Displacement Field

Digital image correlation is a measurement technique that allows one to retrieve displacement fields "separating" two digital images of the same sample at different stages of loading. Because of its remarkable sensitivity, it is not only possible to detect cracks with sub-pixel opening, which would not be visible, but also to provide accurate estimates of stress intensity factors. For this purpose suitable tools have been devised to minimize the sensitivity to noise. Working with digital images allows the experimentalist to deal with a wide range of scales from atomistic to geophysical one with the same tools. Various examples are shown at different scales, as well as some recent extensions to three dimensional cracks based on X-ray Computed micro-tomographic images.

A novel, computationally efficient and robust scheme for multiple initial point prediction has been proposed in this paper. A combination of spatial and temporal predictors has been used for initial motion vector prediction, determination of magnitude and direction of motion and search pattern selection. Initially three predictors from the spatio-temporal neighboring blocks are selected. If all these predictors point to the same quadrant then a simple search pattern based on the direction and magnitude of the predicted motion vector is selected. However if the predictors belong to different quadrants then we start the search from multiple initial points to get a clear idea of the location of minimum point. We have also defined local minimum elimination criteria to avoid being trapped in local minimum. In this case multiple rood search patterns are selected. The predictive search center is closer to the global minimum and thus decreases the effect of monotonic error surface assumption and its impact on the motion field. Its additional advantage is that it moves the search closer to the global minimum hence increases the computation speed. Further computational speed up has been obtained by considering the zero-motion threshold for no motion blocks. The image quality measured in terms of PSNR also shows good results.

Aluminum polycrystals with columnar coarse grains are plastically compressed in a channel die. The spatial distribution of the accumulated plastic surface strains is determined by measuring the displacement fields using photogrametry. For this purpose digital stereological image pairs of the sample surface are taken at the beginning and after each deformation step. The displacement field is derived from them by applying an image analysis method based on pattern recognition to the data before and after straining. The three components of the plastic displacement vector field are used to derive the surface portion of the plastic strain tensor field. The microtexture of the specimens is determined by the analysis of electron backscattering patterns obtained in a scanning electron microscope. The experiments are interpreted by comparing them to the corresponding crystal plasticity finite element simulations.

In this paper, an elastic, rectangular, and simply supported, sigmoid functionally graded material (S-FGM) beam of thick thickness subjected to uniformly distributed transverse loading has been investigated. The S-FGM system consists of ceramic (Al 2 O 3) and metal (Al) phases varying through the thickness of beam. Major classes of representative theories such as classical laminate beam theory (CLBT), first-order shear deformation theory (FSDT) and high-order theories (HOTs) have been considered and a unified kinematic formulation is then proposed. The Poisson's ratio of the thick S-FGM beam is assumed to be constant, but their Young's moduli vary continuously throughout the thickness direction according to the volume fraction of constituents defined by sigmoid function. The numerical illustrations concern bending response of S-FGM rectangular beams. Qualitative and quantitative assessments of displacement and stress fields have been presented and discussed.

The form of the low-temperature interactions between defects in neutral glasses is reconsidered. We analyze the case where the defects can be modeled either as simple two-level tunneling systems, or tunneling rotational impurities. The coupling to strain fields is determined up to second order in the displacement field. It is shown that the linear coupling generates not only the usual 1/r 3 Ising-like interaction between the rotational tunneling defect modes, which causes them to freeze around a temperature T G , but also a random field term. At lower temperatures the inversion symmetric tunneling modes are still active-however, the coupling of these to the frozen rotational modes, now via the second-order coupling to phonons, generates another random field term acting on the inversion symmetric modes (as well as shorter-range 1/r 5 interactions between them). Detailed expressions for all these couplings are given.

The experimental behavior of sisal fiber reinforced cement composites subjected to high speed tension load was studied. High strain rates were achieved by using a high rate servo-hydraulic testing machine. A state-of-the-art high speed Phantom camera was also used to take images from the specimen during the test. The images were used in a digital image correlation model to determine the displacement fields and to calculate crack spacing. The effect of strain rate was investigated by comparing static and dynamic tensile tests which were performed at strain rates ranging from 5.5 × 10−6 to 24.6 s−1, respectively. A numerical tension stiffening model based on nonlinear finite difference method was used to simulate tensile cracking behavior of sisal fiber cementitious composites. The composite presented strain rate sensitivity for ultimate tensile strength and strain capacity with a dynamic amplification factor of 1.26.

Integrating video coding and denoising is a novel processing paradigm, bringing mutual benefits to both video processing tools. In this paper, we propose a novel video denoising approach of which the main idea is reusing motion estimation resources from the video coding module for video denoising. In most cases, the motion fields produced by real-time video codecs cannot be directly employed in video denoising, since they, as opposed to noise filters, tolerate errors in the motion field. In order to solve this problem, we propose a novel motion-field filtering step that refines the accuracy of the motion estimates to a degree that is required for denoising. Additionally, a novel temporal filter is proposed that is robust against errors in the estimated motion field. Numerical results demonstrate that the proposed denoising scheme is of low-complexity and compares favorably to the state-of-the-art video denoising methods.

A third-order Hermitian zig-zag plate theory is presented as development of the classical cubic zig-zag displacement field. In addition to the capabilities of the previous model ((i) transverse shear flexibility, (ii) through-the-thickness continuity of the transverse shear stresses, (iii) traction-free condition on the two external surfaces of the laminate and (iv) possibility to study damaged interfaces), the Hermitian model offers some interesting improvements ((i) through-the-thickness linear varying transverse displacement, (ii) evaluation of the normal transverse deformability in general and of the corresponding normal stress in particular, (iii) traction equilibrium condition on the external surfaces and (iv) use of the displacements and transverse shear stresses of the external surfaces as degrees of freedom of the plate model). By means of the virtual work principle of the three-dimensional linear elasticity theory, the two-dimensional equations of motion and boundary conditions are obtained. Some numerical results are finally presented to show the particular nature of the through-the-thickness Hermitian shape functions and to test the model performances in evaluating the transverse normal stress.

Pulsed lasers are used in a variety of materials processing applications that range from heating for metallurgical transformation to scribing vehicle identification numbers on anodized aluminum strips. These lasers are commonly configured to deliver a large quantity of heat energy in very short time intervals and over very small areas due to the manner in which radiant energy is stored within, and then released from, the laser resonator. At the present time, little is known about the effect of pulse duration on thermomechanical distortion during heating without phase change. To explore this issue, a boundary element method was developed to calculate temperature, displacement, and thermal stress fields in a layer that is rigidly bonded to an inert semi-space. The layer absorbs thermal energy from a repetitively pulsed laser in the plane of its free surface. The effects of two pulse durations, which differ by four-orders-of-magnitude, were examined in this work. The temporal profiles ...

This paper deals with re®ned ®nite element models based on higher-order displacement ®elds applied to the mechanical and electrical behavior of laminated composite plate structures with embedded and/or surface bonded piezoelectric actuators and sensors. Simulated annealing, a stochastic global optimization technique is implemented to ®nd the optimal location of piezoelectric actuators in order to maximize its eciency. The same technique is also used to solve optimization problems of piezolaminated plate structures where the discrete design variables are the ply orientation angles of orthotropic layers. The implemented scheme helps to recover from the premature convergence to a local optimum, without the need of reinitiating the optimal design process, as it is the case of the gradient-based methods with continuous design variables. To show the performance of the proposed optimization methods, two illustrative and simple examples are presented and discussed.

Recent advances in imaging technology now provide us with 3D images of developing organs. These can be used to extract 3D geometries for simulations of organ development. To solve models on growing domains, the displacement fields between consecutive image frames need to be determined. Here we develop and evaluate different landmark-free algorithms for the determination of such displacement fields from image data. In particular, we examine minimal distance, normal distance, diffusion-based and uniform mapping algorithms and test these algorithms with both synthetic and real data in 2D and 3D. We conclude that in most cases the normal distance algorithm is the method of choice and wherever it fails, diffusion-based mapping provides a good alternative.

Far from the crack tip process zone where non-linear phenomena take place, the mechanical behavior of a cracked medium can be analyzed within the framework of elasticity. Apart from the classical singular stress field associated with the elastic behavior, the effect of a confined process zone is decomposed over a set of (supersingular) fields. Because these fields are indexed by the exponent of their decay with distance from the crack tip, the dominant effect of non-linear mechanisms is characterized by the amplitudes of the first super-singular fields (modes I and II).

A solution for the two-dimensional scattering and diffraction of plane SH waves by canyons of arbitrary shape in an elastic half space is presented. The wave field for arbitrary geometry in this paper is computed numerically by the method of weighted residues (moment method). The wave displacement field computed by the present residual method for the case of a semi-circular canyon was shown to agree analytically and numerically with that computed by the exact closed form series solution. The same observations about ground amplifications, their dependence on frequencies and orientations of the incident waves, can be stated here for canyons of arbitrary shape as previously made for circular canyons.

This paper offers a systematic approach for obtaining the order of stress singularity for different selfsimilar and self-affine fractal cracks. Mode II and Mode III fractal cracks are studied and are shown to introduce the same order of stress singularity as Mode I fractal cracks do. In addition to these three classical modes, a Mode IV is discovered, which is a consequence of the fractal fracture. It is shown that, for this mode, stress has a weaker singularity than it does in the classical modes of fracture when self-affine fractal cracks are considered, and stress has the same order of singularity when self-similar cracks are considered. Considering this new mode of fracture, some single-mode problems of classical fracture mechanics could be mixed-mode problems in fractal fracture mechanics. By imposing a continuous transition from fractal to classical stress and displacement fields, the complete forms of the stress and displacement fields around the tip of a fractal crack are found. Then a universal relationship between fractal and classical stress intensity factors is derived. It is demonstrated that for a Mode IV fractal crack, only one of the stress components is singular; the other stress components are identically zero. Finally, stress singularity for three-dimensional bodies with self-affine fractal cracks is studied. As in the twodimensional case, the fourth mode of fracture introduces a weaker stress singularity for self-affine fractal cracks than classical modes of fracture do.

A continuum finite elements (FE) formulation involving discontinuity of the displacement field to simulate fracture mechanics problems for brittle or quasi-brittle solids is proposed. A homogeneous discontinuity is assumed in a cracked finite element, and a new simple stress-based implementation of the displacement discontinuity is introduced by an appropriate stress field correction to simulate, as usually done in an elastic-plastic classical FE formulation, the mechanical effects of the crack, i.e. the proposed formulation does not introduce any discontinuous displacement field by mean of special or modified shape functions. Both linear elastic and elastic-plastic behaviour of the non-cracked material can be considered. 2D fracture problems are solved by the proposed procedure, to predict the load-displacement behaviour as well as the crack patterns in brittle structures. The new proposed simple FE formulation for discontinuous problems is computationally economic, and maintains the internal continuity of the numerical model with well-known numerical benefits.

AbstractÐNatural selection is the spirit of the genetic algorithm (GA): by keeping the good genes in the current generation, thereby producing better ospring during evolution. The crossover function ensures the heritage of good genes from parent to ospring. Meanwhile, the process of mutation creates a special gene, the character of which does not exist in the parent generation. A program based on genetic algorithms using C language is constructed to invert the parameters of an earthquake-ruptured fault. The veri®cation and application of this code is shown to demonstrate its capabilities. It is determined that this code is able to ®nd the global extreme and can be used to solve more practical problems with constraints gathered from other sources. It is shown that GA is superior to other inverting schema in many aspects. This easy handling and yet powerful algorithm should have many suitable applications in the ®eld of geosciences. #

In the paper the modelling of thermo-mechanical effects in the process of friction welding of corundum ceramics and aluminium is presented. The modelling is performed by means of finite element method. The corundum ceramics contains 97% of Al2O3. The mechanical and temperature fields are considered as coupled fields. Simulation of loading of the elements bonded with the heat flux from friction heat on the contact surface is also shown. The heat flux was modified in the consecutive time increments of numerical solutions by changeable pressure on contact surface. Time depending temperature distribution in the bonded elements is also determined. The temperature distribution on the periphery of the cylindrical surfaces of the ceramics and Al was compared to the temperature measurements done with a thermovision camera. The results of the simulation were compared to those obtained from the tests performed by means of a friction welding machine.

The problem of matching two images can be posed as finding a displacement field which assigns each point of the reference image to a point in the test image. In this paper we present an iterative algorithm to estimate the probability density function relating the intensity distribution of two MR scanners, based on the topological constraints embedded in the elastic matching model. The set of images used as input for the algorithm is the Harvard Atlas. The density estimation resulting from this method is compared with two other algorithms which do not assume any prior information about the media being imaged. The results show that the density estimation obtained with the elastic matching approach produce more realistic deformed images and is suitable to represent MR sensor models

Owing the phase image method (Hytch, 1998), strain fields can be derived from HREM images. The method is here applied to the nanoscale precipitates responsible for hardening in Aluminum alloys. Since the method is a very sensitive one, we have examined the impact of several aspects of the image quality (noise, fluctuations, distortion). The strain field information derived from the HREM image analysis is further introduced in a simulation of the dislocation motion in the matrix.

The challenging topic of a cylinder in line contact with bars of finite thickness, reproducing typical fretting fatigue experiments, is studied by means of the super moiré interferometry technique. The authors consider a normal load on a model producing a contact area of about 4 mm, and subsequently on a tangential load at nearly the sliding limit. The displacement fields, due to the normal load, show that the maximum principal stresses at the edge of the contact area are significantly different from those predicted for the half plane, as well as for bars with a significant thickness, so that the dimension of the contact area and the pressure distribution are nearly the same as those of the half plane. This is confirmed by numerical results obtained by Fellows et al. [7]. Moreover, the experimental results show that the surface stresses induced are not as dependent on the thickness of the bar as those induced by the normal load.

Conventional deformation measurement techniques, such as utilizing a LVDT, a demountable mechanical strain gauge (demec gauge), and an electrical strain gauge, despite their vast usage in experimental studies, suffer several disadvantages, including high cost, time-consuming specimen preparation, and the inability to obtain the whole displacement or strain fields. The aforementioned drawbacks on one hand and the importance of deformation measurements in all civil engineering laboratory tests on the other hand have led researchers to develop other measurement techniques, especially image-based techniques, capable of evaluating whole deformation fields. Among all of these recently developed methods, particle image velocimetry (PIV) has attracted much interest in all branches of civil engineering experimental investigations; PIV is a powerful image-based technique for evaluating both displacement and strain fields by analyzing successive digital images of a field undergoing deformation. Despite its great potential, however, few studies have been reported that use PIV for obtaining deformations for structural tests, especially for evaluating displacement and strain fields in a conventional bending test. Consequently, the intention of the current paper is to show the performance of the PIV technique for displacement and strain field measurement in bending tests of steel and RC beams subjected to four-point flexural loading. Based on different validation experiments of the current study, the PIV technique can be widely used as an alternative to conventional displacement and strain measurement techniques in bending tests. Moreover, the PIV technique demonstrated a great potential for investigating the fracture process in RC beams during the test process.