On the performance of strain smoothing for quadratic and enriched finite element approximations (XFEM/GFEM/PUFEM)

By using the strain smoothing technique proposed by Chen et al. (Comput. Mech. 2000; 25: 137-156) for meshless methods in the context of the finite element method (FEM), Liu et al. (Comput. Mech. 2007; 39(6): 859-877) developed the Smoothed FEM (SFEM). Although the SFEM is not yet well understood mathematically, numerical experiments point to potentially useful features of this particularly simple modification of the FEM. To date, the SFEM has only been investigated for bilinear and Wachspress approximations and is limited to linear reproducing conditions. The goal of this paper is to extend the strain smoothing to higher order elements and to investigate numerically in which condition strain smoothing is beneficial to accuracy and convergence of enriched finite element approximations. We focus on three widely used enrichment schemes, namely: (a) weak discontinuities; (b) strong discontinuities; (c) near-tip linear elastic fracture mechanics functions. The main conclusion is that strain smoothing in enriched approximation is only beneficial when the enrichment functions are polynomial (cases (a) and (b)), but that non-polynomial enrichment of type (c) lead to inferior methods compared to the standard enriched FEM (e.g. XFEM). Copyright (C) 2011 John Wiley & Sons, Ltd.

Asymptotic and finite element analyses of mode III dynamic crack growth at a ductile-brittle interface

In this work, dynamic crack growth along a ductile-brittle interface under anti-plane strain conditions is studied. The ductile solid is taken to obey the J(2) flow theory of plasticity with linear isotropic strain hardening, while the substrate is assumed to exhibit linear elastic behavior. Firstly, the asymptotic near-tip stress and velocity fields are derived. These fields are assumed to be variable-separable with a power singularity in the radial coordinate centered at the crack tip. The effects of crack speed, strain hardening of the ductile phase and mismatch in elastic moduli of the two phases on the singularity exponent and the angular functions are studied. Secondly, full-field finite element analyses of the problem under small-scale yielding conditions are performed. The validity of the asymptotic fields and their range of dominance are determined by comparing them with the results of the full-field finite element analyses. Finally, theoretical predictions are made of the variations of the dynamic fracture toughness with crack velocity. The influence of the bi-material parameters on the above variation is investigated.

Stability analysis of stochastically parametered nonconservative columns

Nonconservatively loaded columns. which have stochastically distributed material property values and stochastic loadings in space are considered. Young's modulus and mass density are treated to constitute random fields. The support stiffness coefficient and tip follower load are considered to be random variables. The fluctuations of external and distributed loadings are considered to constitute a random field. The variational formulation is adopted to get the differential equation and boundary conditions. The non self-adjoint operators are used at the boundary of the regularity domain. The statistics of vibration frequencies and modes are obtained using the standard perturbation method, by treating the fluctuations to be stochastic perturbations. Linear dependence of vibration and stability parameters over property value fluctuations and loading fluctuations are assumed. Bounds for the statistics of vibration frequencies are obtained. The critical load is first evaluated for the averaged problem and the corresponding eigenvalue statistics are sought. Then, the frequency equation is employed to transform the eigenvalue statistics to critical load statistics. Specialization of the general procedure to Beck, Leipholz and Pfluger columns is carried out. For Pfluger column, nonlinear transformations are avoided by directly expressing the critical load statistics in terms of input variable statistics.

Finite element simulations of ductile rupture in a constrained metal foil

A numerical study of the ductile rupture in a metal foil constrained between two stiff ceramic blocks is performed. The finite element analysis is carried out under the conditions of mode I, plane strain, small-scale yielding. The rate-independent version of the Gurson model that accounts for the ductile failure mechanisms of microvoid nucleation, growth and coalescence is employed to represent the behavior of the metal foil. Different distributions of void nucleating sites in the metal foil are considered for triggering the initiation of discrete voids. The results clearly show that far-field triaxiality-induced cavitation is the dominant failure mode when the spacing of the void nucleating sites is large. On the contrary, void coalescence near the notch tip is found to be the operative failure mechanism when closely spaced void nucleating sites are considered.

Graphical method to determine the parameters of the two-parameter fracture model for concrete

To evaluate the parameters in the two-parameter fracture model, i.e. the critical stress intensity factor and critical crack tip opening displacement for the fracture of plain concrete in Mode 1 for the given test configuration and geometry, considerable computational effort is necessary. A simple graphical method has been proposed using normalized fracture parameters for the three-point bend (3PB) notched specimen and the double-edged notched (DEN) specimen. A similar graphical method is proposed to compute the maximum load carrying capacity of a specimen, using the critical fracture parameters both for 3PB and DEN configurations.

Degradation and Failure of Field Emitting Carbon Nanotube Arrays

It has been observed experimentally that the collective field emission from an array of Carbon Nanotubes (CNTs) exhibits fluctuation and degradation, and produces thermal spikes, resulting in electro-mechanical fatigue and failure of CNTs. Based on a new coupled multiphysics model incorporating the electron-phonon transport and thermo-electrically activated breakdown, a novel method for estimating accurately the lifetime of CNT arrays has been developed in this paper. The main results are discussed for CNT arrays during the field emission process. It is shown that the time-to-failure of CNT arrays increases with the decrease in the angle of tip orientation. This observation has important ramifications for such areas as biomedical X-ray devices using patterned films of CNTs.

Graphics Processing Units for the Real-time Linear Elastostatic Simulation of Liver

Biomedical engineering solutions like surgical simulators need High Performance Computing (HPC) to achieve real-time performance. Graphics Processing Units (GPUs) offer HPC capabilities at low cost and low power consumption. In this work, it is demonstrated that a liver which is discretized by about 2500 finite element nodes, can be graphically simulated in realtime, by making use of a GPU. Present work takes into consideration the time needed for the data transfer from CPU to GPU and back from GPU to CPU. Although behaviour of liver is very complicated, present computer simulation assumes linear elastostatics. One needs to use the commercial software ANSYS to obtain the global stiffness matrix of the liver. Results show that GPUs are useful for the real-time graphical simulation of liver, which in turn is needed in simulators that are used for training surgeons in laparoscopic surgery. Although the computer simulation should involve rendering also, neither rendering, nor the time needed for rendering and displaying the liver on a screen, is considered in the present work. The present work is just a demonstration of a concept; the concept is not really implemented and validated. Future work is to develop software which can accomplish real-time and very realistic graphical simulation of liver, with rendered image of liver on the screen changing in real-time according to the position of the surgical tool tip approximated as the mouse cursor in 3D.

Barriers to plantation activities in different agro-ecological zones of Southern India

This paper analyses environmental and socio-economic barriers for plantation activities on local and regional level and investigates the potential for carbon finance to stimulate the increased rates of forest plantation on wasteland, i.e., degraded lands, in southern India. Building on multidisciplinary field work and results from the model GCOMAP, the aim is to (1) identify and characterize the barriers to plantation activities in four agro-ecological zones in the state of Karnataka and (2) investigate what would be required to overcome these barriers and enhance the plantation rate and productivity. The results show that a rehabilitation of the wasteland based on plantation activities is not only possible but also anticipated by the local population and would lead to positive environmental and socio-economic effects at a local level. However, in many cases, the establishment of plantation activities is hindered by a lack of financial resources, low land productivity and water scarcity. Based on the model used and the results from the field work, it can be concluded that certified emission reductions such as carbon credits or other compensatory systems may help to overcome the financial barrier; however, the price needs to be significantly increased if these measures are to have any large-scale impact.

Numerical simulations of fracture initiation in ductile solids under mode I, dynamic loading

In this paper, an overview of some recent computational studies by the authors on ductile crack initiation under mode I, dynamic loading is presented. In these studies, a large deformation finite element procedure is employed along with the viscoplastic version of the Gurson constitutive model that accounts for the micro-mechanical processes of void nucleation, growth and coalescence. A three-point bend fracture specimen subjected to impact, and a single edge notched specimen loaded by a tensile stress pulse are analysed. Several loading rates are simulated by varying the impact speed or the rise time and magnitude of the stress pulse. A simple model involving a semi-circular notch with a pre-nucleated circular hole situated ahead of it is considered. The growth of the hole and its interaction with the notch tip, which leads to plastic strain and porosity localization in the ligament connecting them, is simulated. The role of strain-rate dependence on ductile crack initiation at high loading rates, and the specimen geometry effect on the variation of dynamic fracture toughness with loading rate are Investigated.

Re-examination of crack opening model of interface fracture

The complex singularity associated with a crack at the interface between two dissimilar, isotropic and homogeneous materials leads to mathematical artefacts, such as stress oscillations and crack face interpenetrations in the vicinity of the crack tip. To avoid these unrealistic features, Sinclair (Sinclair GB. On the stress singularity at an interface crack. International Journal of Fracture 1980;16(2):111-9) assumed a finite crack opening angle (COA) such that the singularity lambda became real equal to 1/2. This paper extends the COA model by considering real singularities not necessarily equal to 1/2. When COA is 0 degrees: the interface crack singularity is complex with a real part equal to 1/2. On increasing COA, the imaginary part of the singularity decreases and becomes zero at a threshold value of COA; at this point, the singularity is a real, repeated value. A further increase in COA results in a pair of real singularities. Different crack opening configurations and material combinations are studied, and results presented for threshold COAs and associated values of singularity. Stress analyses for these three regimes: (a) complex, (b) real pair and (c) real repeated singularities, are reported. It is seen that additional complexities are present in the last case. Typical results for stress fields are also included for comparing with standard fields. (C) 1999 Elsevier Science Ltd. All rights reserved.

A differential geometric method for kinematic analysis of two- and three-degree-of-freedom rigid body motions

In this paper, we present a novel differential geometric characterization of two- and three-degree-of-freedom rigid body kinematics, using a metric defined on dual vectors. The instantaneous angular and linear velocities of a rigid body are expressed as a dual velocity vector, and dual inner product is defined on this dual vector, resulting in a positive semi-definite and symmetric dual matrix. We show that the maximum and minimum magnitude of the dual velocity vector, for a unit speed motion, can be obtained as eigenvalues of this dual matrix. Furthermore, we show that the tip of the dual velocity vector lies on a dual ellipse for a two-degree-of-freedom motion and on a dual ellipsoid for a three-degree-of-freedom motion. In this manner, the velocity distribution of a rigid body can be studied algebraically in terms of the eigenvalues of a dual matrix or geometrically with the dual ellipse and ellipsoid. The second-order properties of the two- and three-degree-of-freedom motions of a rigid body are also obtained from the derivatives of the elements of the dual matrix. This results in a definition of the geodesic motion of a rigid body. The theoretical results are illustrated with the help of a spatial 2R and a parallel three-degree-of-freedom manipulator.

Constraint loss under dynamic loading in rate independent plastic solids

The objectives of this paper are to examine the loss of crack tip constraint in dynamically loaded fracture specimens and to assess whether it can lead to enhancement in the fracture toughness at high loading rates which has been observed in several experimental studies. To this end, 2-D plane strain finite element analyses of single edge notched (tension) specimen and three point bend specimen subjected to time varying loads are performed. The material is assumed to obey the small strain J(2) flow theory of plasticity with rate independent behaviour. The results demonstrate that a valid J-Q field exists under dynamic loading irrespective of the crack length and specimen geometry. Further, the constraint parameter Q becomes strongly negative at high loading rates, particularly in deeply cracked specimens. The variation of dynamic fracture toughness K-dc with stress intensity rate K for cleavage cracking is predicted using a simple critical stress criterion. It is found that inertia-driven constraint loss can substantially enhance K-dc for (K) over dot > 10(5) MPa rootm/s.

Health monitoring,of a helicopter rotor in forward flight using fuzzy logic

A fuzzy logic system is developed for helicopter rotor system fault isolation. Inputs to the fuzzy logic system are measurement deviations of blade bending and torsion response and vibration from a "good" undamaged helicopter rotor. The rotor system measurements used are flap and lag bending tip deflections, elastic twist deflection at the tip, and three forces and three moments at the rotor hub. The fuzzy logic system uses rules developed from an aeroelastic model of the helicopter rotor with implanted faults to isolate the fault while accounting for uncertainty in the measurements. The faults modeled include moisture absorption, loss of trim mass, damaged lag damper, damaged pitch control system, misadjusted pitch link, and damaged flap. Tests with simulated data show that the fuzzy system isolates rotor system faults with an accuracy of about 90-100%. Furthermore, the fuzzy system is robust and gives excellent results, even when some measurements are not available. A rule-based expert system based on similar rules from the aeroelastic model performs much more poorly than the fuzzy system in the presence of high levels of uncertainty.

Fracture and R-curves in high volume fraction Al2O3/Al composites

Fracture toughness and fracture mechanisms in Al2O3/Al composites are described. The unique flexibility offered by pressureless infiltration of molten Al alloys into porous alumina preforms was utilized to investigate the effect of microstructural scale and matrix properties on the fracture toughness and the shape of the crack resistance curves (R-curves). The results indicate that the observed increment in toughness is due to crack bridging by intact matrix ligaments behind the crack tip. The deformation behavior of the matrix, which is shown to be dependent on the microstructural constraints, is the key parameter that influences both the steady-state toughness and the shape of the R-curves. Previously proposed models based on crack bridging by intact ductile particles in a ceramic matrix have been modified by the inclusion of an experimentally determined plastic constraint factor (P) that determines the deformation of the ductile phase and are shown to be adequate in predicting the toughness increment in the composites. Micromechanical models to predict the crack tip profile and the bridge lengths (L) correlate well with the observed behavior and indicate that the composites can be classified as (i) short-range toughened and (ii) long-range toughened on the basis of their microstructural characteristics.

Surfactant-mediated Synthesis of Functional Metal Oxide Nanostructures via Microwave Irradiation-assisted Chemical Synthesis

Nanostructured materials have attracted considerable interest in recent years due to their properties which differ strongly from their bulk phase and potential applications in nanoscale electronic and optoelectronic devices. Metal oxide nanostructures can be synthesized by variety of different synthesis techniques developed in recent years such as thermal decomposition, sol-gel technique, chemical coprecipitation, hydrothermal process, solvothermal process, spray pyrolysis, polyol process etc. All the above processes go through a tedious synthesis procedure followed by prolonged heat treatment at elevated temperature and are time consuming. In the present work we describe a rapid microwave irradiation-assisted chemical synthesis technique for the growth of nanoparticles, nanorods, and nanotubes of a variety of metal oxides in the presence of an appropriate surfactant, without the use of any templates The method is simple, inexpensive, and helps one to prepare nanostructures in a very simple way, and in a very short time, measured in minutes. The synthesis procedure employs high quality metalorganic complexes (typically -diketonates) featuring a direct metal-to-oxygen bond in its molecular structure. The complex is dissolved in a suitable solvent, often with a surfactant added, and the solution then subjected to microwave irradiation in a domestic microwave oven operating at 2.45 GHz frequency with power varying from 160-800 W, from a few seconds to a few minutes, leading to the formation of corresponding metal oxides. This method has been used successfully to synthesize nanostructures of a variety of binary and ternary metal oxides such as ZnO, CdO, Fe2O3, CuO, Ga2O3, Gd2O3, ZnFe2O4, etc. There is an observed variation in the morphology of the nanostructures with the change of different parameters such as microwave power, irradiation time, appropriate solvent, surfactant type and concentration. Cationic, anionic, nonionic and polymeric surfactants have been used to generate a variety of nanostructures. Even so, to remove the surfactant, there is either no need of heat treatment or a very brief exposure to heat suffices, to yield highly pure and crystalline oxide materials as prepared. By adducting the metal complexes, the shape of the nanostructures can be controlled further. In this manner, very well formed, single-crystalline, hexagonal nanorods and nanotubes of ZnO have been formed. Adducting the zinc complex leads to the formation of tapered ZnO nanorods with a very fine tip, suitable for electron emission applications. Particle size and their monodispersity can be controlled by a suitable choice of a precursor complex, the surfactant, and its concentration. The resulting metal oxide nanostructures have been characterized by X-ray diffraction, field emission scanning electron microscopy, transmission electron microscopy, FTIR spectroscopy, photoluminescence, and electron emission measurements.