Showing papers on "Displacement field published in 2002"

Traction fields, moments, and strain energy that cells exert on their surroundings

Abstract: Adherent cells exert tractions on their surroundings. These tractions can be measured by observing the displacements of beads embedded on a flexible gel substrate on which the cells are cultured. This paper presents an exact solution to the problem of computing the traction field from the observed displacement field. The solution rests on recasting the relationship between displacements and tractions into Fourier space, where the recovery of the traction field is especially simple. We present two subcases of the solution, depending on whether or not tractions outside the observed cell boundaries are set to be zero. The implementation is computationally efficient. We also give the solution for the traction field in a representative human airway smooth muscle cell contracted by treatment with histamine. Finally, we give explicit formulas for reducing the traction and displacement fields to contraction moments, the orientation of the principal axes of traction, and the strain energy imparted by the cell to the substrate.

Non-planar 3d crack growth by the extended finite element and level sets- part ii: level set update

Abstract: We present a level set method for treating the growth of non-planar three-dimensional cracks.The crack is defined by two almost-orthogonal level sets (signed distance functions). One of them describes the crack as a two-dimensional surface in a three-dimensional space, and the second is used to describe the one-dimensional crack front, which is the intersection of the two level sets. A Hamilton–Jacobi equation is used to update the level sets. A velocity extension is developed that preserves the old crack surface and can accurately generate the growing surface. The technique is coupled with the extended finite element method which approximates the displacement field with a discontinuous partition of unity. This displacement field is constructed directly in terms of the level sets, so the discretization by finite elements requires no explicit representation of the crack surface. Numerical experiments show the robustness of the method, both in accuracy and in treating cracks with significant changes in topology. Copyright © 2002 John Wiley & Sons, Ltd.

Systematic errors in digital image correlation due to undermatched subset shape functions

Abstract: Digital image correlation techniques are commonly used to measure specimen displacements by finding correspondences between an image of the specimen in an undeformed or reference configuration and a second image under load. To establish correspondences between the two images, numerical techniques are used to locate an initially square image subset in a reference image within an image taken under load. During this process, shape functions of varying order can be applied to the initially square subset. Zero order shape functions permit the subset to translate rigidly, while first-order shape functions represent an affine transform of the subset that permits a combination of translation, rotation, shear and normal strains. In this article, the systematic errors that arise from the use of undermatched shape function, i.e., shape functions of lower order than the actual displacement field, are analyzed. It is shown that, under certain conditions, the shape functions used can be approximated by a Savitzky-Golay low-pass filter applied to the displacement functions, permitting a convenient error analysis. Furthermore, this analysis is not limited to the displacements, but naturally extends to the higher-order terms included in the shape functions. This permits a direct analysis of the systematic strain errors associated with an undermatched shape function. Detailed numerical studies are presented for the case of a second-order displacement field and first- and second-order shape functions. Finally, the relation of this work to previously published studies is discussed.

Multiscale displacement field measurements of compressed mineral-wool samples by digital image correlation

Abstract: We propose a multiscale approach to determine the displacement field by digital image correlation. The displacement field is first estimated on a coarse resolution image and progressively finer details are introduced in the analysis as the displacement is more and more securely and accurately determined. Such a scheme has been developed to increase the robustness, accuracy, and reliability of the image-matching algorithm. The procedure is used on two different types of examples. The first one deals with a representative image that is deformed precisely and purposefully to assess the intrinsic performances. In particular, the maximum measurable strain is determined. The second case deals with a series of pictures taken during compression experiments on mineral-wool samples. The different steps of the procedure are analyzed and their respective role is assessed. Both reflection and transmission images are tested.

Experimental investigation of plastic grain interaction

Abstract: 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.

Fracture in mode I using a conserved phase-field model.

Abstract: We present a continuum phase-field model of crack propagation. It includes a phase-field that is proportional to the mass density and a displacement field that is governed by linear elastic theory. Generic macroscopic crack growth laws emerge naturally from this model. In contrast to classical continuum fracture mechanics simulations, our model avoids numerical front tracking. The added phase-field smooths the sharp interface, enabling us to use equations of motion for the material (grounded in basic physical principles) rather than for the interface (which often are deduced from complicated theories or empirical observations). The interface dynamics thus emerges naturally. In this paper, we look at stationary solutions of the model, mode I fracture, and also discuss numerical issues. We find that the Griffith's threshold underestimates the critical value at which our system fractures due to long wavelength modes excited by the fracture process.

Nonrigid registration of 3-D free-hand ultrasound images of the breast

Abstract: Three-dimensional (3-D) ultrasound imaging of the breast enables better assessment of diseases than conventional two-dimensional (2-D) imaging. Free-hand techniques are often used for generating 3-D data from a sequence of 2-D slice images. However, the breast deforms substantially during scanning because it is composed primarily of soft tissue. This often causes tissue misregistration in spatial compounding of multiple scan sweeps. To overcome this problem, in this paper, instead of introducing additional constraints on scanning conditions, we use image processing techniques. We present a fully automatic algorithm for 3-D nonlinear registration of free-hand ultrasound data. It uses a block matching scheme and local statistics to estimate local tissue deformation. A Bayesian regularization method is applied to the sample displacement field. The final deformation field is obtained by fitting a B-spline approximating mesh to the sample displacement field. Registration accuracy is evaluated using phantom data and similar registration errors are achieved with (0.19 mm) and without (0.16 mm) gaps in the data. Experimental results show that registration is crucial in spatial compounding of different sweeps. The execution time of the method on moderate hardware is sufficiently fast for fairly large research studies.

Dispersion and excitability of guided acoustic waves in isotropic beams with arbitrary cross section

Abstract: A finite element (FE) technique for computing the properties of guided waves that can exist in an isotropic beam of arbitrary cross section is presented The FE model uses a two-dimensional mesh to represent a cross section through the beam and cyclic axial symmetry conditions to prescribe the displacement field perpendicular to the mesh FE results are presented for plate and angle sections Excitability functions are calculated and implications for transducer placement are considered

Correlation image velocimetry: a spectral approach

Abstract: A method, believed to be new, is introduced to evaluate displacement fields from the analysis of a deformed image compared with a reference image. In contrast to standard methods, which determine a piecewise constant displacement field, the present method gives direct access to spectral decomposition of the displacement field. A minimization procedure is derived and used twice: first, to determine an affine displacement field and, then, the spectral components of the residual displacement. Although the method is applicable to any space dimension, only cases dealing with one-dimensional signals are reported: First, a purely synthetic example is discussed to estimate the intrinsic performance of the method, and a second case deals with a profile extracted from a sample of compressed glass wool.

Earthquake Response and Energy Evaluation of Inelastic Structures

Abstract: A computational method is derived to characterize the energy in inelastic structures and the transfer among various energy forms over the duration of an earthquake. This computational method is based on the force analogy method, which uses a change in displacement field to represent the inelastic behavior of structure instead of the traditional method of changing stiffness. The evaluation of plastic energy due to inelastic deformation in the structure becomes very simple using the force analogy method, where the accumulation of plastic energy due to plastic rotations is exactly equal to the elastic moment multiplied by the change in plastic rotations. In addition, this plastic energy formula can be used for any material with predefined stress-strain relationship, and therefore the transfer of energy among various forms can be calculated at any specific time. Once the energy equation is derived, numerical analyses are performed on a single degree of freedom system to study the characteristics of energy transfer. This is then extended to study the transfer of energy among various forms in a multidegree of freedom system. These two studies show that the analytically derived equation for plastic energy is accurate in studying the structural energy response due to earthquake excitations.

Spectral approach to displacement evaluation from image analysis

Abstract: A new approach to determine the displacement field between a reference and a deformed image is introduced. The method is based on a spectral decomposition of the displacement field which is determined through a multi-scale approach. The method is tested here on an artificial example by using computer-generated images devoid of boundary effects ( i.e. , periodic boundary conditions are used in the image texture and displacement field). The performance of the proposed algorithm allows for the determination of the prescribed displacement field up to machine precision, for a strain field whose trace extends from −50% to 40% with a root-mean-square average of 15%, within sub-minute runs on a standard PC.

Free vibration of sandwich plates with laminated faces

Abstract: Description is given of the development of a spline finite strip method for predicting the natural frequencies and modes of conventional rectangular sandwich plates. The faceplates are treated as being classically thin and may be of composite laminated construction. The core is modelled as a three-dimensional body. Finite strip stiffness and mass properties are based on a displacement field which represents eight fundamental through-thickness displacements as a series of products of longitudinal B-spline functions and crosswise Lagrangian or Hermitian polynominal shape functions. The solution procedure utilizes the efficient superstrip concept in conjunction with the extended Sturm sequence-bisection approach. A variety of applications of the developed analysis capability is described which demonstrates the nature of the convergence of the finite strip predictions of natural frequencies and the close comparison of these predictions with available results in the literature, and also the use of the capability in parametric studies.

Linear elastic chain with a hyper-pre-stress

Abstract: To account for surface relaxation in ultra-thin films, we consider the simplest one-dimensional discrete chain with harmonic interactions of up to second nearest neighbors We assume that the springs, describing interactions of the nearest neighbors (NN) and next to nearest neighbors (NNN) have incompatible reference lengths, which introduce a hyper-pre-stress and results in a formation of the exponential surface boundary layers For a finite body loaded by a system of (double) forces at the boundary, we explicitly find the displacement field and compute the energies of the inhomogeneous stressed and reference configurations We then obtain a simple expression for the hyper-pre-stress-related contribution to the surface energy and show an unusual scaling of the total energy with the film thickness For ultra-thin films we report an anomalous stiffness increase due to the overlapping of the surface boundary layers Implications of the micro level hyper-pre-stress in fracture mechanics and in the theory of non-Bravais lattices are also discussed

Interlaminar Stress Analysis of Shell Structures with Piezoelectric Patch Including Thermal Loading

Abstract: Interlaminar stress distribution in smart composite shells using a coupled thermal-piezoelectric-mechanical model is investigated. To maintain local accuracy of stress distributions, the trial displacement field is assumed layerwise higher order and C 0 continuous through the entire laminate thickness, accommodating zigzag in-plane warping and interlaminar shear stress continuity. The temperature and electrical fields are modeled using higher-order descriptions that can satisfy surface flux boundary conditions at structural surfaces and equipotential conditions at electrode surfaces. These assumptions ensure computational efficiency. A variational principle, addressing the interaction between thermal, piezoelectric, and mechanical fields, is used to derive the governing equations of equilibrium. The proposed theory is used to investigate the cylindrical bending problem of simply supported composite host structures with attached piezoelectric actuators, subject to a combination of mechanical, piezo-electric, and thermal loading. The interlaminar stress distributions under comprehensive loading are presented for different geometries and stacking sequences. The effects of two-way piezoelectric and thermal coupling on the stress distributions are investigated. The significance of the thermal mismatch effect on interlaminar stress distribution is also discussed. The results from present theory are validated with available exact elasticity solutions.