A comparison of stress intensity factors through crack closure integral and other approaches using eXtended element-free Galerkin method

In this paper, a new approach for extracting stress intensity factors (SIFs) by the extended element-free Galerkin method, through a crack closure integral (CCI) scheme, is proposed. The CCI calculation is used in conjunction with a local smoothing technique to improve the accuracy of the computed SIFs in a number of case studies of linear elastic fracture mechanics. The cases involve problems of mixed-mode, curved crack and thermo-mechanical loading. The SIFs by CCI, displacement and stress methods are compared with those based on the M-integral technique reported in the literature. The proposed CCI method involves very simple relations, and still gives good accuracy. The convergence of the results is also examined.

Element-Free Galerkin modelling of composite damage

Delamination and matrix cracking are routine damage mechanisms, observed by post-mortem analysis of laminated structures containing geometrical features such as notches or bolts. Current finite element tools cannot explicitly model an intralaminar matrix microcrack, except if the location of the damage is specified a priori. In this work, a meshless technique, the Element-Free Galerkin (EFG) method, is utilized for the first time to simulate delamination (interlaminar) and intralaminar matrix microcracking in composite laminates.

Element-Free Galerkin Modelling of Crack Migration in Composite Laminates

The development of a virtual testing environment, as a cost-effective industrial design tool in the design and analysis of composite structures, requires the need to create models efficiently, as well as accelerate the analysis by reducing the number of degrees of freedom, while still satisfying the need for accurately tracking the evolution of a debond, delamination or crack front. The eventual aim is to simulate both damage initiation and propagation in components with realistic geometrical features, where crack propagation paths are not trivial. Meshless approaches, and the Element-Free Galerkin (EFG) method, are particularly suitable for problems involving changes in topology and have been successfully applied to simulate damage in homogeneous materials and concrete. In this work, the method is utilized to model initiation and mixed-mode propagation of cracks in composite laminates, and to simulate experimentally-observed crack migration which is difficult to model using standard finite element analysis. N

Computation of stress intensity factors in functionally graded materials using partition-of-unity meshfee method

This paper describes the computation of stress intensity factors (SIFs) for cracks in functionally graded materials (FGMs) using an extended element-free Galerkin (XEFG) method. The SIFs are extracted through the crack closure integral (CCI) with a local smoothing technique, non-equilibrium and incompatibility formulations of the interaction integral and the displacement method. The results for mode I and mixed mode case studies are presented and compared with those available in the literature. They are found to be in good agreement where the average absolute error for the CCI with local smoothing, despite its simplicity, yielded a high level of accuracy.

Crack propagation in non-homogenous materials: Evaluation of mixed-mode SIFs, T-stress and kinking angle using a variant EFG method

A new variant of the Element-Free Galerkin (EFG) method, that combines the diffraction method, to characterize the crack tip solution, and the Heaviside enrichment function for representing discontinuity due to a crack, has been used to model crack propagation through non-homogenous materials. In the case of interface crack propagation, the kink angle is predicted by applying the maximum tangential principal stress (MTPS) criterion in conjunction with consideration of the energy release rate (ERR). The MTPS criterion is applied to the crack tip stress field described by both the stress intensity factor (SIF) and the T-stress, which are extracted using the interaction integral method. The proposed EFG method has been developed and applied for 2D case studies involving a crack in an orthotropic material, crack along an interface and a crack terminating at a bi-material interface, under mechanical or thermal loading; this is done to demonstrate the advantages and efficiency of the proposed methodology. The computed SIFs, T-stress and the predicted interface crack kink angles are compared with existing results in the literature and are found to be in good agreement. An example of crack growth through a particle-reinforced composite materials, which may involve crack meandering around the particle, is reported.

Modified crack closure integral technique for extraction of SIFs in meshfee methods

A new approach for extracting stress intensity factors (SIFs) by the element-free Galerkin (EFG) class of methods through a modified crack closure integral (MCCI) scheme is proposed. Its primary feature is that it allows accurate calculation of mode I and mode II SIFs with a relatively simple and straightforward analysis even when a coarser nodal density is employed. The details of the adoption of the MCCI technique in the EFG method are described. Its performance is demonstrated through a number of case studies including mixed-mode and thermal problems in linear elastic fracture mechanics (LEFM). The results are compared with published theoretical solutions and those based on the displacement method, stress method, crack closure integral in conjunction with local smoothing (CCI–LS) technique, as well as the M-integral method. Its advantages are discussed.

Micromechanical Modelling of Non-Homogenous Materials by Meshless Methods

A detailed study of bi-material composites, using meshless methods (MMs), is presented in this paper. Firstly, representative volume elements (RVEs) for different bi-material combinations are analysed by the element-free Galerkin (EFG) method in order to confirm the effective properties of heterogeneous material through homogenization. The results are shown to be in good agreement with experimental results and those obtained using the finite element method (FEM) which required a higher node density. Secondly, a functionally graded material (FGM), with a crack, is analysed using the EFG method. This investigation was motivated by the possibility of replacing the distinct fibrematrix interface with a FGM interface. Finally, an illustrative example showing crack propagation, in a two-dimension micro-scale model of a SiC/Al composite is presented. 

Full-Wave Analysis of Layered Aperture Arrays

The new rigorous numerical-analytical technique based upon Galerkin method with the entire domain basis functions has been developed and applied to the study of the periodic aperture arrays containing multiple dissimilar apertures of complex shapes in stratified medium. The rapid uniform convergence of the solutions has enabled a comprehensive parametric study of complex array arrangements. The developed theory has revealed new effects of the aperture shape and layout on the array performance. The physical mechanisms underlying the TM wave resonances and Luebbers' anomaly have been explained for the first time.

Calculation of loss in conductors of a superconducting shielded slotted line and a coplanar waveguide

Finite conductivity in superconductors is taken into account by approximate boundary conditions imposed directly when deriving pair summatory equations, which are solved using the Galerkin method and the basis describing the edge singularity.

Synthesis of visible-light-activated yellow amorphous TiO2 photocatalyst

Visible-light-activated yellow amorphous TiO₂ (yam- TiO ₂) was synthesised by a simple and organic-free precipitation method. TiN, an alternative precursor for TiO₂ preparation, was dissolved in hydrogen peroxide under acidic condition (pH∼1) adjusted by nitric acid. The yellow precipitate was obtained after adjusting pH of the resultant red brown solution to 2 with NH₄OH. The BET surface area of this sample was 261 m²/g. The visible light photoactivity was evaluated on the basis of the photobleaching of methylene blue (MB) in an aqueous solution by using a 250 W metal halide bulb equipped with UV cutoff filter (λ>420 nm) under aerobic conditions. Yam- TiO₂ exhibits an interesting property of being both surface adsorbent and photoactive under visible light. It was assigned to the η²-peroxide, an active intermediate form of the addition of H₂O₂ into crystallined TiO₂ photocatalyst. It can be concluded that an active intermediate form of titanium peroxo species in photocatalytic process can be synthesised and used as a visible-light-driven photocatalyst

Stiffness analysis of polymeric composites using the finite element method

The ability to predict the mechanical behavior of polymer composites is crucial for their design and manufacture. Extensive studies based on both macro- and micromechanical analyses are used to develop new insights into the behavior of composites. In this respect, finite element modeling has proved to be a particularly powerful tool. In this article, we present a Galerkin scheme in conjunction with the penalty method for elasticity analyses of different types of polymer composites. In this scheme, the application of Green's theorem to the model equation results in the appearance of interfacial flux terms along the boundary between the filler and polymer matrix. It is shown that for some types of composites these terms significantly affect the stress transfer between polymer and fillers. Thus, inclusion of these terms in the working equations of the scheme preserves the accuracy of the model predictions. The model is used to predict the most important bulk property of different types of composites. Composites filled with rigid or soft particles, and composites reinforced with short or continuous fibers are investigated. For each case, the results are compared with the available experimental results and data obtained from other models reported in the literature. Effects of assumptions made in the development of the model and the selection of the prescribed boundary conditions are discussed.