scholarly journals The Reconstruction of Displacement Fields of Defects in Crystals from Electron Micrographs

1969 ◽  
Vol 22 (3) ◽  
pp. 345 ◽  
Author(s):  
AK Head
Keyword(s):  
Electron Micrographs ◽  
Displacement Field ◽  
Defects In Crystals ◽  
Displacement Fields ◽  
Beam Diffraction

It is shown that the theorem of Part I, namely, that there is a unique reversible connection between displacement fields and electron micrographs for the case of two-beam diffraction and analytic displacement fields, can be extended to many-beam diffraction conditions. The case of a systematic set of diffracting vectors is parallel to the two-beam case with a unique reversible connection between one component of the displacement field and one micrograph. In the general many-beam case there is a unique reversible connection between the vector displacement field and three micrographs.

scholarly journals The Reconstruction of Displacement Fields of Defects in Crystals from Electron Micrographs. I. Analytic Fields

1969 ◽  
Vol 22 (1) ◽  
pp. 43 ◽  
Author(s):  
AK Head
Keyword(s):  
Electron Microscope ◽  
Electron Micrographs ◽  
Approximation Theory ◽  
Displacement Field ◽  
Image Formation ◽  
Defects In Crystals ◽  
Electron Micrograph ◽  
Phase Information ◽  
Displacement Fields ◽  
Electron Microscope Image

The following theorem and corollaries are proved. If the two-beam column approximation theory of electron microscope image formation is assumed and if the displacement field of the object is analytic with zero derivative at infinity, and such that there is a direction in the object along which displacements are constant, then from an electron micrograph that records intensities but no phase information there is an explicit and unique reconstruction of the component of the displacement field of the object in the direction of the diffracting vector, except possibly in some specified singular cases for which the reconstruction cannot be started uniquely.

The Study in the Displacement Field near Crack of the Plexiglass by Frequency Domination Method of the White Speckle

2006 ◽  
Vol 306-308 ◽  
pp. 357-362 ◽  
Author(s):  
Xin Hua Ji ◽  
Fang Yu Xu ◽  
Jin Long Chen ◽  
Yu Wen Qin
Keyword(s):  
Light Source ◽  
Displacement Field ◽  
Vibration Isolation ◽  
Laser Speckle ◽  
Displacement Fields ◽  
Fracture Properties ◽  
Normal Environment

The fracture properties of Plexiglass bright the attentions of the researchers as it is the import material used in aero-planes industry The white speckle technique could obtain displacement fields nondestructively under the normal environment. Compare to the laser speckle method there are no interference light source and the vibration isolation needed. In the paper the principle of the technique is described and the displacement field near crack and SIF are measured. The results show that the technique is very suitable to the application in industry.

scholarly journals Electric field–tunable superconductivity in alternating-twist magic-angle trilayer graphene

Science ◽  
2021 ◽  
Vol 371 (6534) ◽  
pp. 1133-1138 ◽  
Author(s):  
Zeyu Hao ◽  
A. M. Zimmerman ◽  
Patrick Ledwith ◽  
Eslam Khalaf ◽  
Danial Haie Najafabadi ◽  
...  
Keyword(s):  
Displacement Field ◽  
Weak Coupling ◽  
Twist Angle ◽  
Magic Angle ◽  
Van Hove Singularity ◽  
Displacement Fields ◽  
Graphene Layers ◽  
Vdw Heterostructure ◽  
Quantum Phenomena ◽  
Trilayer Graphene

Engineering moiré superlattices by twisting layers in van der Waals (vdW) heterostructures has uncovered a wide array of quantum phenomena. We constructed a vdW heterostructure that consists of three graphene layers stacked with alternating twist angles ±θ. At the average twist angle θ ~ 1.56°, a theoretically predicted “magic angle” for the formation of flat electron bands, we observed displacement field–tunable superconductivity with a maximum critical temperature of 2.1 kelvin. By tuning the doping level and displacement field, we found that superconducting regimes occur in conjunction with flavor polarization of moiré bands and are bounded by a van Hove singularity (vHS) at high displacement fields. Our findings display inconsistencies with a weak coupling description, suggesting that the observed moiré superconductivity has an unconventional nature.

Stress Interference in Three-Dimensional Torsion

1965 ◽  
Vol 32 (1) ◽  
pp. 21-25 ◽  
Author(s):  
R. A. Eubanks
Keyword(s):  
Stress Concentration ◽  
Displacement Field ◽  
Series Solution ◽  
Three Dimensional ◽  
Pure Torsion ◽  
Displacement Fields ◽  
Stress And Displacement Fields ◽  
Spherical Cavities ◽  
Infinite Extent ◽  
Axis Of Symmetry

An explicit series solution is presented for the stress and displacement fields in an elastic body of infinite extent containing two equidiameter spherical cavities. At large distances from the cavities the displacement field coincides with that which arises from pure torsion about the axis of symmetry. Numerical results are presented in graphs which demonstrate the interference of the two sources of stress concentration.

Large Deformation Geometric Nonlinear Beam Element Based on U.L. Format

2012 ◽  
Vol 446-449 ◽  
pp. 3596-3603
Author(s):  
Yong Jun Xia ◽  
Qian Miao
Keyword(s):  
Displacement Field ◽  
Strain Tensor ◽  
Quadratic Function ◽  
Beam Element ◽  
Interpolation Polynomial ◽  
Bernoulli Beam ◽  
Displacement Fields ◽  
First Order ◽  
Geometric Nonlinear ◽  
Euler Bernoulli Beam

Based on the geometric deformation of the Euler-Bernoulli beam element, the geometric nonlinear Euler-Bernoulli beam element based on U.L. formulation is derived. The element’s transverse first-order displacement field is constructed using the cubic Hermite interpolation polynomial, and the first-order Lagrange interpolation polynomial is used for the axial displacement field. Then the additional displacements induced from the rotation of the elemental are included into the transverse and longitudinal displacement fields, so those displacement fields are expressed as the quadratic function of nodal displacement. Afterwards the nonlinear finite element formulas of Euler-Bernoulli beam element under the form of U.L. formulation are derived using Cauchy strain tensor and the principle of virtual displacements. The total equilibrium equation and tangent stiffness for large displacement geometric nonlinear analysis of frame are obtained in the total coordinate system. The correctness of this element is proved by typical example.

The Effects of Dimension Ratio on the Micropolar Peridynamic Model

2010 ◽  
Author(s):  
Y. Ferhat ◽  
I. Ozkol
Keyword(s):  
Finite Element ◽  
Finite Element Methods ◽  
Displacement Field ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Elastic Behavior ◽  
Displacement Fields ◽  
Peridynamic Theory ◽  
Peridynamic Model ◽  
Central Forces

The aim of this study is to investigate the capability of the micropolar peridynamic theory to analyze elastic behavior of plates with various length and width. Since the quantities such as stress and strain are related to displacement field, only the displacement fields of these structures are computed using the micropolar peridynamic model while Poisson’s ratios are kept constant. The results are compared both to the analytical solution of the classical elasticity theory and to the solution of displacement based finite element methods. The software package ANSYS is used for FEM results. To compute the displacement field, a programming code is developed using MATHEMATICA. In the peridynamic theory the constitutive model contains only central forces and can be applied only to the materials having 1/4 Poisson’s ratio. It is the biggest shortcoming of the peridynamic theory. To overcome strict Poisson’s ratio limitation of the peridynamic theory, the micropolar peridynamic theory is proposed. The micropolar peridynamic model allows peridynamic moments, in addition to peridynamic central forces, to interact with the particles inside the material horizon. The introduction of the moments to the theory allows us to deal with the materials having Poisson’s ratio different from 1/4. This modification can be seen as the generalization of the peridynamic theory. Furthermore, the micropolar peridynamic theory can be easily implemented using the finite element methods. This provides easy application of the boundary conditions to the physical model in hand. In this work, by applying the micropolar peridynamic theory, we observed that the displacement fields of the plates are strongly affected by dimensional ratio of the plates. However, it is naturally expected that the micropolar and classical theories should give the same results, at least to a certain extend. This strong dependability on the dimensions of the structure can be a significant shortcoming of the micropolar peridynamic theory.

Calculation of 3D internal displacement fields from 3D X-ray computer tomographic images

1995 ◽  
Vol 449 (1937) ◽  
pp. 537-554 ◽  
Keyword(s):  
Displacement Field ◽  
Permanent Deformation ◽  
Gradient Algorithm ◽  
Internal Displacement ◽  
Small Displacement ◽  
Lagrange Equations ◽  
Displacement Fields ◽  
Plane Shear ◽  
Tomographic Images ◽  
X Ray

We present a new method for computing the internal displacement fields associated with permanent deformations of 3D composite objects with complex internal structure for fields satisfying the small displacement gradient approximation of continuum mechanics. We compute the displacement fields from a sequence of 3D X-ray computed tomography (CT) images. By assuming that the intensity of the tomographic images represents a conserved property which is incompressible, we develop a constrained nonlinear regression model for estimation of the displacement field. Successive linear approximation is then employed and each linear subsidiary problem is solved using variational calculus. We approximate the resulting Euler-Lagrange equations using a finite set of linear equations using finite differencing methods. We solve these equations using a conjugate gradient algorithm in a multiresolution framework. We validate our method using pairs of synthetic images of plane shear flow. Finally, we determine the 3D displacement field in the interior of a cylindrical asphalt/aggregate core loaded to a state of permanent deformation.

scholarly journals Visualization of an internal sand displacement field around a laterally loaded vertical pile

2021 ◽  
Author(s):  
Ranga Walakulu Arachchi
Keyword(s):  
Displacement Field ◽  
Laser Light ◽  
Processing Technique ◽  
Image Processing Technique ◽  
Displacement Fields ◽  
Strain Fields ◽  
Transparent Soil ◽  
Optical Test ◽  
Set Up ◽  
Laterally Loaded

In this research, an internal sand displacement field around a laterally loaded vertical pile is visualized using transparent soil and an image processing technique called digital image cross-correlation (DIC). DIC is a region-based image processing technique which can calculate the displacement field between two images. Transparent soil is made of silica gel with a pore fluid having the same refractive index. Transparent soil has been studied to have the strength and deformation properties similar to natural soil. An optical test set-up is developed to capture the images during loading. This optical test set-up consists of a camera, a laser light, a line generator lens, a loading frame, a Plexiglas mould, and a PC. The saturated fine sand in loose condition is modeled in this research. A laser light sheet is generated to slice the transparent soil model by passing a laser beam through the line generator lens. A distinctive laser speckle pattern is generated through the interaction between the laser light and transparent soil. A series of images are taken from the camera while a scaled pile is being loaded laterally. The displacement fields are calculated by cross-correlating two consecutive images and the corresponding strain fields are deduced from the displacement fields. The development of both displacement and strain fields is investigated by studying deformation and strains at different loading stages. The test results are similar to the published data. This research improves the understanding of soil movement around a laterally loaded pile. It also advances the physical modeling technique using transparent soil.

scholarly journals Visualization of an internal sand displacement field around a laterally loaded vertical pile

2021 ◽  
Author(s):  
Ranga Walakulu Arachchi
Keyword(s):  
Displacement Field ◽  
Laser Light ◽  
Processing Technique ◽  
Image Processing Technique ◽  
Displacement Fields ◽  
Strain Fields ◽  
Transparent Soil ◽  
Optical Test ◽  
Set Up ◽  
Laterally Loaded

In this research, an internal sand displacement field around a laterally loaded vertical pile is visualized using transparent soil and an image processing technique called digital image cross-correlation (DIC). DIC is a region-based image processing technique which can calculate the displacement field between two images. Transparent soil is made of silica gel with a pore fluid having the same refractive index. Transparent soil has been studied to have the strength and deformation properties similar to natural soil. An optical test set-up is developed to capture the images during loading. This optical test set-up consists of a camera, a laser light, a line generator lens, a loading frame, a Plexiglas mould, and a PC. The saturated fine sand in loose condition is modeled in this research. A laser light sheet is generated to slice the transparent soil model by passing a laser beam through the line generator lens. A distinctive laser speckle pattern is generated through the interaction between the laser light and transparent soil. A series of images are taken from the camera while a scaled pile is being loaded laterally. The displacement fields are calculated by cross-correlating two consecutive images and the corresponding strain fields are deduced from the displacement fields. The development of both displacement and strain fields is investigated by studying deformation and strains at different loading stages. The test results are similar to the published data. This research improves the understanding of soil movement around a laterally loaded pile. It also advances the physical modeling technique using transparent soil.

Using delaunay triangularization to characterize non-affine displacement fields during athermal, quasistatic deformation of amorphous solids

Soft Matter ◽  
2021 ◽  
Vol 17 (38) ◽  
pp. 8612-8623
Author(s):  
Weiwei Jin ◽  
Amit Datye ◽  
Udo D. Schwarz ◽  
Mark D. Shattuck ◽  
Corey S. O'Hern
Keyword(s):  
Displacement Field ◽  
Simple Shear ◽  
Strain Field ◽  
Local Strain ◽  
Amorphous Solid ◽  
Amorphous Solids ◽  
Displacement Fields

Representation of the local strain field using Delaunay triangularization and the associated quadrupolar, non-affine displacement field for an amorphous solid undergoing athermal, quasistatic simple shear.

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