Determination of displacement and strain fields using dual-beam holographic-moiré interferometry

A procedure is described to determine the surface strains of objects of arbitrary shape using the same setup. The shape of the object is determined by contouring holography. The displacements are determined by holographic-moiré in the form of contour-line maps for the displacement components inx, y andz direction. From these maps, the so called basic strains' are derived as if the object were flat. Formulas are given to transform these basic strains' into surface strains.     

Full-Field Surface 3D Shape and Displacement Measurements Using an Unfocused Plenoptic Camera

Full-field surface 3D shape and displacement measurements using a single commercial unfocused plenoptic camera (Lytro Illum) are reported in this work. Before measurements, the unfocused plenoptic camera is calibrated with two consecutive steps, including lateral calibration and depth calibration. Each raw image of a checkerboard pattern recorded by Lytro Illum is first extracted to an array of sub-aperture images (SAIs), and the center sub-aperture images (CSAIs) at diverse poses are used for lateral calibration to determine intrinsic and extrinsic parameters. The parallax maps between the CSAI and the remaining SAIs at each pose are then determined for depth parameters estimation using depth calibration. Furthermore, a newly developed physical-based depth distortion model is established to correct the serious distortion of the depth field. To realize shape and deformation measurements, the raw images of a test sample with speckle patterns premade on its surface are captured by Lytro Illum and extracted to arrays of SAIs. The parallax maps between the CSAI and the target SAIs are obtained using subset-based digital image correlation. Based on the pre-computed intrinsic and depth parameters and the disparity map, the full-field surface 3D shape and displacement of a test object are finally determined. The effectiveness and accuracy of the proposed approach are evaluated by a set of experiments involving the shape reconstruction of a cylinder, in-plane and out-of-plane displacement measurements of a flat plate and 3D full-field displacement measurements of a cantilever beam. The preliminary results indicate that the proposed method is expected to become a novel approach for full-field surface 3D shape and displacement measurements.     

Testing the accuracy of the overlap criterion

Here we investigate the accuracy of the overlap criterion when applied to a simple near-integrable model in both its 2D and 3D versions. To this end, we consider, respectively, two and three quartic oscillators as the unperturbed system, and couple the degrees of freedom by a cubic, non-integrable perturbation. For both systems we compute the unperturbed resonances up to order O(ε²), and model each resonance by means of the pendulum approximation in order to estimate the theoretical critical value of the perturbation parameter for a global transition to chaos. We perform several surface of sections for the bi-dimensional case to derive an empirical value to be compared to our theoretical estimation. Although both values are of the same order of magnitude, there is a significant difference between them. For the 3D case a numerical estimate is attained that we observe matches quite well the critical value resulting from theoretical means. This confirms once again that calculating resonances up to O(ε²) suffices in order the overlap criterion to work out.     

Sensitivity of in-Plane Strain Measurement to Calibration Parameter for out-of-Plane Specimen Rotations

In practice, out-of-plane motions usually are not avoidable during experiments. Since 2D–DIC measurements are vulnerable to parasitic deformations due to out-of-plane specimen motions, three-dimensional digital image correlation (StereoDIC or 3D–DIC) oftentimes is employed. The StereoDIC method is known to be capable of accurate deformation measurements for specimens subjected to general three-dimensional motions, including out-of-plane rotations and displacements. As a result, there has been limited study of the deformation measurements obtained when using StereoDIC to measure the displacement and strain fields for a specimen subjected only to out-of-plane rotation. To assess the accuracy of strain measurements obtained using stereovision systems and StereoDIC when a specimen undergoes appreciable out of plane rotation, rigid body out-of-plane rotation experiments are performed in the range ?40⁰?≤?θ?≤?40⁰ using a two-camera stereovision system. Results indicate that (a) for what would normally be considered “small angle” calibration processes, the measured normal strain in the foreshortened specimen direction due to specimen rotation increases in a non-linear manner with rotation angle, with measurement errors exceeding ±1400με and (b) for what would normally be considered “large angle” calibration processes, the magnitude of the errors in the strain are reduced to ±300με. To theoretically assess the effect of calibration parameters on the measurements, two separate analyses are performed. First, theoretical strains due to out-of-plane rigid body rotation are determined using a pinhole camera model to project a series of three-dimensional object points into the image plane using large angle calibration parameters and then re-project the corresponding sensor plane coordinates back into the plane using small angle calibration parameters. Secondly, the entire imaging process is also simulated in order to remove experimental error sources and to further validate the theory. Results from both approaches confirmed the same strain error trends as the experimental strain measurements, providing confidence that the source of the errors is the calibration process. Finally, variance based sensitivity analyses show that inaccuracy in the calibrated stereo angle parameter is the most significant factor affecting the accuracy of the measured strain.     

使用单彩色相机的单相机三维数字图像相关方法

介绍了一种基于单个彩色相机的新型全靶面、单相机三维数字图像相关(3D-DIC)方法。借助于设计巧妙的颜色分光光路,被测物体表面图像可以通过两条不同的光路达到相机靶面,采集的标定靶和实验件表面的彩色图像可以分离得到蓝色和红色子图像。通过使用3D-DIC分析标定靶和实验件表面分离后的蓝色和红色子图像,可以获得物体表面的三维形貌和变形。形貌测量、面内和离面平移、以及静动态三维变形实验验证了该单彩色相机3D-DIC方法的有效性和测量精准度。由于可避免双相机同步,且能实现无分辨率损失的全靶面三维形貌和变形测量,本文方法在需要实现瞬态位移和变形测量的爆炸、冲击、振动等领域中具有广阔重要的应用前景。     

Comparison of methods to estimate the scour downstream of a ski jump

This study analyzes the expected depth and scour shape in the Toachi River (Ecuador) as a result of the construction of the Toachi Dam in order to avoid problems with progressive scour. The dam has a maximum height of 59 m to the foundations. The free surface weir ends in a ski jump and has been designed to operate with a peak discharge of 1213 m³/s. As each method has its limitations, the scour is studied with four complementary procedures: 1) a 1:50 Froude scale similitude laboratory model used as validation case; 2) 36 empirical formulae derived from models and prototypes; 3) a semi-empirical methodology based on pressure fluctuations-erodibility index; and 4) FLOW-3D numerical simulations. The expected scour depth is 6.65 m for the design flow. The results are close to the physical model. In the numerical analysis, turbulence is treated using the three RANS approaches. The choice of the turbulence model and the bed load coefficient in the Meyer-Peter & Müller formula are of great importance. The best results were obtained using the RNG k-ε turbulence model and a bed load coefficient below 7.     

A 3D Displacement Control by Digital Image Correlation for the Multiaxial Testing of Materials with a Stewart Platform

A Digital Image Correlation technique is proposed to control a quasi-static 6 degrees of freedom testing machine. This machine is based on a hexapod architecture, allowing displacements of several tens of centimeters and degrees, and with force capacities of several tens of kN and kN.m. The control technique is based on the measurement of the set of actuator lengths, from images of the end-effector of the machine. A firstattempt is shown with a single camera. Thoughrelevant, the results present too high uncertainties for the aimed applications. Several cameras are then used to improve the 3D rigid body motion displacement measurement of the end-effector. Thecamera positions are free, with an automatic calibration method assessing the needed coefficients for the control. The set of actuator lengths is then searched by global minimization of the difference between the current image and the reference image of each camera (i.e., the minimization is not performed independently for each camera). The algorithm is implemented on Graphical Processing Units to achieve computation times lower than 50 ms. An in-depth experimental validation of the whole setup is performed. For an actuator length range of 200 μm, the actuator length uncertainties are around 0.4 μm with 3 cameras. The errors of displacement of the end-effector are less than 2 μm, partially due to the validation setup itself.     

Validation of 1D model for methane/air/Pt combustion in stagnation flow

A 2D model is built on the package of FLUENT to study the effects of radial aspect ratio (R/W), length-to-width ratio (L/W), strain rate (S _R), and buoyancy (Ri=Gr/Re ²) on the validation of the simplified 1D model. In the present 2D model, the methane/air homogeneous reaction mechanism of Peters and the methane/air/platinum heterogeneous reaction mechanism of Deutschmann are applied. By comparison between the 1D and 2D numerical results, it is found that the validation of 1D model is highly related with the catalytic stagnation reactor configuration. For length-to-width ratio L/W = 1 configuration, 1D laminar model is applicable when the radial aspect ratio R/W > 0.4. For R/W = 0.6, the reactor exhibited 1D characteristics when L/W < 1. Compared with the temperature and species profiles, the velocity distribution along the axis is more sensitive to the change of radial aspect ratio and length-to-width ratio. With increasing of the strain rate, the flame front goes closer to the catalytic wall surface and the difference between the 1D and 2D results decreases. For a valid 1D simulation, it is recommended that the strain rate should be greater than 20 s^-1. The effects of natural convection can be neglected when Ri < 5.     

K+ uptake by root systems grown in soil under salinity: I. A mathematical model

A novel theoretical model is proposed for K⁺ uptake by intact root systems from saline soil considering interactions with Na⁺, Ca²⁺ and Mg²⁺. The model assumes radial movement of ions towards the root governed by advection and diffusion flux mechanisms, and chemical exchange of the four cations according to Gapon isotherms, with Cl^? as the accompanying anion. Influx of K⁺ to the root surface is assumed as a function of its concentration in the soil solution at the root. This influx is governed by a saturable-cooperative term and a linear term for low and high K⁺ concentrations, respectively. Influx of Na⁺, above a critical value of its concentration, increases linearly with its concentration in the soil solution at the root surface. Uptake of Ca^{+ 2+} is controlled by the balance between influxes of anions and cations, which induces efflux of H⁺ or HCO ₃ ^? , and interacts with calcite in a calcareous soil. The model may provide information about the behavior of ions at the root-soil interface which cannot be measuredin situ.     

Evolution of deviations from the spherical shape of a vapor bubble in supercompression

This paper considers the evolution of small deviations of a cavitation bubble from a spherical shape during its single compression under conditions of experiments on acoustic cavitation of deuterated acetone. Vapor motion in the bubble and the surrounding liquid is defined as a superposition of the spherical component and its non-spherical perturbation. The spherical component is described taking into account the nonstationary heat conductivity of the liquid and vapor and the nonequilibrium nature of the vaporization and condensation on the interface. At the beginning of the compression process, the vapor in the bubble is considered an ideal gas with a nearly uniform pressure. In the simulation of the high-rate compression stage, realistic equations of state are used. The non-spherical component of motion is described taking into account the effect of liquid viscosity, surface tension, vapor density in the bubble, and nonuniformity of its pressure. Estimates are obtained for the amplitude of small perturbations (in the form of harmonics of degree n = 2, 3, ... with the wavelength λ = 2πR/n, where R is the bubble radius) of the spherical shape of the bubble during its compression until reaching extreme values of pressure, density, and temperature. These results are of interest in the study of bubble fusion since the non-sphericity of the bubble prevents its strong compression.     

大视场双目投影条纹方法中的相机参数标定与优化研究

投影条纹法具有高精度、高分辨的特点,且实验设备简单,对实验环境要求低,适宜于不同尺度的三维形貌测量.双目投影条纹法通常采用有标准参照物的相机标定方法获取相机参数,以实现物体表面三维形貌重建.然而,在大型结构的三维形貌测量中参照物的相对尺度较小,传统的基于重投影的相机标定方法在特征检测中引入的误差会被放大,从而影响三维表...     

Energy Scaling Laws for Conically Constrained Thin Elastic Sheets

We investigate low-energy deformations of a thin elastic sheet subject to a displacement boundary condition consistent with a conical deformation. Under the assumption that the displacement near the sheet’s center is of order h|logh|, where h?1 is the thickness of the sheet, we establish matching upper and lower bounds of order h ²|logh| for the minimum elastic energy per unit thickness, with a prefactor determined by the geometry of the associated conical deformation. These results are established first for a 2D model problem and then extended to 3D elasticity.     

Numerical simulations of Z-pinch experiments to create supersonic differentially-rotating plasma flows

The aim of this work is to produce and study a high energy density laboratory plasma relevant to astrophysical accretion disks. To this end, an experimental setup based on a modified cylindrical wire array was devised, which employs a cusp magnetic field to introduce angular momentum into the system. The setup was studied numerically with the three-dimensional, resistive magneto-hydrodynamic code GORGON. Simulations show that a differentially-rotating flow is formed, with typical rotation velocity and Mach number values of 60 km/s and M_φ ～ 5 respectively. The plasma is radiatively cooled and presents a Reynolds number higher than 10⁷. In addition, the magnetic Reynolds number and the plasma β are >1. Such a plasma is of interest for the study of hydrodynamic and magneto-hydrodynamic instabilities, and turbulence generation in differentially-rotating plasma flows.     

Finite deformation thermo-mechanical behavior of thermally induced shape memory polymers

Shape memory polymers (SMPs) are polymers that can demonstrate programmable shape memory effects. Typically, an SMP is pre-deformed from an initial shape to a deformed shape by applying a mechanical load at the temperature T_H>T_g. It will maintain this deformed shape after subsequently lowering the temperature to T_L<T_g and removing the externally mechanical load. The shape memory effect is activated by increasing the temperature to T_D>T_g, where the initial shape is recovered. In this paper, the finite deformation thermo-mechanical behaviors of amorphous SMPs are experimentally investigated. Based on the experimental observations and an understanding of the underlying physical mechanism of the shape memory behavior, a three-dimensional (3D) constitutive model is developed to describe the finite deformation thermo-mechanical response of SMPs. The model in this paper has been implemented into an ABAQUS user material subroutine (UMAT) for finite element analysis, and numerical simulations of the thermo-mechanical experiments verify the efficiency of the model. This model will serve as a modeling tool for the design of more complicated SMP-based structures and devices.     

Effects of irregular two-dimensional and three-dimensional surface roughness in turbulent channel flows

Wall-resolved Large Eddy Simulation of fully developed turbulent channel flows over two different rough surfaces is performed to investigate on the effects of irregular 2D and 3D roughness on the turbulence. The two geometries are obtained through the superimposition of sinusoidal functions having random amplitudes and different wave lengths. In the 2D configuration the irregular shape in the longitudinal direction is replicated in the transverse one, while in the 3D case the sinusoidal functions are generated both in streamwise and spanwise directions. Both channel walls are roughened in such a way as to obtain surfaces with statistically equivalent roughness height, but different shapes. In order to compare the turbulence properties over the two rough walls and to analyse the differences with a smooth wall, the simulations are performed at the same Reynolds number Re_τ = 395. The same mean roughness height h = 0.05δ (δ the half channel height) is used for the rough walls.The roughness function obtained with the 3D roughness is larger than in the 2D case, although the two walls share the same mean height. Thus, the considered irregular 3D roughness is more effective in reducing the flow velocity with respect to the 2D roughness, coherently with the literature results that identified a clear dependence of the roughness function on the effective slope (see Napoli et al. (2008)), higher in the generated 3D rough wall. The analysis of higher-order statistics shows that the effects of the roughness, independently on its two- or three-dimensional shape, are mainly confined in the inner region, supporting the Townsend’s wall similarity hypothesis. The tendency towards the isotropization is investigated through the ratio between the resolved Reynolds stress components, putting in light that the 3D irregular rough wall induces an higher reduction of the anisotropy, with respect to the 2D case.     

Experimental study of shock waves from the interaction of a supersonic plasma jet with an ambient gas

Preliminary results of the interaction of a supersonic, radiatively cooled plasma jet with an ambient gas are presented. The experimental setup consists of a radial foil, a mum-thick aluminium disc held between two concentric electrodes and subjected to a 1.4 MA, 250-ns current pulse from the MAGPIE generator. The plasma flow, with typical velocities of ~70?C90?km/s, is produced by the J?× B force acting on the plasma ablated from the foil. A jet is formed from the convergence of this ablated plasma on the axis of the system. A new setup allows the jet to interact with an argon ambient (particle density N ~10^16-17 cm^?3) from a supersonic gas nozzle (Mach ~9). First results are characterised by the presence of several (previously unseen) shock structures, which are formed from the interaction of the jet with the argon ambient.     

Plastic surface strain mapping of bent sheets by image correlation

A technique using a single CCD camera, a precision rotation/translation stage, a telecentric zoom lens, and digital image correlation software is described for measuring surface profiles and surface plastic strain distributions of a bent thin sheet. The measurement principles, based on both parallel and pinhole perspective projections, are outlined and the relevant mathematical equations for computing the profiles and displacement fields on a curved surface are presented. The typical optical setup as well as the experimental measurement and digital image correlation analysis procedure are described. The maximum errors in the in-plane and out-of-plane coordinates or displacements are about ±5 and ±25 μm, respectively, and the maximum errors in surface strain mapping are about 0.1% or less based on a series of evaluation tests on flat and curved sample surfaces over a physical field of view of 15.2 × 11.4 mm². As an application example, the shape and surface plastic strain distribution example, the shape and surface plastic strain distributions around a bent apex of a flat 2 mm thick automotive aluminum AA5182-O sheet, which underwent a 90° bend with three bend ratios of 2t, 1t, and 0.6t, are determined using the proposed technique.     

Dépose dynamique d'un micro-objet saisi par adhésionManipulation of micro-objects using adhesion forces and dynamical effects

This paper describes a dynamical strategy for releasing micro objects picked-up by means of adhesion forces. While sticking effects are used in order to capture an object by adequately choosing a high surface energy constitutive material for the end-effector, these same effects handicap considerably the release. We propose to take advantage of the inertial effects of both the end-effector and the manipulated object to overbalance adhesion forces and to achieve the release. Simulations show that for this purpose, accelerations as high as 10⁵ m/s² are needed. Successful manipulation of a 40 μm radius glass sphere is demonstrated. To cite this article: S. Haliyo et al., C. R. Mecanique 331 (2003).     

On third order density contrast expansion of the evolution equation for wrinkled unsteady premixed flames

The dynamics of flat-on-average wrinkled flame front propagating through gaseous premixtures is considered. Leading the asymptotic expansions in powers of the burnt to unburned fractional density contrast (0<γ<1) to third order, an evolution equation (called S3) is obtained for the instantaneous front shapes. It reduces to Sivashinsky's original equation (called S1) as γ?0. It also modifies a previous attempt by Sivashinsky and Clavin (called S2) to improve it. Numerical integrations of the S3 equation reveals that the new quadratic and cubic non-linearities featured at 3rd order happen to mutually compensate partially one another for realistic γ's, and are negligible at γ?1. As a result, the flame shape and speed solutions to S3 nearly coincide with those of a S1/S2 type of equation, even for a 10-fold density variation (γ=0.9) and for unsteady situations, provided a singleO(1) coefficient a(γ) be adjusted therein, once for all for each γ. The O(γ²) (and small) correction to it mainly originates from a quartic non-linearity of geometrical origin. The agreement carries over to comparisons with some DNS of 2D steady wrinkled fronts. A phenomenological (yet asymptotically correct at γ?1 and exact in the linear limit) interpolating model equation is finally proposed to try and account for inertia effects associated with fast transients (e.g. acoustics related) while reproducing the above results on steady patterns.     

Stress singularity analysis around the singular point on the stress singularity line in three-dimensional joints

The characteristics of the stress fields around a singular point on the stress singularity line of dissimilar materials in three-dimensional joints are investigated using BEM. Contour for the order of stress singularity around the point is mapped on Dundurs’ parameters plane using eigen value analysis by FEM. The results in 3D joints are compared with those in 2D joints having the same cross section and material combination. The order of stress singularity around the singular point on the stress singularity line in 3D joints is almost identical with that in 2D joints in the singularity region. However, the zero boundary of singularity in 3D joints is slightly different from that in 2D joints. Furthermore, the multiple root of p = 1 exists in the eigen value analysis by FEM. Therefore, logarithmic singularity possibly occurs around the singular point on the stress singularity line. Then, the stress distributions around this point are expressed by the combination of the r^λ term and logarithmic singularity terms. Finally, the characteristics of the stress intensity factors of the r^λ term and logarithmic singularity terms around the singular points are investigated.