Deformation Of Pdms Membrane And Microcantilever By A Water Droplet: Comparison Between Mooney-Rivlin And Linear Elastic Constitutive Models

In this paper, we studied the role of vertical component Of Surface tension of a water droplet on the deformation of membranes and microcantilevers (MCLs) widely used in lab-on-a-chip and micro-and nano-electromechanical system (MEMS/NEMS). Firstly, a membrane made of a rubber-like material, poly(dimethylsiloxane) (PDMS), was considered. The deformation was investigated using the Mooney-Rivlin (MR) model and the linear elastic constitutive relation, respectively. By comparison between the numerical solutions with two different models, we found that the simple linear elastic model is accurate enough to describe such kind of problem, which would be quite convenient for engineering applications. Furthermore, based on small-deflection beam theory, the effect of a liquid droplet on the deflection of a MCL was also studied. The free-end deflection of the MCL was investigated by considering different cases like a cylindrical droplet, a spherical droplet centered on the MCL and a spherical droplet arbitrarily positioned on the MCL. Numerical simulations demonstrated that the deflection might not be neglected, and showed good agreement with our theoretical analyses. (C) 2008 Elsevier Inc. All rights reserved.

A STUDY OF MODE-I DELAMINATION RESISTANCE OF A THERMOPLASTIC COMPOSITE

This paper describes the mode I delamination behaviour of a unidirectional carbon-fibre/poly(phenylene ether ketone)(PEK-C) composite. Tests have been performed on double cantilever beam (DCB) specimens. Several data reduction schemes are used to obtain the critical strain energy release rate, G(IC), and the results are compared. It is shown that when using a DCB test to determine the fracture toughness, corrections must be employed. The experimental methods have been described for ascertaining the correction terms, and the results are consistent after modification. Some of the authors' results are different from those of other authors, particularly the negative correction term for crack length, the larger exponent (n > 3) in the relationship C = Ra(n), and decrements of flexural modulus with the crack growth when using the simple beam theory to predict the bending behaviour of DCB specimens. The possible reasons are discussed.

Aberration measurement of projection optics in lithographic tools based on two-beam interference theory

The degradation of image quality caused by aberrations of projection optics in lithographic tools is a serious problem in optical lithography. We propose what we believe to be a novel technique for measuring aberrations of projection optics based on two-beam interference theory. By utilizing the partial coherent imaging theory, a novel model that accurately characterizes the relative image displacement of a fine grating pattern to a large pattern induced by aberrations is derived. Both even and odd aberrations are extracted independently from the relative image displacements of the printed patterns by two-beam interference imaging of the zeroth and positive first orders. The simulation results show that by using this technique we can measure the aberrations present in the lithographic tool with higher accuracy. (c) 2006 Optical Society of America.

Strain gradient theory with couple stress for crystalline solids

A new phenomenological strain gradient theory for crystalline solid is proposed. It fits within the framework of general couple stress theory and involves a single material length scale Ics. In the present theory three rotational degrees of freedom omega (i) are introduced, which denote part of the material angular displacement theta (i) and are induced accompanying the plastic deformation. omega (i) has no direct dependence upon u(i) while theta = (1 /2) curl u. The strain energy density omega is assumed to consist of two parts: one is a function of the strain tensor epsilon (ij) and the curvature tensor chi (ij), where chi (ij) = omega (i,j); the other is a function of the relative rotation tensor alpha (ij). alpha (ij) = e(ijk) (omega (k) - theta (k)) plays the role of elastic rotation reason The anti-symmetric part of Cauchy stress tau (ij) is only the function of alpha (ij) and alpha (ij) has no effect on the symmetric part of Cauchy stress sigma (ij) and the couple stress m(ij). A minimum potential principle is developed for the strain gradient deformation theory. In the limit of vanishing l(cs), it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in detail. For simplicity, the elastic relation between the anti-symmetric part of Cauchy stress tau (ij), and alpha (ij) is established and only one elastic constant exists between the two tensors. Combining the same hardening law as that used in previously by other groups, the present theory is used to investigate two typical examples, i.e., thin metallic wire torsion and ultra-thin metallic beam bend, the analytical results agree well with the experiment results. While considering the, stretching gradient, a new hardening law is presented and used to analyze the two typical problems. The flow theory version of the present theory is also given.

A New Deformation Theory with Strain Gradient Effects

A new phenomenological deformation theory with strain gradient effects is proposed. This theory, which belongs to nonlinear elasticity, fits within the framework of general couple stress theory and involves a single material length scale l. In the present theory three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom u(i). omega(i) has no direct dependence upon ui and is called the micro-rotation, i.e. the material rotation theta(i) plus the particle relative rotation. The strain energy density is assumed to only be a function of the strain tensor and the overall curvature tensor, which results in symmetric Cauchy stresses. Minimum potential principle is developed for the strain gradient deformation theory version. In the limit of vanishing 1, it reduces to the conventional counterparts: J(2) deformation theory. Equilibrium equations, constitutive relations and boundary conditions are given in details. Comparisons between the present theory and the theory proposed by Shizawa and Zbib (Shizawa, K., Zbib, H.M., 1999. A thermodynamical theory gradient elastoplasticity with dislocation density Censor: fundamentals. Int. J. Plast. 15, 899) are given. With the same hardening law as Fleck et al. (Fleck, N.A., Muller, G.H., Ashby, M.F., Hutchinson, JW., 1994 Strain gradient plasticity: theory and experiment. Acta Metall. Mater 42, 475), the new strain gradient deformation theory is used to investigate two typical examples, i.e. thin metallic wire torsion and ultra-thin metallic beam bend. The results are compared with those given by Fleck et al, 1994 and Stolken and Evans (Stolken, J.S., Evans, A.G., 1998. A microbend test method for measuring the plasticity length scale. Acta Mater. 46, 5109). In addition, it is explained for a unit cell that the overall curvature tensor produced by the overall rotation vector is the work conjugate of the overall couple stress tensor. (C) 2002 Elsevier Science Ltd. All rights reserved.

The magnetic jet theory of double source in radio galaxy

The two-dimensional accelerating theory about solar wind is applied to the study of theaccelerating process of jet beam in the radio galaxy. The flowing features are given with theanalytic method, and the basic flow is along the direction of the jet beam. The mechanism ofacceleration from subsonic to supersonic flow is discussed. At the same time, some fine struc-tures about the double sources in the radio galaxy are explained.

New Strain Gradient Theory And Analysis

A new strain gradient theory which is based on energy nonlocal model is proposed in this paper, and the theory is applied to investigate the size effects in thin metallic wire torsion, ultra-thin beam bending and micro-indentation of polycrystalline copper. First, an energy nonlocal model is suggested. Second, based on the model, a new strain gradient theory is derived. Third, the new theory is applied to analyze three representative experiments.

Distortion of beam shape by a rotating double-prism wide-angle laser beam scanner

We describe the rigorous results of a wide-angle laser beam scanner, obtained with the help of the vector refraction theory. Using the rigorous results, the distortion of the beam shape is discussed. The distortion to the beam varies with the different relative angles of double prisms. The scanner expands the beam in some directions while it contracts the beam in other directions. According to the conservation of energy, the distribution of the laser intensity is changed as well. (c) 2006 Society of Photo-Optical Instrumentation Engineers.

The effect of the rotating double-prism wide-angle laser beam scanner on the beam shape

In this paper, we describe a wide-angle laser beam scanner and the rigorous result of the wide-angle laser beam scanner was obtained with the help of the vector refraction theory. Using the rigorous results, the distortion of the beam shape was discussed. The distortion of the beam shape is varying with the different relative angles of the double prisms. According to the conservation of the energy, the distribution of the laser intensity is changed too. (c) 2005 Elsevier GmbH. All rights reserved.

Influence of recording conditions on crossed-beam photorefractive gratings in doubly doped LiNbO3 crystals

The influence of the recording conditions, including the widths of the recording beams, the width ratio of the recording beams, and the recording angles, on the properties of crossed-beam photorefractive gratings in doubly doped LiNbO3 crystals is studied. A theoretical model that combines the band transport model with two-dimensional coupled-wave theory is proposed. The numerical calculations of the space-charge field, the intensity profiles of the diffracted beam, and the diffraction efficiency are presented. (C) 2006 Optical Society of America.

Diffraction properties of volume holographic gratings for an ultrashort pulsed beam with different polarization states readout

The diffraction properties of volume holographic gratings are studied when the gratings are illuminated by an ultrashort pulsed beam with different polarization states. The developed coupled wave theory of Kogelnik is used. Considering the dispersion effect of the grating media, solutions for the diffracted and transmitted intensities, diffraction efficiencies and the bandwidths of the gratings are given in transmission volume holographic gratings and reflection volume holographic gratings. The bandwidths of the gratings are reduced by the dispersion effect of the grating media. They also have different influences on the diffraction of an ultrashort pulsed beam with different polarization states. For different values of the ratio of the spectral bandwidth of the input pulse to that of the grating, the changes of the spectral and temporal distributions of the diffracted intensities, as well as the diffraction efficiencies of the gratings are shown.

Distortion of beam shape by a rotating double-prism wide-angle laser beam scanner

We describe the rigorous results of a wide-angle laser beam scanner, obtained with the help of the vector refraction theory. Using the rigorous results, the distortion of the beam shape is discussed. The distortion to the beam varies with the different relative angles of double prisms. The scanner expands the beam in some directions while it contracts the beam in other directions. According to the conservation of energy, the distribution of the laser intensity is changed as well. (c) 2006 Society of Photo-Optical Instrumentation Engineers.

Diffraction of an ultrashort pulsed beam with arbitrary polarization state from a volume holographic grating in LiNbO3 crystals

Based on a modified coupled wave theory of Kogelnik, we have studied the diffraction of an ultrashort pulsed beam with an arbitrary polarization state from a volume holographic grating in photorefractive LiNbO3 crystals. The results indicate that the diffracted intensity distributions in the spectral and temporal domains and the diffraction efficiency of the grating are both changed by the polarization state and spectral bandwidth of the input pulsed beam. A method is given of choosing the grating parameters and input conditions to obtain a large variation range of the spectral bandwidth of the diffracted pulsed beam with an appropriate diffraction efficiency. Our study presents a possibility of using a volume holographic grating recorded in anisotropic materials to shape a broadband ultrashort pulsed beam by modulating its polarization state.

Laser beam shaping system with a radial birefringent filter

Reshaping of a Gaussian laser beam into a uniform or other intensity distribution is required for various applications. The laser beam shaping system with a radial birefringent filter is presented in this paper. With such a system the Gaussian beams can be transformed into uniform or annular beams. The theory and simulation of the proposed systems are described in detail. The primary advantage of such a system is that the out beam pro. le can be tunable with the rotation of the radial birefringent element.

Analysis of an ultrashort pulsed finite beam diffracted by volume gratings

We obtain analytical solutions of the coupled wave equations that describe the Bragg diffraction of ultrashort pulsed finite beams by a thick planar grating, using two-dimensional coupled wave theory. The diffraction properties for the case of an ultrashort pulsed finite beam with Gaussian profiles in both the time and spatial domains are investigated. The spectral bandwidth of the diffracted beam, the Bragg selectivity bandwidth and the diffraction efficiency of the volume grating are influenced by the geometry parameter and the input bandwidth. Therefore extra attention should be paid to designing optical elements based on volume gratings for use with ultrashort pulsed waves in applications of pulse shaping and processing.