerous posture for MSF was 30° ankle eversion for the 3rd metatarsal at 70% PO. These results provide a guide, including what postures to avoid for the 2nd and 3rd MSF among people who are at high risk of MSF.