The advances in the Extended Finite Element Method enable the prediction of crack initiation and propagation without prior knowledge about the crack pattern. In this regard, the purpose of this study was to investigate human femoral fracture location using voxel-based Finite Element simulation. The simulation was developed in terms of an anisotropic failure mechanism coupled to the Extended Finite Element Method to describe the femoral progressive fracture pattern in specimen-specific models. An anisotropic failure mechanism (4 damage criteria) was developed based on the combination of Hashin failure criteria and maximum principal stress criterion to capture femur fracture behavior dependency on femur anisotropy and heterogeneity. Three specimen-specific femur FE models were constructed based on CT-scan images under a particular loading condition. The load was applied to the head of the femur at an angle of -15 degrees relative to the sagittal and coronal planes. To demonstrate the potential of the current approach, a one-to-one comparison of predicted Extended Finite Element Method fracture pattern and experimental results were performed. An acceptable agreement was obtained between the predicted and observed fracture patterns suggesting that the proposed failure mechanism in the Extended Finite Element Method is capable to simulate femoral fracture type and progressive crack propagation. The presented results indicated that the crack on-set location and subsequent crack trajectories can be correctly captured using the proposed anisotropic failure mechanism in the Extended Finite Element Method.

In this paper, the behavior of a stationary crack in a generalized diffusion-thermoelasticity medium under temperature and concentration shock has been investigated. Cracks have been modeled using the Extended Finite Element Method and stress intensity factors have been obtained using the interaction integral Method. To study the phenomenon of heat dissipation and concentration, generalized Green-Naghdi and non-Fickian theories have been used. The Extended Finite Element Method has been developed to discrete equations in space and the Newmark implicit Method has been used to calculate time integrals. For different loads (heat shock and concentration), stress intensity factors and temperature and concentration distribution at the crack tip have been studied. The effect of stress wave velocity, concentration wave and temperature wave on stress intensity factors for straight and oblique cracks has also been investigated. It is observed that for the case where the speed of the stress wave, and the temperature wave are the same and greater than the speed of the concentration wave, the increase of the stress intensity factors is faster and higher in other states.

The Extended Finite Element Method (X-FEM) is a numerical Method for modeling discontinuties, such as cracks, within the standard Finite Element framework. In X-FEM, special functions are added to the Finite Element approximation. For crack modeling in linear elasticity, appropriate functions are used for modeling discontinuties along the crack length and simulating the singularity in the crack tip Element. As a result, the degrees of freedom (D.O.F.) for the nodes arround the crack tip and the crack length are increased, the so-called node-enrichment scheme. This virtual crack modeling, which is mesh independent, avoids the usage of refined mesh and singular Elements arround the crack tip, and does not require remeshing during crack growth simulation. In this paper the principles of the X-FEM are described. A new Method, based on the local orthogonal coordinate system, is proposed for the node-enrichment scheme. The development of a special-purpose computer code for modeling 2D cracks using the X-FEM and the new Method is presented. The code and the new Method are verified through the analyses of different standard cracked geometries.

The Finite Element Method (FEM), and other numerical Methods, in recent years, is widely used in modeling of the fracture problem. Remeshing requirements and mesh sensitivity are the major disadvantages in analyzing crack growth using conventional FEM Methods. Recently, advanced FEM Methods, such as the Extended Finite Element Method (X-FEM), have been proposed to model discontinuities through the Elements. The advantage of these Methods is that remeshing is not required in the crack growth process. The cohesive crack Method is a simplified field model to simulate the complicated behavior of the crack growth in quasi-brittle materials. In this paper, we use the advantages of the X-FEM and crack length control Method for modeling of the cohesive crack growth.

one of the simplest numerical integration Method which provides a large saving in computational efforts, is the well known one-point Gauss quadrature which is widely used for 4 nodes quadrilateral Elements. On the other hand, the biggest disadvantage to one-point integration is the need to control the zero energy modes, called hourglassing modes, which arise. The efficiency of four different anti-hourglassing approaches, Flanagan (elastic approach), Dyna3d, Hansbo and Liu have been investigated. The first two approaches have been used in 2 and 3-D explicit codes and the latter have been employed in 2-D implicit codes. For 2-D explicit codes, the computational time was reduced by 55% and 60% for elastic and Dyna3d, respectively. However, for 3-D codes the reduction was dependent on the number of Elements and was obtained between 50% and 70%. Also, the error due to the application of elastic Methods was less than that for Dyna3d when the results were compared with those obtained from 2-points Gauss quadrature. Nevertheless, the convergence occurred more rapidly and the oscillations were damped out more quickly for Dyna3d approach. For implicit codes, the anti-hourglassing Methods had no effect on the computations and therefore a 2-points Gauss quadrature is recommended for implicit codes as it provide the results more accurately

In this study, the Extended Finite Element Method was used for modeling dynamic fracture in Kirchhoff plate and shell problems. A new set of tip functions was extracted from analytical solutions of Kirchhoff plates. The semi-discrete Method was used to simulate the dynamic behavior. An unconditionally stable implicit Newmark scheme was used for temporal discretization. The performance of the code in simulation of dynamic behaviors was proved by solving several benchmark problems and comparing the obtained results with other numerical and analytical solutions. Also, the problem of cracked thin tubes under gaseous detonation loading was simulated by the dynamic XFEM code. The results were compared with analytical and other numerical solutions and the obtained results showed that the Method has good capability for simulation of these problems.

Challenging and complex nature of the numerical analysis of crack problems have attracted the interest of many researchers in past decades and several techniques have been proposed for these problems. One of these techniques is the Extended Finite Element Method in which the crack tip field modeling is improved by enrichment of shape functions and the crack can intersect the Elements. On the other hand, we have adaptive Finite Element Method which aims to improve the accuracy of displacement and stress fields near the crack tip by remeshing process. Researchers have reported the drawbacks of each of these two techniques. In this paper the drawbacks of the previous techniques are covered with proper combination of these two techniques. By this combination the crack can pass through the Elements and there is no need for crack tracking by mesh. In addition the estimated error is limited to desirable bands and stress intensity factor can be computed numerically with acceptable accuracy.

Ensuring seismic resilience in earthquake-prone regions is imperative for structural safety. Fiber-Reinforced Concrete (FRC) columns hold promise for enhancing structural performance under seismic conditions. This study seeks to comprehensively evaluate their seismic behavior. The primary objective of this research is to assess and compare the seismic performance of various FRC column types, including polypropylene fibers (PFRC), steel fibers (SFRC), and hybrid combinations (HyFRC), in contrast to conventional reinforced concrete (RC) columns. To achieve this, the study employs Extended Finite Element Method combined with Concrete Damage Plasticity (XFEM-CDP) in Abaqus to scrutinize static and dynamic responses. The nonlinear static pushover analysis unveiled a notable improvement in seismic resistance across all FRC types when compared to RC columns. Incremental dynamic analyses (IDA) are conducted using the selected suite of 10 near fault as-recorded ground motions to evaluate the inelastic seismic responses of different FRC bridge columns. XFEM-CDP simulations in Abaqus captured multiple aspects of FRC columns, such as concrete cracking, loss of stiffness and plastic behavior. Seismic fragility analysis of these FRC columns is conducted considering four damage states: a) longitudinal steel yielding, b) core concrete crushing, c) steel bar buckling, and d) longitudinal steel bar fracture. The results indicated that HyFRC columns exhibit the lowest damage vulnerability compared to PFRC and SFRC variants.