Elastic displacement field of point defects in anisotropic cubic crystals

1972 ◽  
Vol 255 (4) ◽  
pp. 315-324 ◽  
Author(s):  
P. H. Dederichs ◽  
J. Pollmann
Keyword(s):  
Point Defects ◽  
Displacement Field ◽  
Elastic Displacement ◽  
Cubic Crystals

scholarly journals MFS fading regularization method for the identification of boundary conditions from partial elastic displacement field data

2018 ◽  
Author(s):  
L. Caillé ◽  
J L. Hanus ◽  
F. Delvare ◽  
N. Michaux-Leblonda
Keyword(s):  
Inverse Problem ◽  
Boundary Conditions ◽  
Displacement Field ◽  
Regularization Method ◽  
Synthetic Data ◽  
Fundamental Solutions ◽  
Image Correlation ◽  
Method Of Fundamental Solutions ◽  
Elastic Displacement ◽  
Isotropic Elasticity

A method is proposed to solve an inverse problem in twodimensional linear isotropic elasticity. The inverse problem consists of the determination of both the entire displacement field and the boundary conditions inaccessible to the measurement from the partial knowledge of the displacement field. The algorithm is based on a fading regularization method (FRM) and is numerically implemented using the method of fundamental solutions (MFS). The inverse technique is first validated with synthetic data and is then applied to the interpretation of experimental measurements obtained by digital image correlation (DIC).

Analysis of Complex Surface Displacements above a Storage Cavern Field in NW-Germany, Observed by InSAR

2021 ◽  
Author(s):  
Markus Even ◽  
Malte Westerhaus ◽  
Verena Simon
Keyword(s):  
Displacement Field ◽  
Pressure Response ◽  
Phase Model ◽  
Basic Method ◽  
Elastic Displacement ◽  
The North ◽  
Geophysical Model ◽  
Surface Displacements ◽  
Pressure Changes ◽  
East West

<p>The cavern field at Epe has been brined out of a salt deposit belonging to the lower Rhine salt flat, which extends under the surface of the North German lowlands and part of the Netherlands, and is used to store e.g. natural gas, brine and petroleum. Cavern convergence and operational pressure changes cause surface displacements that have been studied for this work with the help of SAR interferometry (InSAR) using distributed and persistent scatterers. Vertical and East-West movements have been determined based on Sentinel-1 data from ascending and descending orbit. Simple geophysical modeling is used to support InSAR processing and helps to interpret the observations. In particular, an approach is presented that allows to relate the deposit pressures with the observed surface displacements. Seasonal movements occurring over a fen situated over the western part of the storage site further complicate the analysis. Findings are validated with ground truth from levelling and groundwater level measurements.</p><p>For porous storage sites the geomechanic response can be described as elastic: displacement is almost proportional to reservoir pressure and displays the same pronounced seasonal behavior. At Epe the visco-elastic response of the salt layer has to be considered. The general appearance of the surface displacement is that of a strongly smoothed and shifted version of the cavern pressure curve. To deal with this situation a temporal model for displacement with pressure changes (pressure response) is derived that relates cavern pressure with observed displacement based on the theory for visco-elastic behavior of a Kelvin-Voigt body.</p><p>In order to deal successfully with the challenging displacement field at Epe several algorithmic improvements were implemented. To obtain a more complete picture of the displacement field DS pre-processing has been combined with StaMPS. Furthermore, StaMPS was modified in order to support unwrapping with a phase model composed of linear trend, pressure response and a seasonal component (caused by ground water level changes). Finally, refining the iterative estimation scheme of StaMPS helped avoiding leakage of the displacement signal to the spatially correlated noise term.</p><p>Determining vertical and east-west displacements from InSAR line-of-sight displacements is fundamental for interpretation and integration with levelling data. In this study, a basic method of orbit combination and another one supported by a simplistic geophysical model were applied in order to obtain 2D-displacements. For the basic method the north-south component was handled as if it were zero, while the geophysical model predicts the LOS effect of NS displacements. It assumes that caverns act as spherical pressure/volume sources embedded in an elastic half space (“Mogi” sources). To incorporate the visco-elastic component, each cavern is encompassed by a spherical salt shell that obeys the Kelvin-Voigt differential equations. The model is used here to describe either the parameters of the linear component of the displacement model or of the pressure response. A novelty of the orbit combinations implemented for this study is that the different components of the phase model are combined separately. This allows for a better understanding of the phenomena that contribute to the displacement field.</p>

Representation of Finite Cracks by Dislocation Pileups: An Application to Atomic Simulation of Fracture

1995 ◽  
Vol 408 ◽  
Author(s):  
Vijay Shastry ◽  
Diana Farkas
Keyword(s):  
Displacement Field ◽  
Anisotropic Body ◽  
Interatomic Interaction ◽  
Elastic Displacement ◽  
Mode I ◽  
Multiple Cracks ◽  
Atomic Simulation ◽  
Variable Approach ◽  
Finite Crack ◽  
Eam Potential

AbstractThe elastic displacement field solution of a semi-infinite crack in an anisotropic body, calculated using a complex variable approach due to Sih and Liebowitz, is usually used by atomistic simulations of fracture. The corresponding expression for the displacement field of a finite crack is numerically cumbersome since it involves multiple square roots of complex numbers. In this study, displacement field of the crack is calculated by superposing the displacements of dislocations in an equivalent double pileup, equilibrated under mode I conditions. An advantage of this method is its extensibility to atomistic studies of more complex systems containing multiple cracks or interfaces. The pileup representation of the finite crack is demonstrated as being equivalent to its corresponding continuum description using the example of a double ended crack in α-Fe, loaded in mode I. In these examples, the interatomic interaction in α-Fe is described by an empirical embedded atom (EAM) potential.

Description of the Atomic Positions Around Interfacial Ledges in Terms of the Somigliana Dislocation Model

1991 ◽  
Vol 238 ◽  
Author(s):  
R. Bonnet ◽  
M. Loubradou
Keyword(s):  
Experimental Evidence ◽  
Displacement Field ◽  
Elastic Field ◽  
Point Of View ◽  
Low Energy ◽  
Elastic Displacement ◽  
Dislocation Model ◽  
Structural Units ◽  
Hexagonal Crystals ◽  
Translation State

ABSTRACTIn many materials, crystalline interfaces are facetted. The experimental evidence is that on each side of an interfacial ledge, or along the facets meeting along a common line, low energy atomic structural units are preserved which accommodate elastically angular or/and length misfit(s). Each facet can be considered as a Somigliana dislocation (SD) whose core is extended on the facet. The elastic displacement field of a SD is derived in an anisotropic continuum, for any orientation of the facet relative to a given Cartesian frame. From an atomic point of view, the translation state of the two crystals on each side of the facet is defined. The dislocation content attached to a ledge or a dihedral angle formed by two joining facets along a common side is also analyzed. The local elastic field related to these cases are derived and applications are presented for depicting the positions of the atomic columns in theoretical plots. Comparisons are made with some other theoretical works and HRTEM images. Examples illustrate the application of the Somigliana model to grain boundaries in hexagonal crystals (Mg, WC), and an interphase interface Ni3AI/Ni3Nb.

High Resolution EBSD-Based Dislocation Microscopy

2011 ◽  
Vol 702-703 ◽  
pp. 11-17 ◽  
Author(s):  
Brent L. Adams ◽  
David T. Fullwood ◽  
J.A. Basinger ◽  
T. Hardin
Keyword(s):  
Boundary Condition ◽  
High Resolution ◽  
Displacement Field ◽  
Sample Surface ◽  
Elastic Displacement ◽  
Polycrystalline Materials ◽  
Additional Information ◽  
Stress Equilibrium ◽  
Total Displacement ◽  
Fundamental Limitation

Significant advances are reported in the application of HR-EBSD to the imaging of the dislocation structure of polycrystalline materials. The central assumption of the method is the compatibility of the total displacement field, which relates the (Nye) dislocation tensor to the (partially measurable) curl of the elastic displacement field. Two key challenges must be addressed, including: a) the fundamental limitation imposed by the electron-opacity of typical materials, which limits the measurement of gradients in the displacement field in the direction normal to the sample surface; and b) the inability of HR-EBSD to recover the spherical (elastic) distortions of the lattice. This second challenge can be overcome if a traction free boundary condition is applied. It is illustrated that consideration of the familiar stress equilibrium relations gives additional information, which may enable estimates of the missing components of the Nye tensor. An example of application of HR-EBSD to a Mg-Ce sample is presented.

Neutron-Zwischenreflex-Scattering from Point Defects in Crystals

1986 ◽  
Vol 69 ◽  
Author(s):  
H. Dosch ◽  
J. Peisl
Keyword(s):  
Point Defects ◽  
Displacement Field ◽  
Defect Structure ◽  
Host Lattice ◽  
Local Defect ◽  
Defect Model ◽  
Defect Site ◽  
X Ray Scattering ◽  
Tetrahedral Sites ◽  
Diffuse Neutron

AbstractDiffuse neutron or x-ray scattering close to the Bragg peaks (Huang scattering) and far away from Bragg peaks (Zwischenreflex-scattering) supplies detailed information on point defects and small agglomerates in crystals [1]. The defect structure, i.e. the lattice location, the displacements of the near neighbours and the strength and symmetry of the long ranged displacement field can be determined. In order to demonstrate the power of this technique, we report on recent experimental results. Interstitially dissolved N and O in Nb are located on octahedral sites and create rather large displacements in their vicinity. Their long ranged displacement field shows the symmetry of the defect site. The light interstitials H and D in Nb are located on tetrahedral sites and their long ranged displacement field shows the symmetry of the host lattice. A rather complicated defect model is necessary in order to explain the local defect structure.

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