Showing papers on "Displacement field published in 2011"

Freehand HDR Imaging of Moving Scenes with Simultaneous Resolution Enhancement

Abstract: Despite their high popularity, common high dynamic range (HDR) methods are still limited in their practical applicability: They assume that the input images are perfectly aligned, which is often violated in practise. Our paper does not only free the user from this unrealistic limitation, but even turns the missing alignment into an advantage: By exploiting the multiple exposures, we can create a super-resolution image. The alignment step is performed by a modern energy-based optic flow approach that takes into account the varying exposure conditions. Moreover, it produces dense displacement fields with subpixel precision. As a consequence, our approach can handle arbitrary complex motion patterns, caused by severe camera shake and moving objects. Additionally, it benefits from several advantages over existing strategies: (i) It is robust under outliers (noise, occlusions, saturation problems) and allows for sharp discontinuities in the displacement field. (ii) The alignment step neither requires camera calibration nor knowledge of the exposure times. (iii) It can be efficiently implemented on CPU and GPU architectures. After the alignment is performed, we use the obtained subpixel accurate displacement fields as input for an energy-based, joint super-resolution and HDR (SR-HDR) approach. It introduces robust data terms and anisotropic smoothness terms in the SR-HDR literature. Our experiments with challenging real world data demonstrate that these novelties are pivotal for the favourable performance of our approach.

Real-Time Regularized Ultrasound Elastography

Abstract: This paper introduces two real-time elastography techniques based on analytic minimization (AM) of regularized cost functions. The first method (1D AM) produces axial strain and integer lateral displacement, while the second method (2D AM) produces both axial and lateral strains. The cost functions incorporate similarity of radio-frequency (RF) data intensity and displacement continuity, making both AM methods robust to small decorrelations present throughout the image. We also exploit techniques from robust statistics to make the methods resistant to large local decorrelations. We further introduce Kalman filtering for calculating the strain field from the displacement field given by the AM methods. Simulation and phantom experiments show that both methods generate strain images with high SNR, CNR and resolution. Both methods work for strains as high as 10% and run in real-time. We also present in vivo patient trials of ablation monitoring. An implementation of the 2D AM method as well as phantom and clinical RF-data can be downloaded.

Generalized continua and non-homogeneous boundary conditions in homogenisation methods

Abstract: Extensions of classical homogenization methods are presented that are used to replace a composite material by an effective generalized continuum model. Homogeneous equivalent second gradient and micromorphic models are considered, establishing links between the macroscopic generalized stress and strain measures and the fields of displacement, strain and stress inside a volume element of composite material. Recently proposed non-homogeneous boundary conditions to be applied to the unit cell, are critically reviewed. In particular, it is shown that such polynomial expansions of the local displacement field must be complemented by a generally non-periodic fluctuation field. A computational strategy is introduced to unambiguously determine this fluctuation. The approach is well-suited for elastic as well as elastoplastic composites.

Voxel-Scale Digital Volume Correlation

Abstract: Among various correlation techniques to find the displacement field of a volume imaged by X-ray tomography at several deformation states, a new approach is proposed where the displacement is measured down to the voxel scale and determined from a mechanically regularized system using the equilibrium gap method, and an additional boundary regularization. It is shown that even if the underlying material behavior is not very well known, this approach leads to extremely small correlation residuals. An excellent stability of the estimated displacement field for noisy (reconstructed) volumes is also observed.

Technical overview of the equivalent static loads method for non-linear static response structural optimization

Abstract: Linear static response structural optimization has been developed fairly well by using the finite element method for linear static analysis. However, development is extremely slow for structural optimization where a non linear static analysis technique is required. Optimization methods using equivalent static loads (ESLs) have been proposed to solve various structural optimization disciplines. The disciplines include linear dynamic response optimization, structural optimization for multi-body dynamic systems, structural optimization for flexible multi-body dynamic systems, nonlinear static response optimization and nonlinear dynamic response optimization. The ESL is defined as the static load that generates the same displacement field by an analysis which is not linear static. An analysis that is not linear static is carried out to evaluate the displacement field. ESLs are evaluated from the displacement field, linear static response optimization is performed by using the ESLs, and the design is updated. This process proceeds in a cyclic manner. A variety of problems have been solved by the ESLs methods. In this paper, the methods are completely overviewed. Various case studies are demonstrated and future research of the methods is discussed.

Analysis of Tunneling-Induced Ground Movements Using Transparent Soil Models

Abstract: Ground movements induced by shallow tunnels affect the safety of nearby underground and aboveground structures. Therefore, the reliable prediction of these movements is important. A transparent soil model is used to investigate not only the surface settlement profile induced by shield tunneling, but also the distribution of soil deformation within the soil mass near the tunnel. The observed surface settlements are consistent with the normal probability curve commonly used for predicting settlement, with only the inflection points or trough width parameters somewhat different. The measured data are consistent with field measurements in that the trough width parameter is independent of the volume loss and linearly proportional to the tunnel depth. An analysis of the displacement field inside the transparent soil models indicates that the subsurface settlement trough at different depths can be approximated by a normal probability curve; and the horizontal displacement can be expressed by the trough width parameter and the volume loss, at the point at which maximum horizontal displacement occurs at the point of inflection. Additionally, the measurements indicate that subsurface ground movements can be in excess of the observed surface settlement, which can adversely affect underground utilities.

Direct Extraction of Cohesive Fracture Properties from Digital Image Correlation: A Hybrid Inverse Technique

Abstract: The accuracy of an adopted cohesive zone model (CZM) can affect the simulated fracture response significantly. The CZM has been usually obtained using global experimental response, e.g., load versus either crack opening displacement or load-line displacement. Apparently, deduction of a local material property from a global response does not provide full confidence of the adopted model. The difficulties are: (1) fundamentally, stress cannot be measured directly and the cohesive stress distribution is non-uniform; (2) accurate measurement of the full crack profile (crack opening displacement at every point) is experimentally difficult to obtain. An attractive feature of digital image correlation (DIC) is that it allows relatively accurate measurement of the whole displacement field on a flat surface. It has been utilized to measure the mode I traction-separation relation. A hybrid inverse method based on combined use of DIC and finite element method is used in this study to compute the cohesive properties of a ductile adhesive, Devcon Plastic Welder II, and a quasi-brittle plastic, G-10/FR4 Garolite. Fracture tests were conducted on single edge-notched beam specimens (SENB) under four-point bending. A full-field DIC algorithm was employed to compute the smooth and continuous displacement field, which is then used as input to a finite element model for inverse analysis through an optimization procedure. The unknown CZM is constructed using a flexible B-spline without any “a priori” assumption on the shape. The inversely computed CZMs for both materials yield consistent results. Finally, the computed CZMs are verified through fracture simulation, which shows good experimental agreement.

Frame-based elastic models

Abstract: We present a new type of deformable model which combines the realism of physically-based continuum mechanics models and the usability of frame-based skinning methods. The degrees of freedom are coordinate frames. In contrast with traditional skinning, frame positions are not scripted but move in reaction to internal body forces. The displacement field is smoothly interpolated using dual quaternion blending. The deformation gradient and its derivatives are computed at each sample point of a deformed object and used in the equations of Lagrangian mechanics to achieve physical realism. This allows easy and very intuitive definition of the degrees of freedom of the deformable object. The meshless discretization allows on-the-fly insertion of frames to create local deformations where needed. We formulate the dynamics of these models in detail and describe some precomputations that can be used for speed. We show that our method is effective for behaviors ranging from simple unimodal deformations to complex realistic deformations comparable with Finite Element simulations. To encourage its use, the software will be freely available in the simulation platform SOFA.

An inverse finite element method for determining the anisotropic properties of the cornea

Abstract: An inverse finite element method was developed to determine the anisotropic properties of bovine cornea from an in vitro inflation experiment. The experiment used digital image correlation (DIC) to measure the three-dimensional surface geometry and displacement field of the cornea at multiple pressures. A finite element model of a bovine cornea was developed using the DIC measured surface geometry of the undeformed specimen. The model was applied to determine five parameters of an anisotropic hyperelastic model that minimized the error between the measured and computed surface displacement field and to investigate the sensitivity of the measured bovine inflation response to variations in the anisotropic properties of the cornea. The results of the parameter optimization revealed that the collagen structure of bovine cornea exhibited a high degree of anisotropy in the limbus region, which agreed with recent histological findings, and a transversely isotropic central region. The parameter study showed that the bovine corneal response to the inflation experiment was sensitive to the shear modulus of the matrix at pressures below the intraocular pressure, the properties of the collagen lamella at higher pressures, and the degree of anisotropy in the limbus region. It was not sensitive to a weak collagen anisotropy in the central region.

Strain evolution in the single point incremental forming process: digital image correlation measurement and finite element prediction

Abstract: Incremental Sheet Forming (ISF) is a relatively new class of sheet forming processes that allow the manufacture of complex geometries based on computer-controlled forming tools in replacement (at least partially) of dedicated tooling. This paper studies the straining behaviour in the Single Point Incremental Forming (SPIF) variant (in which no dedicated tooling at all is required), both on experimental basis using Digital Image Correlation (DIC) and on numerical basis by the Finite Element (FE) method. The aim of the paper is to increase understanding of the deformation mechanisms inherent to SPIF, which is an important issue for the understanding of the high formability observed in this process and also for future strategies to improve the geometrical accuracy. Two distinct large-strain FE formulations, based on shell and first-order reduced integration brick elements, are used to model the sheet during the SPIF processing into the form of a truncated cone. The prediction of the surface strains on the outer surface of the cone is compared to experimentally obtained strains using the DIC technique. It is emphasised that the strain history as calculated from the DIC displacement field depends on the scale of the strain definition. On the modelling side, it is shown that the mesh density in the FE models plays a similar role on the surface strain predictions. A good qualitative agreement has been obtained for the surface strain components. One significant exception has however been found, which concerns the circumferential strain evolution directly under the forming tool. The qualitative discrepancy is explained through a mechanism of through-thickness shear in the experiment, which is not fully captured by the present FE modelling since it shows a bending-dominant accommodation mechanism. The effect of different material constitutive behaviours on strain prediction has also been investigated, the parameters of which were determined by inverse modelling using a specially designed sheet forming test. Isotropic and anisotropic yield criteria are considered, combined with either isotropic or kinematic hardening. The adopted constitutive law has only a limited influence on the surface strains. Finally, the experimental surface strain evolution is compared between two cones with different forming parameters. It is concluded that the way the plastic zone under the forming tool accommodates the moving tool (i.e. by through-thickness shear or rather by bending) depends on the process parameters. The identification of the most determining forming parameter that controls the relative importance of either mechanism is an interesting topic for future research.

Mechanical characterization of hyperelastic polydimethylsiloxane by simple shear test

Abstract: Polydimethylsiloxane (PDMS) is a commercially silicone rubber widely used in mechanical sensors, electronic products and medical devices. This paper describes and analyzes the mechanical behavior of polymer PDMS under large shear deformations. The goal of this work is to estimate experimentally the angular distortions associated with different applied forces, considering a simple shear test based on single lap joints. The experimental procedure to obtain the displacement field is carried out using the digital image correlation (DIC) method, which is an optical-numerical experimental approach developed for full-field and non-contact measurements. The material parameters, associated with classical Mooney-Rivlin model, are estimated from experimental data by means of Levenberg-Marquardt method. Furthermore, due to nonlinear stress–strain behavior observed in experimental data, it is proposed a new nonlinear model and two new parameters are determined in the same way.

A new locking-free formulation for planar, shear deformable, linear and quadratic beam finite elements based on the absolute nodal coordinate formulation

Abstract: Many widely used beam finite element formulations are based either on Reiss- ner's classical nonlinear rod theory or the absolute nodal coordinate formulation (ANCF). Advantages of the second method have been pointed out by several authors; among the ben- efits are the constant mass matrix of ANCF elements, the isoparametric approach and the existence of a consistent displacement field along the whole cross section. Consistency of the displacement field allows simpler, alternative formulations for contact problems or in- elastic materials. Despite conceptional differences of the two formulations, the two models are unified in the present paper. In many applications, a nonlinear large deformation beam element with bending, ax- ial and shear deformation properties is needed. In the present paper, linear and quadratic ANCF shear deformable beam finite elements are presented. A new locking-free continuum mechanics based formulation is compared to the classical Simo and Vu-Quoc formulation based on Reissner's virtual work of internal forces. Additionally, the introduced linear and quadratic ANCF elements are compared to a fully parameterized ANCF element from the literature. The performance of the respective elements is evaluated through analysis of con- ventional static and dynamic example problems. The investigation shows that the obtained linear and quadratic ANCF elements are advantageous compared to the original fully para- meterized ANCF element.

Multiple-Camera Instrumentation of a Single Point Incremental Forming Process Pilot for Shape and 3D Displacement Measurements: Methodology and Results

Abstract: A multiple-camera system (more than two cameras) has been developed to measure the shape variations and the 3D displacement field of a sheet metal part during a Single Point Incremental Forming (SPIF) operation. The modeling of the multiple-camera system and the calibration procedure to determine its parameters are described. The sequence of images taken during the forming operation is processed using a multiple-view Digital Image Correlation (DIC) method and the 3D reconstruction of the part shape is obtained using a Sparse Bundle Adjustment (SBA) method. Two experiments that demonstrate the potentiality of the method are described.

Simultaneous and Integrated Strain Tensor Estimation From Geodetic and Satellite Deformation Measurements to Obtain Three-Dimensional Displacement Maps

Abstract: We propose a new technique, named SISTEM, based on the elastic theory, to efficiently estimate 3-D displacements for producing deformation maps by integrating sparse Global Positioning System (GPS) measurements of deformations and differential interferometric synthetic aperture radar (DInSAR) maps of movements of the Earth's surface. Previous approaches in the literature to combine GPS and DInSAR data require two steps: a first step in which sparse GPS measurements are interpolated in order to fill in GPS displacements in the DInSAR grid and a second step to estimate the 3-D surface displacement maps by using a suitable optimization technique. One of the advantages of the proposed approach, compared to previous ones, is that it does not require the preliminary interpolation of the observed deformation pattern. Indeed, we propose a linear matrix equation which accounts for both the GPS and DInSAR data whose solution simultaneously provides the strain tensor, the displacement field, and the rigid body rotation tensor. The mentioned linear matrix equation is solved by using the weighted least square (WLS), thus assuring both numerical robustness and high computation efficiency. The methodology was tested on both synthetic and experimental data, these last from GPS and DInSAR measurements carried out on Mount Etna during the 2003-2004 period. In order to appreciate the accuracy of the results, the estimated standard errors computed by the WLS are provided. These tests also allow optimizing the choice of specific parameters of this algorithm. This method can be further exploited to account for other available data sets, such as additional interferograms or other geodetic data (e.g., leveling, tilt, etc.), in order to achieve higher accuracy.

A coupled two-scale computational scheme for the failure of periodic quasi-brittle thin planar shells and its application to masonry

Abstract: A coupled two-scale framework is presented for the failure of periodic masonry shell structures, in which membrane-flexural couplings appear. The failure behaviour of textured heterogeneous materials such as masonry is strongly influenced by their mesostructure. Their periodicity and the quasi-brittle nature of their constituents result in complex behaviours such as damage-induced anisotropy properties with localisation of damage, which are difficult to model by means of macroscopic closed-form constitutive laws. The multi-scale computational strategies aim at solving this issue by deducing a homogenised response at the structural scale from a representative volume element (RVE), based on constituents properties and averaging theorems. The constituents inside the RVE may be modelled using any closed-form formulation, depending on the physics to represent. Scale transitions for homogenisation towards a Kirchhoff-Love shell behaviour were recently proposed. The microstructure is represented by a unit cell on which a strain-periodic displacement field is imposed. The localisation of damage at the structural scale is represented by means of embedded strong discontinuities incorporated in the shell description. Based on an assumption of single period failure, the behaviour of these discontinuities is extracted from further damaging RVEs, denoted as localising volume elements (LVEs). An acoustic tensor-based criterion adapted to shell kinematics is used to detect the structural-scale failure and find its orientation. For the material behaviour of the coarse-scale discontinuities, an enhanced upscaling procedure based on an approximate energy consistency has been proposed recently for the in-plane case and is extended to the out-of-plane case. Such a multi-scale scheme can be implemented using parallel computation tools. The corresponding multi-scale simulation results are compared to direct fine-scale computations used as a reference for the case of masonry, showing a good agreement in terms of load bearing capacity, of failure mechanisms and of associated energy dissipation.

Frictional slip plane growth by localization detection and the extended finite element method (XFEM)

Abstract: This paper is concerned with developing a numerical tool for detecting instabilities in elasto-plastic solids (with an emphasis on soils) and inserting a discontinuity at these instabilities allowing the boundary value problem to proceed beyond these instabilities. This consists of implementing an algorithm for detection of strong discontinuities within a finite element (FE) framework. These discontinuities are then inserted into the FE problem through the use of a displacement field enrichment technique called the extended finite element method (XFEM). The newly formed discontinuities are governed by a Mohr–Coulomb frictional law that is enforced by a penalty method. This implementation within an FE framework is then tested on a compressive soil block and a soil slope where the discontinuity is inserted and grown according to the localization detection. Copyright © 2010 John Wiley & Sons, Ltd.

A Sixth-Order Theory of Shear Deformable Beams With Variational Consistent Boundary Conditions

Abstract: This paper presents the derivation of a new beam theory with the sixth-order differential equilibrium equations for the analysis of shear deformable beams. A sixth-order beam theory is desirable since the displacement constraints of some typical shear flexible beams clearly indicate that the boundary conditions corresponding to these constraints can be properly satisfied only by the boundary conditions associated with the sixth-order differential equilibrium equations as opposed to the fourth-order equilibrium equations in Timoshenko beam theory. The present beam theory is composed of three parts: the simple third-order kinematics of displacements reduced from the higher-order displacement field derived previously by the authors, a system of sixth-order differential equilibrium equations in terms of two generalized displacements w and φ x of beam cross sections, and three boundary conditions at each end of shear deformable beams. A technique for the analytical solution of the new beam theory is also presented. To demonstrate the advantages and accuracy of the new sixth-order beam theory for the analysis of shear flexible beams, the proposed beam theory is applied to solve analytically three classical beam bending problems to which the fourth-order beam theory of Timoshenko has created some questions on the boundary conditions. The present solutions of these examples agree well with the elasticity solutions, and in particular they also show that the present sixth-order beam theory is capable of characterizing some boundary layer behavior near the beam ends or loading points.

A multi-field coupled FEM model for one-step-forming process of spark plasma sintering considering local densification of powder material

Abstract: A mechanical constitutive model of powder material is introduced to a fully coupled thermal–electric–mechanical finite element model to simulate the one-step-forming spark plasma sintering (SPS) process of metal powders. The effects of displacement field and local density distribution on sintering are considered in this article, which are generally neglected in the existing SPS models. The mechanical, thermal, and electrical parameters of powders are assumed as functions of local relative density and temperature. The simulated varying displacement field remodels the distributions of temperature and electric potential by changing the contact thermoelectric resistances. For the 20, 40, and 60 MPa external pressures, the simulation indicates that the sintering temperature and the temperature gradient within powders are decreased by enhancing the external pressure, and the comprehensive effect of stress promotes the densification of the colder regions. Thus, the interrelationship between the temperature gradient and the intrinsic stress distribution plays an important role in the densification mechanism of SPS powders.

Identification of cohesive zone model and elastic parameters of fiber-reinforced cementitious composites using digital image correlation and a hybrid inverse technique

Abstract: Traditional methods for the inverse identification of elastic properties and local cohesive zone model (CZM) of solids utilize only global experimental data. In contrast, this paper addresses the inverse identification of elastic properties and CZM of a range of materials, using full-field displacement through an optimization technique in a finite element (FE) framework. The new experimental–numerical hybrid approach has been applied to fiber-reinforced cementitious composites (FRCC). PVA microfibers are used at four volume fractions: 0.5%, 1%, 2% and 3%. Digital image correlation (DIC) technique is used to measure surface displacement fields of the test specimens. Four-point bend tests are carried out for the measurement of the modulus of elasticity, E, and the Poisson’s ratio, ν, while single edge-notched beams (SENB) are used for measurement of mode-I CZM parameters. A finite element update inverse formulation, which is based on minimization of the difference between measured and computed displacement field, is used for both identification problems. For the identification of E and ν, linearized form of the Hooke’s tensor in plane stress condition has been derived for two-dimensional linear elasticity in FE frame, and Newton–Raphson solver is employed for the inverse problem. For the identification of the CZM, generic spline curves have been used for the parameterization of any CZM thus avoiding the need of an assumption of the CZM shape, while derivative-free Nelder–Mead optimization with CZM shape regularization is employed as the solution method, which reduces the complexity of numerical implementation and improves robustness. The computed E and ν are consistent with published results. The computed CZMs of the FRCCs with different fiber volume fractions reveal a strain-hardening characteristic. The computed CZM is used in direct problem simulation, the results of which are consistent with the experimental global response.

A homogeneous limit methodology and refinements of computationally efficient zigzag theory for homogeneous, laminated composite, and sandwich plates

Abstract: The Refined Zigzag Theory (RZT) for homogeneous, laminated composite, and sandwich plates is revisited to offer a fresh insight into its fundamental assumptions and practical possibilities. The theory is introduced from a multiscale formalism starting with the inplane displacement field expressed as a superposition of coarse and fine contributions. The coarse displacement field is that of first-order shear-deformation theory, whereas the fine displacement field has a piecewise-linear zigzag distribution through the thickness. The resulting kinematic field provides a more realistic representation of the deformation states of transverse-shear-flexible plates than other similar theories. The condition of limiting homogeneity of transverse-shear properties is proposed and yields four distinct variants of zigzag functions. Analytic solutions for highly heterogeneous sandwich plates undergoing elastostatic deformations are used to identify the best-performing zigzag functions. Unlike previously used methods, which often result in anomalous conditions and nonphysical solutions, the present theory does not rely on transverse-shear-stress equilibrium constraints. For all material systems, there are no requirements for use of transverse-shear correction factors to yield accurate results. To model homogeneous plates with the full power of zigzag kinematics, infinitesimally small perturbations in the transverse shear properties are derived, thus enabling highly accurate predictions of homogeneous-plate behavior without the use of shear correction factors. The RZT predictive capabilities to model highly heterogeneous sandwich plates are critically assessed, demonstrating its superior efficiency, accuracy, and a wide range of applicability. This theory, which is derived from the virtual work principle, is well-suited for developing computationally efficient, C0 a continuous function of (x1,x2) coordinates whose first-order derivatives are discontinuous along finite element interfaces and is thus appropriate for the analysis and design of high-performance load-bearing aerospace structures. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010

Identification algorithm for fracture parameters by combining DIC and FEM approaches

Abstract: This research program focuses on a hybrid experimental and numerical approach to identifying the mechanical state in the vicinity of a crack. The digital image correlation, as corrected by interpolating a theoretical displacement field, enables determining the crack opening intensity factors representative of the kinematic state of crack lips. A finite element model is introduced for calculating stress intensity factors. The parallelism derived from the DIC method and FEM approach is presented by means of a specific identification algorithm that allows computing the energy release rate within a common finite element mesh. This algorithm is then illustrated by testing the opening-mode configuration for a PVC sample.