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There is not a unified modelling approach to finite element failure analysis of concrete dams. Different behaviours of a dam predicted by different fracture methods with various material constitutive models may significantly influence on the dam safety evaluation. The purpose of this paper is to present a general comparative investigation to examine whether the nonlinear responses of concrete dams obtained from different fracture modelling approaches are comparable in terms of crack propagation and failure modes.

Three fracture modelling approaches, including the extended finite element method with a cohesive law (XFEM-COH), the crack band finite element method with a plastic-damage relation (FEPD), and the Drucker-Prager (DP) elasto-plastic model, are chosen to analyse damage and cracking behaviour of concrete gravity dams under overloading conditions. The failure process and loading capacity of a dam are compared.

The numerical results indicate that the three approaches are all applicable to predict loading capacity and safety factors of gravity dams. However, both XFEM-COH and FEPD give more reasonable crack propagation and failure modes in comparison with DP. Therefore, when cracking patterns are the major concern for safety evaluation of concrete dams, it is recommended that XFEM-COH and FEPD rather than DP be used.

The comparison of cracking behaviours of concrete dams obtained from different fracture modelling approaches is conducted. The applicability of the modelling approaches for failure analysis of concrete dams is discussed, and from the results presented in this work, it is significant to consider the suitability of the selected fracture modelling approach for dam safety evaluation.

The purpose of this paper is to evaluate the capabilities of the generalized finite element method (GFEM) under the context of the geometrically nonlinear analysis. The effect of large displacements and deformations, typical of such analysis, induces a significant distortion of the element mesh, penalizing the quality of the standard finite element method approximation. The main concern here is to identify how the enrichment strategy from GFEM, that usually makes this method less susceptible to the mesh distortion, may be used under the total and updated Lagrangian formulations.

An existing computational environment that allows linear and nonlinear analysis, has been used to implement the analysis with geometric nonlinearity by GFEM, using different polynomial enrichments.

The geometrically nonlinear analysis using total and updated Lagrangian formulations are considered in GFEM. Classical problems are numerically simulated and the accuracy and robustness of the GFEM are highlighted.

This study shows a novel study about GFEM analysis using a complete polynomial space to enrich the approximation of the geometrically nonlinear analysis adopting the total and updated Lagrangian formulations. This strategy guarantees the good precision of the analysis for higher level of mesh distortion in the case of the total Lagrangian formulation. On the other hand, in the updated Lagrangian approach, the need of updating the degrees of freedom during the incremental and iterative solution are for the first time identified and discussed here.

It has been usual to prefer an enrichment pattern independent of the mesh when applying singular functions in the Generalized/eXtended finite element method (G/XFEM). This choice, when modeling crack tip singularities through extrinsic enrichment, has been understood as the only way to surpass the typical poor convergence rate obtained with the finite element method (FEM), on uniform or quasi-uniform meshes conforming to the crack. Then, the purpose of this study is to revisit the topological enrichment strategy in the light of a higher-order continuity obtained with a smooth partition of unity (PoU). Aiming to verify the smoothness' impacts on the blending phenomenon, a series of numerical experiments is conceived to compare the two GFEM versions: the conventional one, based on piecewise continuous PoU's, and another which considers PoU's with high-regularity.

The stress approximations right at the crack tip vicinity are qualified by focusing on crack severity parameters. For this purpose, the material forces method originated from the configurational mechanics is employed. Some attempts to improve solution using different polynomial enrichment schemes, besides the singular one, are discussed aiming to verify the transition/blending effects. A classical two-dimensional problem of the linear elastic fracture mechanics (LEFM) is solved, considering the pure mode I and the mixed-mode loadings.

The results reveal that, in the presence of smooth PoU's, the topological enrichment can still be considered as a suitable strategy for extrinsic enrichment. First, because such an enrichment pattern still can treat the crack independently of the mesh and deliver some advantage in terms of convergence rates, under certain conditions, when compared to the conventional FEM. Second, because the topological pattern demands fewer degrees of freedom and impacts conditioning less than the geometrical strategy.

Several outputs are presented, considering estimations for the J–integral and the angle of probable crack advance, this last computed from two different strategies to monitoring blending/transition effects, besides some comments about conditioning. Both h- and p-behaviors are displayed to allow a discussion from different points of view concerning the topological enrichment in smooth GFEM.

Hydrofracturing technology has been widely used in tight oil and gas reservoir exploitation, and the fracture network formed by fracturing is crucial to determining the resources recovery rate. Due to the complexity of fracture network induced by the random morphology and type of fluid-driven fractures, controlling and optimising its mechanisms is challenging. This paper aims to study the types of multiscale mode I/II fractures, the fluid-driven propagation of multiscale tensile and shear fractures need to be studied.

A dual bilinear cohesive zone model (CZM) based on energy evolution was introduced to detect the initiation and propagation of fluid-driven tensile and shear fractures. The model overcomes the limitations of classical linear fracture mechanics, such as the stress singularity at the fracture tip, and considers the important role of fracture surface behaviour in the shear activation. The bilinear cohesive criterion based on the energy evolution criterion can reflect the formation mechanism of complex fracture networks objectively and accurately. Considering the hydro-mechanical (HM) coupling and leak-off effects, the combined finite element-discrete element-finite volume approach was introduced and implemented successfully, and the results showed that the models considering HM coupling and leak-off effects could form a more complex fracture network. The multiscale (laboratory- and engineering-scale) Mode I/II fractures can be simulated in hydrofracturing process.

Based on the proposed method, the accuracy and applicability of the algorithm were verified by comparing the analytical solution of KGD and PKN models. The effects of different in situ stresses and flow rates on the dynamic propagation of hydraulic fractures at laboratory and engineering scales were investigated. when the ratio of in situ stress is small, the fracture propagation direction is not affected, and the fracture morphology is a cross-type fracture. When the ratio of in situ stress is relatively large, the propagation direction of the fracture is affected by the maximum in situ stress, and it is more inclined to propagate along the direction of the maximum in situ stress, forming double wing-type fractures. Hydrofracturing tensile and shear fractures were identified, and the distribution and number of each type were obtained. There are fewer hydraulic shear fractures than tensile fractures, and shear fractures appear in the initial stage of fracture propagation and then propagate and distribute around the perforation.

The proposed dual bilinear CZM is effective for simulating the types of Mode I/II fractures and seizing the fluid-driven propagation of multiscale tensile and shear fractures. Practical fracturing process involves the multi-type and multiscale fluid-driven fracture propagation. This study introduces general fluid-driven fracture propagation, which can be extended to the fracture propagation analysis of potential fluid fracturing, such as other liquids or supercritical gases.

The purpose of this paper is to develop a numerical method to model the simultaneous propagation of multiple hydraulic fractures (HFs) with fluid lags driven from a horizontal wellbore.

Fracture propagation in solid medium is modeled with the extended finite element method and fluid flow is modeled with finite volume method. Three iteration loops are introduced to solve the nonlinear system within each time increment, i.e. a Newtonian iteration to solve the solid-fluid coupling system, a Picard iteration to determine fluid front positions and a secant iteration to update fracture lengths.

The propagation of one single HF with a fluid lag is simulated and agrees well with semi-analytical solutions or other numerical results in the literature. The simultaneous propagation of two HFs are then investigated, which demonstrates the ability of the proposed method in capturing the hydraulic fracturing process with multiple fractures and fluid lags.

With the proposed method, one can simulate the simultaneous propagation of multiple HFs with fluid lags, which play a significant role during early-time propagation or when the confinement stress is relatively low (shallow HFs). Solid deformation and fracturing, fluid flow in fractures and in the wellbore are fully coupled, and three iteration loops are introduced to solve the nonlinear system.

The purpose of this paper is to propose a computational model for thin layers, for problems of linear time-dependent heat conduction. The thin layer is replaced by a zero-thickness interface. The advantage of the new model is that it saves the need to construct and use a fine mesh inside the layer and in regions adjacent to it, and thus leads to a reduction in the computational effort associated with implicit or explicit finite element schemes.

Special asymptotic models have been proposed for linear heat transfer and linear elasticity, to handle thin layers. In these models the thin layer is replaced by an interface with zero thickness, and specific jump conditions are imposed on this interface in order to represent the special effect of the layer. One such asymptotic interface model is the first-order Bövik-Benveniste model. In a paper by Sussmann et al., this model was incorporated in a FE formulation for linear steady-state heat conduction problems, and was shown to yield an accurate and efficient computational scheme. Here, this work is extended to the time-dependent case.

As shown here, and demonstrated by numerical examples, the new model offers a cost-effective way of handling thin layers in linear time-dependent heat conduction problems. The hybrid asymptotic-FE scheme can be used with either implicit or explicit time stepping. Since the formulation can easily be symmetrized by one of several techniques, the lack of self-adjointness of the original formulation does not hinder an accurate and efficient solution.

Most of the literature on asymptotic models for thin layers, replacing the layer by an interface, is analytic in nature. The proposed model is presented in a computational context, fitting naturally into a finite element framework, with both implicit and explicit time stepping, while saving the need for expensive mesh construction inside the layer and in its vicinity.

The purpose of this paper is to propose a new scheme for obtaining acceptable solutions for problems of continuum topology optimization of structures, regarding the distribution and limitation of discretization errors by considering h-adaptivity.

The new scheme encompasses, simultaneously, the solution of the optimization problem considering a solid isotropic microstructure with penalization (SIMP) and the application of the h-adaptive finite element method. An analysis of discretization errors is carried out using an a posteriori error estimator based on both the recovery and the abrupt variation of material properties. The estimate of new element sizes is computed by a new h-adaptive technique named “Isotropic Error Density Recovery”, which is based on the construction of the strain energy error density function together with the analytical solution of an optimization problem at the element level.

Two-dimensional numerical examples, regarding minimization of the structure compliance and constraint over the material volume, demonstrate the capacity of the methodology in controlling and equidistributing discretization errors, as well as obtaining a great definition of the void–material interface, thanks to the h-adaptivity, when compared with results obtained by other methods based on microstructure.

This paper presents a new technique to design a mesh made with isotropic triangular finite elements. Furthermore, this technique is applied to continuum topology optimization problems using a new iterative scheme to obtain solutions with controlled discretization errors, measured in terms of the energy norm, and a great resolution of the material boundary. Regarding the computational cost in terms of degrees of freedom, the present scheme provides approximations with considerable less error if compared to the optimization process on fixed meshes.

This paper aims to study acoustic emission (AE) propagation characteristics by a crack under a moving heat source, which mainly provides theoretical basis and method for the actual crack detection during welding process.

The paper studied the AE characteristics in welding using thermoelastic theory, which investigates the dynamical displacement field caused by a crack and the welding heating effect. In the calculation model, the crack initiation and extension are represented by moment tensor as the AE source, and the welding heat source is the Gauss heat flux distribution. The extended finite element method (XFEM) is implemented to calculate and solve the AE response of a thermoelastic plate with a crack during the welding heating effect. The wavelet transform is applied to the time–frequency analysis of the AE signals.

The paper provides insights about the changing rule of the acoustic radiation patterns influenced by the heating effect of the moving heat source and the AE signal characteristics in thermoelastic plate by different crack lengths and depths. It reveals that the time–frequency characteristics of the AE signals from the simulation are in good agreement with the theoretical ones. The energy ratio of the antisymmetric mode A0 to symmetric mode S0 is a valuable quantitative inductor to estimate the crack depth with a certain regularity.

This paper mainly discusses the application of XFEM to calculate and analyze thermoelastic problems, and has presented few cases based on a specified configuration. Further work will focus on the calculation and analysis under different plate configurations and conditions, which is to obtain more interesting and general conclusions for guiding practice.

The paper is a successful application of XFEM to solve the problem of AE response of a crack in the dynamic welding inhomogeneous heating effect. The paper provides an effective way to obtain the AE signal characteristics in monitoring the welding crack.

The purpose of this paper is to develop an effective numerical algorithm for a gas-melt two-phase flow and use it to simulate a polymer melt filling process. Moreover, the suggested algorithm can deal with the moving interface and discontinuities of unknowns across the interface.

The algebraic sub-grid scales-variational multi-scale (ASGS-VMS) finite element method is used to solve the polymer melt filling process. Meanwhile, the time is discretized using the Crank–Nicolson-based split fractional step algorithm to reduce the computational time. The improved level set method is used to capture the melt front interface, and the related equations are discretized by the second-order Taylor–Galerkin scheme in space and the third-order total variation diminishing Runge–Kutta scheme in time.

The numerical method is validated by the benchmark problem. Moreover, the viscoelastic polymer melt filling process is investigated in a rectangular cavity. The front interface, pressure field and flow-induced stresses of polymer melt during the filling process are predicted. Overall, this paper presents a VMS method for polymer injection molding. The present numerical method is extremely suitable for two free surface problems.

For the first time ever, the ASGS-VMS finite element method is performed for the two-phase flow of polymer melt filling process, and an effective numerical method is designed to catch the moving surface.

The interaction between hydraulic fracture (HF) and natural fracture (NF) in naturally fractured rocks is critical for hydraulic fracturing. This paper aims to focus on investigating the development of tensile and shear debonding zone on the NF caused by the stresses produced by HF, and the influence of NF’s debonding behavior on the interaction between HF and NF.

Theoretically, tensile and shear debonding modes of NF are considered, two dimensionless parameters are proposed to characterize the difficulty of tensile and shear failure of NF, respectively. Numerically, a finite element model combining the extended finite element method and cohesive zone method (CZM) is proposed to study NF’s debonding behavior and its influence on the interaction between HF and NF.

Both theoretical analysis and numerical simulation show the existence of two debonding modes. The numerical results also show that the HF can cross, offset or propagate along the NFs depending on the parameters’ value, resulting in different fracture network and stimulated reservoir volume. When they are large, the NF’s debonding area is small, HF tends to cross the NF and the fracture network is simple; when they are small, the NF’s debonding area is large, HF will propagate along the NF. In addition, HF is easier to propagate along with NF under tensile debonding mode while it is easier to pass through NF under shear debonding mode.

The theoretical and numerical considerations are taken into account in the influence of the debonding of NFs on the interaction between HFs and NFs and the influence on the formation of the fracture network.