Diffraction gratings fabricated in DLC thin films

This work presents the fabrication of two-dimensional diffraction gratings in diamond-like carbon (DLC) thin films, with applications in computer-generated holography and micro optics. In order to achieve high diffraction efficiency and to have a very simple manufacturing process, the device is designed to modulate only the phase of an incoming coherent monochromatic laser beam (632.8 nm, HeNe laser). This modulation is obtained by implementing a binary microrelief in the DLC film, responsible for generating a localized optical path difference of half a wavelength. This microrelief is obtained by anisotropic reactive ion etching of the DLC surface in an oxygen based plasma. The DLC layer was grown by reactive magnetron sputtering, using a methane-based plasma chemistry. AFM measurements show a low-level surface roughness of less than 1% of the operation wavelength, and optical characterization shows a good quality of the reconstructed diffraction patterns. (C) 2010 Elsevier B.V. All rights reserved.

Failure analysis of low velocity impact on thin composite laminates: Experimental and numerical approaches

The dynamic behavior of composite laminates is very complex because there are many concurrent phenomena during composite laminate failure under impact load. Fiber breakage, delaminations, matrix cracking, plastic deformations due to contact and large displacements are some effects which should be considered when a structure made from composite material is impacted by a foreign object. Thus, an investigation of the low velocity impact on laminated composite thin disks of epoxy resin reinforced by carbon fiber is presented. The influence of stacking sequence and energy impact was investigated using load-time histories, displacement-time histories and energy-time histories as well as images from NDE. Indentation tests results were compared to dynamic results, verifying the inertia effects when thin composite laminate was impacted by foreign object with low velocity. Finite element analysis (FEA) was developed, using Hill`s model and material models implemented by UMAT (User Material Subroutine) into software ABAQUS (TM), in order to simulate the failure mechanisms under indentation tests. (C) 2007 Elsevier Ltd. All rights reserved.

Bending of stochastic Kirchhoff plates on Winkler foundations via the Galerkin method and the Askey-Wiener scheme

In this paper, the method of Galerkin and the Askey-Wiener scheme are used to obtain approximate solutions to the stochastic displacement response of Kirchhoff plates with uncertain parameters. Theoretical and numerical results are presented. The Lax-Milgram lemma is used to express the conditions for existence and uniqueness of the solution. Uncertainties in plate and foundation stiffness are modeled by respecting these conditions, hence using Legendre polynomials indexed in uniform random variables. The space of approximate solutions is built using results of density between the space of continuous functions and Sobolev spaces. Approximate Galerkin solutions are compared with results of Monte Carlo simulation, in terms of first and second order moments and in terms of histograms of the displacement response. Numerical results for two example problems show very fast convergence to the exact solution, at excellent accuracies. The Askey-Wiener Galerkin scheme developed herein is able to reproduce the histogram of the displacement response. The scheme is shown to be a theoretically sound and efficient method for the solution of stochastic problems in engineering. (C) 2009 Elsevier Ltd. All rights reserved.

A boundary element formulation for analysis of elastoplastic plates with geometrical nonlinearity

In this paper a new boundary element method formulation for elastoplastic analysis of plates with geometrical nonlinearities is presented. The von Mises criterion with linear isotropic hardening is considered to evaluate the plastic zone. Large deflections are assumed but within the context of small strain. To derive the boundary integral equations the von Karman`s hypothesis is taken into account. An initial stress field is applied to correct the true stresses according to the adopted criterion. Isoparametric linear elements are used to approximate the boundary unknown values while triangular internal cells with linear shape function are adopted to evaluate the domain value influences. The nonlinear system of equations is solved by using an implicit scheme together with the consistent tangent operator derived along the paper. Numerical examples are presented to demonstrate the accuracy and the validity of the proposed formulation.

BEM formulation for von Karman plates

This work deals with nonlinear geometric plates in the context of von Karman`s theory. The formulation is written such that only the boundary in-plane displacement and deflection integral equations for boundary collocations are required. At internal points, only out-of-plane rotation, curvature and in-plane internal force representations are used. Thus, only integral representations of these values are derived. The nonlinear system of equations is derived by approximating all densities in the domain integrals as single values, which therefore reduces the computational effort needed to evaluate the domain value influences. Hyper-singular equations are avoided by approximating the domain values using only internal nodes. The solution is obtained using a Newton scheme for which a consistent tangent operator was derived. (C) 2009 Elsevier Ltd. All rights reserved.

An extended BEM formulation for plates reinforced by rectangular beams

This article presents a BEM formulation developed particularly for analysis of plates reinforced by rectangular beams. This is an extended version of a Previous paper that only took into account bending effects. The problem is now re-formulated to consider bending and membrane force effects. The effects of the reinforcements are taken into account by using a simplified scheme that requires application of ail initial stress field to locally correct the bending and stretching stiffness of the reinforcement regions. The domain integrals due to the presence of the reinforcements are then transformed to the reinforcement/plate interface. To reduce the number of degrees of freedom related to the presence of the reinforcement, the proposed model was simplified to consider only bending and stretching rigidities in the direction of the beams. The complete model can be recovered by applying all six internal force correctors, corresponding to six degrees of freedom per node. Examples are presented to confirm the accuracy of the formulation and to illustrate the level of simplification introduced by this strong reduction in the number of degrees of freedom. (C) 2008 Elsevier Ltd. All rights reserved.

BEM formulation for reinforced plates

This article presents a BEM formulation developed to analyse reinforced plate bending. The reinforcements are formulated using a simplified scheme based on applying an initial moment field adopted to locally correct the stiffness of the reinforcement regions. The domain integrals due to the presence of the reinforcements are then transformed to the reinforcement/plate interface. The increase in system stiffness due to the reinforcements can be taken into account independently for each coefficient. Thus, one can conveniently reduce the number of degrees of freedom required in considering the reinforcement. Only one degree-of-freedom is required at each internal node when taking into account only the flexural stiffness of beams. Examples are presented to confirm the accuracy of the formulation. (C) 2009 Elsevier Ltd. All rights reserved.

Analysis of stiffened plates by the boundary element method

In this paper, a formulation for representation of stiffeners in plane stress by the boundary elements method (BEM) in linear analysis is presented. The strategy is to adopt approximations for the displacements in the central line of the stiffener. With this simplification the Spurious oscillations in the stress along stiffeners with small thickness is prevented. Worked examples are analyzed to show the efficiency of these techniques, especially in the insertion of very narrow sub-regions, in which quasi-singular integrals are calculated, with stiffeners that are much stiffer than the main domain. The results obtained with this formulation are very close to those obtained with other formulations. (C) 2007 Elsevier Ltd. All rights reserved.

Study of the water retention properties of a tropical soil

Some peculiarities of water retention in a tropical lateritic soil of clayey nature are presented and discussed. The typical soil microstructure is shown through thin-layer plates emphasizing soil microaggregation and pore distribution and their repercussion on the soil-water retention curve and on hysteresis. It is shown that the clayey soil has a behavior that to a large extent resembles sandy soil, which is characterized by the relatively high saturated hydraulic conductivity, low air-entry value, and small suction range at which water drainage takes place. The severe weathering processes that originated this soil have produced an altered soil that seems to be homogeneous in terms of physical indices, hydraulic conductivity, and soil-water retention characteristics, up to 4.5 m in depth.

Efficient Modeling of Thin Wires in a Lossy Medium by Finite Elements Applied to Grounding Systems

A procedure is proposed to accurately model thin wires in lossy media by finite element analysis. It is based on the determination of a suitable element width in the vicinity of the wire, which strongly depends on the wire radius to yield accurate results. The approach is well adapted to the analysis of grounding systems. The numerical results of the application of finite element analysis with the suitably chosen element width are compared with both analytical results and those computed by a commercial package for the analysis of grounding systems, showing very good agreement.

An EFG method for the nonlinear analysis of plates undergoing arbitrarily large deformations

The applicability of a meshfree approximation method, namely the EFG method, on fully geometrically exact analysis of plates is investigated. Based on a unified nonlinear theory of plates, which allows for arbitrarily large rotations and displacements, a Galerkin approximation via MLS functions is settled. A hybrid method of analysis is proposed, where the solution is obtained by the independent approximation of the generalized internal displacement fields and the generalized boundary tractions. A consistent linearization procedure is performed, resulting in a semi-definite generalized tangent stiffness matrix which, for hyperelastic materials and conservative loadings, is always symmetric (even for configurations far from the generalized equilibrium trajectory). Besides the total Lagrangian formulation, an updated version is also presented, which enables the treatment of rotations beyond the parameterization limit. An extension of the arc-length method that includes the generalized domain displacement fields, the generalized boundary tractions and the load parameter in the constraint equation of the hyper-ellipsis is proposed to solve the resulting nonlinear problem. Extending the hybrid-displacement formulation, a multi-region decomposition is proposed to handle complex geometries. A criterium for the classification of the equilibrium`s stability, based on the Bordered-Hessian matrix analysis, is suggested. Several numerical examples are presented, illustrating the effectiveness of the method. Differently from the standard finite element methods (FEM), the resulting solutions are (arbitrary) smooth generalized displacement and stress fields. (c) 2007 Elsevier Ltd. All rights reserved.

Finite element and dimensional analysis algorithm for the prediction of mechanical properties of bulk materials and thin films

In this work, the applicability of a new algorithm for the estimation of mechanical properties from instrumented indentation data was studied for thin films. The applicability was analyzed with the aid of both three-dimensional finite element simulations and experimental indentation tests. The numerical approach allowed studying the effect of the substrate on the estimation of mechanical properties of the film, which was conducted based on the ratio h(max)/l between maximum indentation depth and film thickness. For the experimental analysis, indentation tests were conducted on AISI H13 tool steel specimens, plasma nitrated and coated with TiN thin films. Results have indicated that, for the conditions analyzed in this work, the elastic deformation of the substrate limited the extraction of mechanical properties of the film/substrate system. This limitation occurred even at low h(max)/l ratios and especially for the estimation of the values of yield strength and strain hardening exponent. At indentation depths lower than 4% of the film thickness, the proposed algorithm estimated the mechanical properties of the film with accuracy. Particularly for hardness, precise values were estimated at h(max)/l lower than 0.1, i.e. 10% of film thickness. (C) 2010 Published by Elsevier B.V.

Residual stresses in titanium nitride thin films obtained with step variation of substrate bias voltage during deposition

In this work, a series of depositions of titanium nitride (TiN) films on M2 and D2 steel substrates were conducted in a Triode Magnetron Sputtering chamber. The temperature; gas flow and pressure were kept constant during each run. The substrate bias was either decreased or increased in a sequence of steps. Residual stress measurements were later conducted through the grazing X-ray diffraction method. Different incident angles were used in order to change the penetration depth and to obtain values of residual stress at different film depths. A model described by Dolle was adapted as an attempt to calculate the values of residual stress at each incident angle as a function of the value from each individual layer. Stress results indicated that the decrease in bias voltage during the deposition has produced compressive residual stress gradients through the film thickness. On the other hand, much less pronounced gradients were found in one of the films deposited with increasing bias voltage. (C) 2010 Elsevier B.V. All rights reserved.

Impact on HDPE and PVC plates - Experimental tests and numerical simulations

This paper presents first material tests on HDPE and PVC, and subsequently impact tests on plates made of the same materials. Finally, numerical simulations of the plate impact tests are compared with the experimental results. A rather comprehensive series of mechanical material tests were performed to disclose the behaviour of PVC and HDPE in tension and compression. Quasi-static tests were carried out at three rates in compression and two in tension. Digital image correlation. DIC, was used to measure the in-plane strains, revealing true stress-strain curves and allowing to analyze strain-rate sensitivity and isotropy of Poisson`s ratio. In addition, dynamic compression tests were carried out in a split-Hopkinson pressure bar. Quasi-static and dynamic tests were also performed on clamped plates made of the same PVC and HDPE materials, using an optical technique to measure the full-field out-of-plane deformations. These tests, together with the material data, were used for comparative purposes of a finite element analysis. A reasonable agreement between experimental and numerical results was achieved. (C) 2010 Elsevier Ltd. All rights reserved.

Post-failure behaviour of impulsively loaded circular plates

The dynamic plastic response of a simply supported circular plate is analysed. Emphasis is given to the plate behaviour after it has broken free from the supports due to a local material failure. The theoretical rigid plastic analysis predicts various features of the response such as the time to failure, residual kinetic energy and the critical velocity at failure. The residual kinetic energy of the plate could be significant enough to cause secondary impact damage. It is shown that the shape of the plate changes after breaking free from the supports, which is important for forensic investigations. The solution for various cases were proven to be exact in the context of the upper and lower bounds theorems of the theory of plasticity. (C) 2009 Elsevier Ltd. All rights reserved.