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The purpose of this paper is to propose the interaction integral method combing with a XFEM-based local mesh replacement method to evaluate both the stress intensity factors (SIFs) and T-stress at the crack tip near a circular inclusion.

Special attention is pay to the effect of T-stress on crack initiation angle in 2D composite medium. The generalized maximum tangential stress criterion is employed during the simulation which simultaneously involves the effects of the mixed-mode SIFs, the T-stress and a physical length scale r_c (the size of the fracture process zone).

It is shown that T-stress could affect the crack initiation angle significantly for mixed-mode conditions. Varies types of material mismatch are also considered and their influences on T-stress are given quantitatively.

The proposed numerical method allows a considerable flexibility for such problems and provides a basic framework for quasi-static crack growth in materials containing complex interfaces.

The purpose of this paper is to introduce a numerical investigation used to calculate the J-integral of the main crack behavior emanating from a semicircular notch and double semicircular notch and its interaction with another crack which may occur in various positions in (TiB/Ti) functionally graded material (FGM) plate subjected to tensile mechanical load.

For this purpose the variations of the material properties are applied at the integration points and at the nodes by implementing a subroutine USDFLD in the ABAQUS software. The variation of the J-integral according to the position, the length and the angle of rotation of cracks is demonstrated. The variation of the J-integral according to the position, the length and the angle of rotation of cracks is examined; also the effect of different parameters for double notch FGM plate is investigated as well as the effect of band of FGM within the ceramic plate to reduce J-integral.

According to the numerical analysis, all parameters above played an important role in determining the J-integral.

The present study consists in investigating the simulation used to calculate the J-integral of the main crack behavior emanating from a semicircular notch and double semicircular notch and its interaction with another crack which may occur in various positions in (TiB/Ti) FGM plate under Mode I. The J-integral is determined for various load applied. The cracked plate is joined by bonding an FGM layer to TiB plate on its double side. The determination of the gain on J-integral by using FGM layer is highlighted. The calculation of J-integral of FGM’s involves the direction of the radius of the notch in order to reduce the J-integral.

The purpose of this paper is to analyze the repair of a straight and angular crack in the structure using a piezoelectric material under thermo-mechanical loading by the extended finite element method (XFEM) approach. This provides a general and simple solution for the modeling of crack in the structure to analyze the repair.

The extended finite element method is used to model crack geometry. The crack surface is modeled by Heaviside enrichment function while the crack front is modeled by branch enrichment functions.

The effectiveness of the repair is measured in terms of stress intensity factor and J-integral. The critical voltage at which patch repair is most effective is evaluated and presented. Optimal patch shape, location of patch, adhesive thickness and adhesive modulus are obtained for effective repair under thermo-mechanical loading environment.

The presented numerical modeling and simulation by the XFEM approach are of great benefit to analyze crack repair in two-dimensional and three-dimensional structures using piezoelectric patch material under thermo-mechanical loading.

The purpose of this paper is to evaluate some numerical integration strategies used in generalized (G)/extended finite element method (XFEM) to solve linear elastic fracture mechanics problems. A range of parameters are here analyzed, evidencing how the numerical integration error and the computational efficiency are improved when particularities from these examples are properly considered.

Numerical integration strategies were implemented in an existing computational environment that provides a finite element method and G/XFEM tools. The main parameters of the analysis are considered and the performance using such strategies is compared with standard integration results.

Known numerical integration strategies suitable for fracture mechanics analysis are studied and implemented. Results from different crack configurations are presented and discussed, highlighting the necessity of alternative integration techniques for problems with singularities and/or discontinuities.

This study presents a variety of fracture mechanics examples solved by G/XFEM in which the use of standard numerical integration with Gauss quadratures results in loss of precision. It is discussed the behaviour of subdivision of elements and mapping of integration points strategies for a range of meshes and cracks geometries, also featuring distorted elements and how they affect strain energy and stress intensity factors evaluation for both strategies.

In former work, test results of cracks in aluminium panels under cyclic shear buckling showed that cracks in the tensile stress field of a buckle propagate. The main influencing factor for the crack growth rate is the maximum principle stress. A simplified approach for crack propagation analyses based on this finding showed limitations for application on larger cracks because it disregarded the increasing out-of-plane deformation for larger cracks as well as stress redistributions. The purpose of this paper is to improve the results of the simplified approach with the help of finite element method (FEM).

An approach for crack propagation based on FEM is presented taking into account the mutual interaction of cracks and buckling. The finite element (FE) model, which is described in detail, respects the boundary conditions of the test-set-up. Different initial crack positions, loads and panel thicknesses are analyzed. Results of the stress intensity factors KI calculated by the ABAQUS® FE model provide a function which is used to run a crack propagation analysis based on Forman law.

The results of the FE-based crack propagation solution are in good agreement with test results and improve the prediction of the simplified approach. It is not restricted in terms of panel thickness, crack position or applied shear load.

Limitations of the FE-based crack propagation solution compared to the experimental results are discussed. These are, the sensitivity of crack propagation analyses to initial crack length and deviations of the experimental settings from the ideal FE model.

The interaction of cracks and buckling in aluminium shells is mainly disregarded both in research and industrial work, but can be of interest considering, accidental damages in fuselage side shells. Cracks propagate under shear load as it was shown in former work. The FE modeling of the tests presented in this paper proves the mutual interactions of crack propagation and buckling deformation.

The purpose of this paper is to systematically investigate the fluid lag phenomena and its influence in the hydraulic fracturing process, including all stages of fluid-lag evolution, the transition between different stages and their coupling with dynamic fracture propagation under common conditions.

A plane 2D model is developed to simulate the complex evolution of fluid lag during the propagation of a hydraulic fracture driven by an impressible Newtonian fluid. Based on the finite element method, a fully implicit solution scheme is proposed to solve the strongly coupled rock deformation, fluid flow and fracture propagation. Using the proposed model, comprehensive parametric studies are performed to examine the evolution of fluid lag in various geological and operational conditions.

The numerical simulations predict that the lag ratio is around 5% or even lower at the beginning stage of hydraulic fracture under practical geological conditions. With the fracture propagation, the lag ratio keeps decreasing and can be ignored in the late stage of hydraulic fracturing for typical parameter combinations. On the numerical aspect, whether the fluid lag can be ignored depends not only on the lag ratio but also on the minimum mesh size used for fluid flow. In addition, an overall mixed-mode fracture propagation factor is proposed to describe the relationship between diverse parameters and fracture curvature.

In this study, relatively simple physical models such as linear elasticity for solid, Newtonian model for fluid and linear elasticity fracture mechanics for fracture are used. The current model does not account for such effects like leak off, poroelasticity and softening of rock formations, which may also visibly affect the fluid lag depending on specific reservoir conditions.

This study helps to understand the effect of fluid lag during hydraulic fracturing processes and provides numerical experience in dealing with the fluid lag with finite element simulation.

Thermal fractures initiated under cooling at the surfaces of a 2-D or 3-D structure propagate, arrest and coalesce, leading to its structural failure and material-property changes, while the same processes can happen in the rock mass between parallel hydraulic fractures filled with cold fluid, leading to enhanced fracture connectivity and permeability.

This study used a 2-D plane strain fracture model for mixed-mode thermal fractures from two parallel cooling surfaces. Fracture propagation was governed by the theory of linear elastic fracture mechanics, while the displacement and temperature fields were discretized using the adaptive finite element method. This model was validated using two numerical benchmarks with strong fracture curvature and then used to simulate the propagation and coalescence of thermal fractures in a long rock mass.

Modeling results show two regimes: (1) thermal fractures from a cooling surface propagate and arrest by following the theoretical solutions of half-plane fractures before the unfractured portion decreases to 20% rock-mass width and (2) some pairs of fractures from the opposite cooling surfaces tend to eventually coalesce. The fracture coalescence time is in a power law with rock-mass width.

These findings are relevant to both subsurface engineering and material engineering: structure failure is a key concern in the latter, while fracture coalescence can enhance the connectivity of thermal and hydraulic fractures and thus reservoir permeability in the former.

A new hybrid method based on three‐dimensional finite element idealization in the near field and a semi‐analytic scheme using the principles of wave propagation in multilayered half space in the far field is proposed for the dynamic soil‐structure interaction analysis. The distinguishing feature of this technique from direct or indirect boundary integral techniques is that in boundary integral techniques a distribution of sources are considered at the near field boundary. Strengths of these sources are then adjusted to satisfy the continuity conditions across the near‐field/far‐field interface. In the proposed method unknown sources are placed not at the near field boundary but at the location of the structure. Then the Saint‐Venant's principle is utilized to justify that at a distant point the effect of the structure's vibration can be effectively modelled by an equivalent vibrating point force and vibrating moment at the structure's position. Thus the number of unknowns can be greatly reduced here. For soil‐structure interaction analysis by this method one needs to consider only three unknowns (two force components and one in‐plane moment) for a general two‐dimensional problem and six unknowns (three force components and three moment components) for a general three‐dimensional problem. When a vertically propagating elastic wave strikes a structure which is symmetric about two mutually perpendicular vertical planes the structure can only vibrate vertically for dilatational waves and horizontally for shear waves. Under this situation the number of unknowns is reduced to only one whereas in boundary integral and boundary element techniques the number of unknowns is dependent on the number of nodes at the near field boundary, which is generally much greater than six. Several example problems are solved in this paper using this technique for both flexible and rigid structures in multilayered soil media.

The purpose of this paper is to develop an easy-to-implement and accurate fast boundary element method (BEM) for solving large-scale elastodynamic problems in frequency and time domains.

A newly developed kernel-independent fast multipole method (KIFMM) is applied to accelerating the evaluation of displacements, strains and stresses in frequency domain elastodynamic BEM analysis, in which the far-field interactions are evaluated efficiently utilizing equivalent densities and check potentials. Although there are six boundary integrals with unique kernel functions, by using the elastic theory, the authors managed to accelerate these six boundary integrals by KIFMM with the same kind of equivalent densities and check potentials. The boundary integral equations are discretized by Nyström method with curved quadratic elements. The method is further used to conduct the time-domain analysis by using the frequency-domain approach.

Numerical results show that by the fast BEM, high accuracy can be achieved and the computational complexity is brought down to linear. The performance of the present method is further demonstrated by large-scale simulations with more than two millions of unknowns in the frequency domain and one million of unknowns in the time domain. Besides, the method is applied to the topological derivatives for solving elastodynamic inverse problems.

An efficient KIFMM is implemented in the acceleration of the elastodynamic BEM. Combining with the Nyström discretization based on quadratic elements and the frequency-domain approach, an accurate and highly efficient fast BEM is achieved for large-scale elastodynamic frequency domain analysis and time-domain analysis.

The purpose of this paper is to research the interaction between multiple bubbles and their noise radiation considering the influence of compressibility. The influences of bubble spacing, initial inner pressure, buoyance and phase difference are presented with different bubbles arrangements.

Based on wave equation, the new boundary integral equation considering the compressibility is given by the matching between prophase and anaphase approximation of bubble motion and solved with boundary element method. The time-domain characteristics of noise induced by multiple bubbles are obtained by the moving boundary Kirchhoff integral equation. With the surface discretization and coordinate transformation, the bubbles surface is treated as a moving deformable boundary and noise source, and the integral is implemented on the surface directly.

Numerical results show the manner of jet generation will be affected by the phase difference between bubbles. With the increasing of phase difference, the directive property of noise becomes obvious. With the enlargement of initial inner pressure, the sound pressure will arise at the early stage of expanding, and the increasing of buoyance parameter will reduce the sound pressure after the generation of jet. Since the consideration of compressibility, the oscillation amplitude of bubbles will be weakened.

The paper could provide the reference for the research about the dynamics and noise characteristics of multiple bubbles in compressible fluid. And the new method based on boundary integral equation to simulate the multiple bubbles motion and noise radiation is presented.