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.

Time Reversed Electromagnetic Wave Propagation as a Novel Method of Wireless Power Transfer

We investigate the application of time-reversed electromagnetic wave propagation to transmit energy in a wireless power transmission system. “Time reversal” is a signal focusing method that exploits the time reversal invariance of the lossless wave equation to direct signals onto a single point inside a complex scattering environment. In this work, we explore the properties of time reversed microwave pulses in a low-loss ray-chaotic chamber. We measure the spatial profile of the collapsing wavefront around the target antenna, and demonstrate that time reversal can be used to transfer energy to a receiver in motion. We demonstrate how nonlinear elements can be controlled to selectively focus on one target out of a group. Finally, we discuss the design of a rectenna for use in a time reversal system. We explore the implication of these results, and how they may be applied in future technologies.

Coupled reliability and boundary element model for probabilistic fatigue life assessment in mixed mode crack propagation

Fatigue and crack propagation are phenomena affected by high uncertainties, where deterministic methods fail to predict accurately the structural life. The present work aims at coupling reliability analysis with boundary element method. The latter has been recognized as an accurate and efficient numerical technique to deal with mixed mode propagation, which is very interesting for reliability analysis. The coupled procedure allows us to consider uncertainties during the crack growth process. In addition, it computes the probability of fatigue failure for complex structural geometry and loading. Two coupling procedures are considered: direct coupling of reliability and mechanical solvers and indirect coupling by the response surface method. Numerical applications show the performance of the proposed models in lifetime assessment under uncertainties, where the direct method has shown faster convergence than response surface method. (C) 2010 Elsevier Ltd. All rights reserved.

GENERALIZED FINITE ELEMENT METHOD FOR NONLINEAR THREE-DIMENSIONAL ANALYSIS OF SOLIDS

The Generalized Finite Element Method (GFEM) is employed in this paper for the numerical analysis of three-dimensional solids tinder nonlinear behavior. A brief summary of the GFEM as well as a description of the formulation of the hexahedral element based oil the proposed enrichment strategy are initially presented. Next, in order to introduce the nonlinear analysis of solids, two constitutive models are briefly reviewed: Lemaitre`s model, in which damage and plasticity are coupled, and Mazars`s damage model suitable for concrete tinder increased loading. Both models are employed in the framework of a nonlocal approach to ensure solution objectivity. In the numerical analyses carried out, a selective enrichment of approximation at regions of concern in the domain (mainly those with high strain and damage gradients) is exploited. Such a possibility makes the three-dimensional analysis less expensive and practicable since re-meshing resources, characteristic of h-adaptivity, can be minimized. Moreover, a combination of three-dimensional analysis and the selective enrichment presents a valuable good tool for a better description of both damage and plastic strain scatterings.

Multiple random crack propagation using a boundary element formulation

This paper proposes a boundary element method (BEM) model that is used for the analysis of multiple random crack growth by considering linear elastic fracture mechanics problems and structures subjected to fatigue. The formulation presented in this paper is based on the dual boundary element method, in which singular and hyper-singular integral equations are used. This technique avoids singularities of the resulting algebraic system of equations, despite the fact that the collocation points coincide for the two opposite crack faces. In fracture mechanics analyses, the displacement correlation technique is applied to evaluate stress intensity factors. The maximum circumferential stress theory is used to evaluate the propagation angle and the effective stress intensity factor. The fatigue model uses Paris` law to predict structural life. Examples of simple and multi-fractured structures loaded until rupture are considered. These analyses demonstrate the robustness of the proposed model. In addition, the results indicate that this formulation is accurate and can model localisation and coalescence phenomena. (C) 2010 Elsevier Ltd. All rights reserved.

Computational Method to Determine Reflected Ultrasonic Signals From Arbitrary-Geometry Targets

A computational method based on the impulse response and on the discrete representation computational concept is proposed for the determination of the echo responses from arbitrary-geometry targets. It is supposed that each point of the transducer aperture can be considered as a source radiating hemispherical waves to the reflector. The local interaction with each of the hemispherical waves at the reflector surface can be modeled as a plane wave impinging on a planar surface, using the respective reflection coefficient. The method is valid for all field regions and can be performed for any excitation waveform radiated from an arbitrary acoustic aperture. The effects of target geometry, position, and material on both the amplitude and the shape of the echo response are studied. The model is compared with experimental results obtained using broadband transducers together with plane and cylindrical concave rectangular reflectors (aluminum, brass, and acrylic), as well as a circular cavity placed on a plane surface, in a water medium. The method can predict the measured echoes accurately. This paper shows an improved approach of the method, considering the reflection coefficient for all incident hemispherical waves arriving at each point of the target surface.

`Swingle` citrumelo propagation by cuttings for citrus nursery tree production or inarching

`Swingle` citrumelo [Citrus paradisi MacFaden x Poncirus trifoliata (L.) Raf.] has been extensively used as a rootstock in several citrus growing regions of the World, including Southern Brazil where `Rangpur` lime (Citrus limonia Osbeck) is still the predominant variety despite being affected by several important pathogens. in this case, `Swingle` citrumelo is used to produce nursery trees to establish new orchards or to be inarched in adult and healthy groves in order to change the rootstock. We report herein a system to produce trees on `Swingle` citrumelo more rapidly by budding onto non-rooted cuttings, as well as assessing potential to rapidly multiply `Swingle` through rooting of non-budded cuttings. Therefore, two potential products are described: budded trees and rooted rootstock cuttings. `Valencia` sweet orange [Citrus sinensis (L.) Osbeck] was budded at different heights on cuttings derived from eight-month old rootstocks. Grafted and additional non-budded cuttings were then treated with indole-3-butyric acid (500 mg L(-1)) or left untreated before rooting. Three types of cuttings were evaluated: softwood, semi-hardwood and hardwood. The use of nursery trees derived from pre-budded hardwood cuttings of `Swingle` citrumelo is an alternative grafting method on this cultivar. Softwood cuttings with one leaf pair were considered the most adequate material for rapid multiplication of `Swingle` citrumelo by cutting. This could be particularly useful for inarching production or conventional budding after transplant of cutting-derived rootstocks. (C) 2008 Elsevier B.V. All rights reserved.

Chebyshev real wave packet propagation: H+O-2 (J=0) state-to-state reactive scattering calculations

In this paper we explore the relative performance of two recently developed wave packet methodologies for reactive scattering, namely the real wave packet Chebyshev domain propagation of Gray and Balint-Kurti [J. Chem. Phys. 108, 950 (1998)] and the Lanczos subspace wave packet approach of Smith [J. Chem. Phys. 116, 2354 (2002); Chem. Phys. Lett. 336, 149 (2001)]. In the former method, a modified Schrodinger equation is employed to propagate the real part of the wave packet via the well-known Chebyshev iteration. While the time-dependent wave packet from the modified Schrodinger equation is different from that obtained using the standard Schrodinger equation, time-to-energy Fourier transformation yields wave functions which differ only trivially by normalization. In the Lanczos subspace approach the linear system of equations defining the action of the Green operator may be solved via either time-dependent or time-independent methods, both of which are extremely efficient due to the simple tridiagonal structure of the Hamiltonian in the Lanczos representation. The two different wave packet methods are applied to three dimensional reactive scattering of H+O-2 (total J=0). State-to-state reaction probabilities, product state distributions, as well as initial-state-resolved cumulative reaction probabilities are examined. (C) 2002 American Institute of Physics.

Towards the clonal propagation of coconut

Past studies from our laboratory have shown that whole immature, or mature sliced, zygotic embryos are a very good starting explant for coconut somatic embryogenesis. The highest rate of somatic embryogenesis was obtained when certain polyamines were added into the culture medium as well as activated charcoal (AC) to absorb unwanted phenolics. These past studies also showed that the development and maturation of the somatic embryos produced could be improved by the addition of abscisic acid (ABA), alone or with one of several osmotically active agents, into the culture medium. In the present study this well characterised somatic embryogenic system for zygotic tissues is being modified and applied to somatic tissues. This recent approach should be a better method for the rapid production of clonal, true-to-type coconut palms. The present research approach is focused on young leaf section explants which have been found to be very responsive to callus production. Young leaf sections produced optimum callus when cultured on media containing 2,4-D (150 μM) and the amount produced could be increased by soaking the sections in sterile water (15 to 60 minutes) or ascorbic acid (15 to 30 minutes) prior to culturing. Further improvement in callus production, as well as a reduction in the time taken for callogenesis was obtained when casein hydrolysate and/or certain polyamines were added to the callus induction medium. The development of the somatic embryos was improved by using ABA and polyethylene glycol (PEG) in the maturation medium. Despite these initial successes in improving coconut somatic embryogenesis, further studies are now being considered to shorten the time to achieve somatic embryogenesis, to better germinate somatic embryos and to improve the rate of somatic seedling conversion into plantlets.

Predicting cave initiation and propagation

The most widely used method for predicting the onset of continuous caving is Laubscher's caving chart. A detailed examination of this method was undertaken which concluded that it had limitations which may impact on results, particularly when dealing with stronger rock masses that are outside current experience. These limitations relate to inadequate guidelines for adjustment factors to rock mass rating (RMR), concerns about the position on the chart of critical case history data, undocumented changes to the method and an inadequate number of data points to be confident of stability boundaries. A review was undertaken on the application and reliability of a numerical method of assessing cavability. The review highlighted a number of issues, which at this stage, make numerical continuum methods problematic for predicting cavability. This is in particular reference to sensitivity to input parameters that are difficult to determine accurately and mesh dependency. An extended version of the Mathews method for open stope design was developed as an alternative method of predicting the onset of continuous caving. A number of caving case histories were collected and analyzed and a caving boundary delineated statistically on the Mathews stability graph. The definition of the caving boundary was aided by the existence of a large and wide-ranging stability database from non-caving mines. A caving rate model was extrapolated from the extended Mathews stability graph but could only be partially validated due to a lack of reliable data.

Fast, scalable master equation solution algorithms. III. Direct time propagation accelerated by a diffusion approximation preconditioned iterative solver

In this paper we propose a novel fast and linearly scalable method for solving master equations arising in the context of gas-phase reactive systems, based on an existent stiff ordinary differential equation integrator. The required solution of a linear system involving the Jacobian matrix is achieved using the GMRES iteration preconditioned using the diffusion approximation to the master equation. In this way we avoid the cubic scaling of traditional master equation solution methods and maintain the low temperature robustness of numerical integration. The method is tested using a master equation modelling the formation of propargyl from the reaction of singlet methylene with acetylene, proceeding through long lived isomerizing intermediates. (C) 2003 American Institute of Physics.

Simultaneous FT-NIR and ESR analyses to yield propagation rate coefficients for polymerization of methyl methacrylate based monomers

A hyphenated instrumental approach has been used to obtain reliable values for the propagation rate coefficients as a function of conversion for polymerizations of methyl methacrylate (MMA) and a mixture of MMA and ethyleneglycol dimethacrylate (EGDMA) with a 1:1 concentration of double bonds, from near the onset of the Trommsdorf region into the glass region. ESR spectroscopy was used to measure the radical concentration while FT-NIR fibre-optic spectroscopy was employed to measure instantaneously the double-bond concentration within the temperature-controlled cavity of the ESR instrument during polymerization. The advantage of this approach to the measurement of the rate coefficient is that it is equally applicable to branching and linear polymerizations. For the polymerization of methyl methacrylate, the values of the rate coefficient at the lowest conversions at which reliable values could be obtained were in agreement with recently reported values obtained by the PLP-SEC method. For the lowest conversions, the values obtained were 403 1 mol(-1) s(-1) at 306 K for MMA and 5201 mol(-1) s(-1) at 310 K for a 1:1 mixture of MMA and EGDMA. (C) 2003 Society of Chemical Industry.

From local to global importance measures of uncertainty propagation in composite structures

The influence of uncertainties of input parameters on output response of composite structures is investigated in this paper. In particular, the effects of deviations in mechanical properties, ply angles, ply thickness and on applied loads are studied. The uncertainty propagation and the importance measure of input parameters are analysed using three different approaches: a first-order local method, a Global Sensitivity Analysis (GSA) supported by a variance-based method and an extension of local variance to estimate the global variance over the domain of inputs. Sample results are shown for a shell composite laminated structure built with different composite systems including multi-materials. The importance measures of input parameters on structural response based on numerical results are established and discussed as a function of the anisotropy of composite materials. Needs for global variance methods are discussed by comparing the results obtained from different proposed methodologies. The objective of this paper is to contribute for the use of GSA techniques together with low expensive local importance measures.

Uncertainty propagation in inverse reliability-based design of composite structures

An approach for the analysis of uncertainty propagation in reliability-based design optimization of composite laminate structures is presented. Using the Uniform Design Method (UDM), a set of design points is generated over a domain centered on the mean reference values of the random variables. A methodology based on inverse optimal design of composite structures to achieve a specified reliability level is proposed, and the corresponding maximum load is outlined as a function of ply angle. Using the generated UDM design points as input/output patterns, an Artificial Neural Network (ANN) is developed based on an evolutionary learning process. Then, a Monte Carlo simulation using ANN development is performed to simulate the behavior of the critical Tsai number, structural reliability index, and their relative sensitivities as a function of the ply angle of laminates. The results are generated for uniformly distributed random variables on a domain centered on mean values. The statistical analysis of the results enables the study of the variability of the reliability index and its sensitivity relative to the ply angle. Numerical examples showing the utility of the approach for robust design of angle-ply laminates are presented.