Showing papers on "Displacement field published in 1993"

Accurate measurement of three-dimensional deformations in deformable and rigid bodies using computer vision

Abstract: Recently, digital-image-correlation techniques have been used to accurately determine two-dimensional in-plane displacements and strains. An extension of the two-dimensional method to the acquisition of accurate, three-dimensional surfacedisplacement data from a stereo pair of CCD cameras is presented in this paper. A pin-hole camera model is used to express the transformation relating three-dimensional world coordinates to two-dimensional computer-image coordinates by the use of camera extrinsic and intrinsic parameters. Accurate camera model parameters are obtained for each camera independently by (a) using several points which have three-dimensional world coordinates that are accurate within 0.001 mm and (b) using two-dimensional image-correlation methods that are accurate to within 0.05 pixels to obtain the computer-image coordinates of various object positions. A nonlinear, least-squares method is used to select the optimal camera parameters such that the deviations between the measured and estimated image positions are minimized. Using multiple orientations of the cameras, the accuracy of the methodology is tested by performing translation tests. Using theoretical error estimates, error analyses are presented. To verify the methodology for actual tests both the displacement field for a cantilever beam and also the surface, three-dimensional displacement and strain fields for a 304L stainless-steel compact-tension specimen were experimentally obtained using stereo vision. Results indicate that the three-dimensional measurement methodology, when combined with two-dimensional digital correlation for subpixel accuracy, is a viable tool for the accurate measurement of surface displacements and strains.

Efficient higher order composite plate theory for general lamination configurations

Abstract: An efficient higher order plate theory for laminated composites is developed. A composite plate theory for general lamination configurations is obtained by superimposing a cubic varying displacement field on a zig-zag linearly varying displacement. The theory has the same number of dependent unknowns as first-order shear deformation theory, and the number of unknowns is independent of the number of layers. The displacement satisfies transverse shear stress continuity conditions at the interface between layers as well as shear free surface conditions. Thus, an artificial shear correction factor is not needed. To demonstrate and compare with other theories, the analytical solution for cylindrical bending is obtained. The present theory gives deflections and stresses that compare well with other known theories.

Higher‐order MITC general shell elements

Abstract: Two mixed-interpolated general shell finite elements for non-linear analysis-a 9-node element and a 16-node element-are presented. The elements are based on the Mixed Interpolation of Tensorial Components (MITC) approach in which the covariant strain component fields for the in-plane and shear actions are interpolated and tied to the also interpolated displacement field. Both the 9-node element, referred to as the MITC9 element, and the 16-node element, referred to as the MITC16 element, are tested numerically and found to have high predictive capabilities.

Observations of nonlinear elastic wave behavior in sandstone

Abstract: An experimental investigation of nonlinear elastic wave behavior was conducted using a 2‐m‐long cylindrical rod of Berea sandstone in order to study the strong elastic nonlinearity that is characteristic of microcracked materials. Measurements of the displacement field at distance x from the source show rich harmonic content with harmonic amplitudes depending on x, source frequency, and source amplitude. The amplitude of the 2ω harmonic is found to grow linearly with x and as the square of both the source frequency ω and the source amplitude U. This behavior is in agreement with the predictions of nonlinear elasticity theory for a system with cubic anharmonicity. From the measured amplitude of the 2ω harmonic the parameter ‖β‖, a measure of the strength of the cubic anharmonicity, is found to be of order 104 (7.0×103±25%). This value is orders of magnitude greater than that found in ordinary uncracked materials. These results suggest that wave distortion effects due to nonlinear elasticity can be large in seismic wave propagation and significantly influence the relationship of seismic signal to seismic source.

Computer-aided speckle interferometry using spectral amplitude fringes

Abstract: A fully automatic speckle metrology technique is developed. Two speckle patterns of a specimen, one before and one after the specimen deformation, are captured by a video camera. An equivalent double-exposure speckle pattern is obtained by superimposing the two digital images. The superimposed speckle pattern is then segmented into a series of small subimages. For each subimage a fast-Fourier transform is applied and a computer-generated Young’s fringe pattern is obtained. The fringe pattern, which characterizes the local displacement vector, is analyzed by a second fast-Fourier transform. The local displacement vector is determined by a cardinal interpolation and a crest searching around a signal peak in the second spectral domain. An artificial rigid shift between the two images is introduced in the cases of extremely large or small displacements. From analysis of all subimage pairs of the whole superimposed speckle pattern a complete two-dimensional displacement field is deduced. Experimental results using laser as well as white-light speckle patterns are demonstrated.

Frictional contact finite-elements based on mixed variational-principles

Abstract: This paper presents an original approach to the numerical modelling of unilateral contact by the finite element method. The main point is the development of mixed contact finite elements in which the displacement field and the contact stress field (pressure and friction shear) are discretized independently. The theory, based on variational principles, is first presented in the framework of infinitesimal deformations and, subsequently, is extended to large inelastic strains.

A three‐dimensional multilayer composite finite element for stress analysis of composite laminates

Abstract: A three-dimensional multilayer composite finite element method has been developed based on a composite variational functional which takes three in-plane strains ex, ex, exy and three transverse stresses σz, σyz, σxz as the basic variables. The continuity of the transverse stresses σz, σyz, σxz across the laminate thickness is assured a priori by introducing a partial stress field parameter α which is associated with the lower and upper surfaces of a lamina in a laminate. A method has been developed to form the partial stress field based on the assumed displacement field. With this method, a three dimensional (3-D) multilayer composite finite element is formulated for stress analysis of composite laminates. A numerical example is given, which shows some advantages of this composite element.

Radiation from point sources in general anisotropic media

Abstract: SUMMARY A procedure to evaluate the geometrical properties of the slowness surface for arbitrary anisotropic media is presented. This allows us to use results for computing the displacement field from point sources in general anisotropic media utilizing the Gaussian curvature of the slowness surface of the considered waves. Since the formulae used are based on high frequency asymptotics the procedure gives reliable results as long as no parabolic points of the slowness surface are encountered. Radiation patterns of point sources for models representing rocks in the crust and upper mantle are presented and discussed. The radiation from point sources in anisotropic models is compared with the radiation from point sources in average isotropic models to emphasize the differences. Anisotropy is either caused by aligned cracks (crustal rocks) or by aligned olivine crystals (upper mantle rocks). Considering models of aligned cracks differing only in the physical parameters of the crack material (water or gas) significantly different radiation patterns are obtained. Models with wet cracks exhibit focusing of quasi S-wave energy for some directions whereas this effect is not observed for the corresponding model with dry cracks. The quasi S-wave radiation pattern from explosions are multilobed and the wet crack models exhibit more lobes than the dry crack models. The radiation of single forces in olivine shows strong energy focusing (wave tuning) of quasi S waves, however, for realistic compositions of upper mantle rocks with some 10 per cent of preferentially orientated olivine this wave tuning is less pronounced.

Phase diagram and critical behavior of the Si-Ge unmixing transition: A Monte Carlo study of a model with elastic degrees of freedom.

Abstract: A statistical-mechanical model of binary semiconductor alloys, consisting of a distortable diamond lattice whose sites may be occupied by A atoms, B atoms, or vacancies, is studied by Monte Carlo computer simulations. By extending a grand-canonical lattice gas, the model allows for atomic displacements governed by the Keating valence force field. Unphysical boundary conditions are avoided by keeping the pressure constant. This model is similar to a compressible Ising model, but differs from it by the occurrence of a bilinear coupling between spin field and displacement field. The interplay between the chemical and translational degrees of freedom shows up in the form of the unmixing phase diagram of a system whose parameters were chosen in an attempt to mimic a Si-Ge alloy. Methods of thermodynamic integration to obtain the free energies of different phases are discussed. The critical behavior of the unmixing transition is studied by a multihistogram data analysis. The finite-size scaling of the data is in better agreement with mean-field-like critical behavior than with an Ising transition or Fisher-renormalized exponents. Vegard's law is verified, and it is shown that the Keating potential leads to a negative coefficient of thermal expansion.

The singular elastostatic field due to a crack in rubberlike materials

Abstract: Within the framework of finite-strain elastostatics an asymptotic analysis is carried out in order to calculate the singular field near the crack tip in a slab under conditions of plane deformation. A class of Ogden-Ball hyperelastic rubberlike materials and general loading conditions ensuring vanishing tractions on the crack faces near the crack tip are considered. It is shown that the singular deformation field near the crack tip can be specified by applying a rigid body rotation with a subsequent parallel translation to a so-called canonical field. The adjective canonical is adopted here to denote the field with symmetrically opening crack faces, just resembling the displacement field of the symmetric mode in linear elastic fracture mechanics. No analogy with the antisymmetric mode is possible, and the crack equilibrium criterion requires only one stress intensity factor to be determined.

Discrete-layer models for multilayered shells accounting for interlayer continuity

Abstract: Based on adiscrete-layer approach, in a recent series of papers, the first author has developed the equations governing the elastodynamic behaviour of moderately thick multilayered anisotropic plates by making use of a displacement field which allows a non-linear variation of the in-plane displacements through the laminate thickness and fulfilsa priori the static and geometric continuity conditions at the interfaces between two adjacent layers. Based on this approach, in the present paper we derive the equations of motion and variationally consistent boundary conditions of moderately multilayered anisotropic shells. To show the accuracy and reliability of the proposed approach, closed-form solutions are given and compared with results from three-dimensional elasticity and other approximate bi-dimensional models with and without continuous interlayer stresses. Based on this numerical investigation, the proposed approach appears to work very well.

Spatial patterns and size effects in shear zones : A hyperelastic model with higher-order gradients

Abstract: The onset of localization of the deformation is analysed from the results of a two-dimensional bifurcation analysis for a shear zone of infinite extent and of finite thickness. The material is assumed to be incompressible and hyperelastic and, to account for micro-structural effects, to have an energy density that is a function of second-order deformation gradients. With such a model, the onset of strain localization is associated with a bifurcation but not with a change of type of the governing partial differential equations. It is demonstrated that both layer thickness and the exact nature of the boundary conditions affect that bifurcation. As expected, the incremental displacement field that characterizes the first loss of uniqueness has a spatial variation across but not along the shear zone. However, and contrary to a common belief, it is shown that the displacement field could vary in these two directions, for a range of values of the material properties. Consequences of this wavy pattern for the onset of failure during localization are discussed.

Spatiotemporal dynamics due to stick-slip friction in an elastic-membrane system.

Abstract: Frictional stick-slip dynamics is studied experimentally in an elastic continuum by means of a stretched latex membrane in contact with a translating glass rod. In contrast to other laboratory-scale experiments, the characteristic stiffness length here is small compared to the size of the system but large compared to the spatial resolution of the measurements. The internal displacement field u(s,t) is measured in detail with imaging techniques, which are shown to be more sensitive than total-force measurements. The magnitudes \ensuremath{\mu} of slipping events extend over a wide range and include both small localized events and large spatially extended ones. The shape of the distribution P(\ensuremath{\mu}) depends somewhat on the measurement threshold and also varies with the parameters describing the frictional interaction, which are affected by wear. The frictional force increases with velocity and an instability is due to waves of detachment. The temporal statistics of slipping events are also discussed. The experimental results are compared qualitatively to simplified models of earthquake faults.

Polar optical oscillations of layered semiconductor structures in the long-wavelength limit

Abstract: Polar optical oscillations coupled to unretarted electric fields are discussed for the long-wavelength limit with application to layered semiconductor structures (quantum wells, superlattice, etc.). A Lagrangian formalism is adopted for the deduction of the equations of both mechanical and electrical quantities. The obtained equations bear the form of second-order coupled differential equations for the fundamental quantities, displacement field u and electric potential г. Matching boundry conditions are rigorously derived from the equations and interpreted physically. The particular case of materials belonging to the cubic symmetry is discussed with special application to the double heterostructure. Some comments are also made about the case of isotropic constituent materials. We have thus settled a theory for long- wavelength oscillations taking into account dispersion up to quadratic terms in the wave vector (through the introduction of medium internal stresses) with the aim of avoiding some problems which have been detected and discussed in earlier treatments of this subject.

Asymmetric actuation and sensing of a beam using piezoelectric materials

Abstract: The purpose of the present work is the modeling of a beam actuated by a ceramic piezoelectric on the top with a PVDF piezoelectric on the opposite side acting as a sensor The two piezoelectric are different in types, may be of arbitrary length and can be positioned independently along the beam Since there is only one actuator, the asymmetric excitation induces transverse and axial displacement in the beam This asymmetric actuation contrast with the symmetric actuation normally considered in the literature Symmetric actuation implies no axial displacement Here, both piezos are considered perfectly bonded to the beam and the Bernoulli–Euler hypothesis is used for the displacement field The variational approach with Hamilton’s principle is put to use in the theoretical model Hamilton’s principle states that the definite time integral of the Lagrangian shall be stationary This formulation, which is energy based, allows one to consider any boundary conditions and to take into account the dynamic effect

Slow modes in crystals: A method to study elastic constants.

Abstract: We propose a microscopic expression for a displacement field in a crystal and derive nondissipative equations of motion for the slow hydrodynamic and broken-symmetry modes, including the vacancy-diffusion mode. Comparing these equations with the microscopic ideal equations of elasticity we obtain exact expressions for isothermal elastic constants

Crustal Deformation Associated with Two-Dimensional Thrust Faulting.

Abstract: The effect of the source-depth and the dip of the fault on the surface displacement field due to a long thrust fault embedded in an elastic half-space is studied. It is found that, for small dip angles, the displacement field is highly asymmetric about the fault strike, the displacement of the footwall is very small, and the horizontal displacement of the hanging wall shows a wavy pattern. The vertical displacement of the hanging wall is an uplift near the fault. For small dip angles, this uplift is maximum at a point almost vertically above the upper edge of the fault. As we go away from the fault strike, the vertical displacement changes sign, i.e., it becomes subsidence. For small dip angles, this subsidence is maximum at a point roughly vertically above the lower edge of the fault. Steeper fault dips decrease the subsidence relative to the uplift. For a vertical dip-slip fault, the horizontal displacement is completely symmetric about the fault strike and the vertical displacement is completely antisymmetric. The variation of the coseismic and postseismic shear stresses and shear strains for a surface-breaking long thrust fault with depth is studied for a viscoelastic half-space. It is found that, while the coseismic and postseismic shear stresses are of opposite signs, the coseismic and postseismic shear strains are of the same sign.

The mean field theory for image motion estimation

Abstract: It is shown how the MFT (mean field theory) can be applied to MRF (Markov random field) model-based motion estimation. Specifically, the motion is characterized by a coupled MRF including a displacement field (motion continuity), a line field (motion discontinuity), and a segmentation field (identifying uncovered areas). These fields are estimated by using the MFT. The efficacy of this approach is demonstrated on synthetic and real-world images. >