Surface Strain Rate Tensor Field for Iceland Based on a GPS Network

2017 ◽  
pp. 175-191
Author(s):  
Ragnar Sigbjörnsson ◽  
J. Snæbjörnsson ◽  
G. Valsson ◽  
Th. Sigurdsson ◽  
Rajesh Rupakhety
Keyword(s):  
Strain Rate ◽  
Tensor Field ◽  
Surface Strain ◽  
Strain Rate Tensor ◽  
Gps Network

scholarly journals Strain Rates On Rutford Ice Stream, Antarctica (Abstract)

1986 ◽  
Vol 8 ◽  
pp. 207
Author(s):  
N. Stephenson ◽  
C.S.M. Doake
Keyword(s):  
Strain Rate ◽  
Velocity Gradient ◽  
Surface Strain ◽  
Lateral Strain ◽  
Strain Rate Tensor ◽  
Strain Rates ◽  
Average Value ◽  
Divergent Flow ◽  
Ice Stream ◽  
Thickness Variations

In a study of the Rutford Ice Stream, strain rates were measured on a transverse section. Magnitudes ranged up to 40 × 10−3 a−1 but were typically in the order of 3 × 10−3 a−1 with an error of 0.1 χ 10−3 a−1. Variations in the strain rate between adjacent stakes of 0.2 χ 10−3 a−1 to 2 × 10−3 a−1 were matched to the thickness variations on the glacier. For each set of three adjacent stakes, the velocity gradient components of the surface strain rate tensor were calculated by assuming that the gradients were linear over the distance between adjacent stakes. When plotted against distance across the ice stream, each strain rate component revealed different aspects of the flow field. The longitudinal strain rate was compressive, with an almost constant magnitude of 10−3 a−1. The lateral strain rate is extensive, with an average value of 1.1 × 10−3 a−1 which agreed with the angle between the divergent flow lines observed on a Landsat image. Peaks in the lateral strain rate, corresponding to longitudinal bands of thicker ice, showed that these thicker bands were spreading more rapidly at the expense of thinner areas. The two velocity gradient components of the shear rate tensor also reflected differences in ice thickness.

scholarly journals Strain Rates On Rutford Ice Stream, Antarctica (Abstract)

1986 ◽  
Vol 8 ◽  
pp. 207-207
Author(s):  
N. Stephenson ◽  
C.S.M. Doake
Keyword(s):  
Strain Rate ◽  
Velocity Gradient ◽  
Surface Strain ◽  
Lateral Strain ◽  
Strain Rate Tensor ◽  
Strain Rates ◽  
Average Value ◽  
Divergent Flow ◽  
Ice Stream ◽  
Thickness Variations

In a study of the Rutford Ice Stream, strain rates were measured on a transverse section. Magnitudes ranged up to 40 × 10−3 a−1 but were typically in the order of 3 × 10−3 a−1 with an error of 0.1 χ 10−3 a−1. Variations in the strain rate between adjacent stakes of 0.2 χ 10−3 a−1 to 2 × 10−3 a−1 were matched to the thickness variations on the glacier.For each set of three adjacent stakes, the velocity gradient components of the surface strain rate tensor were calculated by assuming that the gradients were linear over the distance between adjacent stakes. When plotted against distance across the ice stream, each strain rate component revealed different aspects of the flow field. The longitudinal strain rate was compressive, with an almost constant magnitude of 10−3 a−1. The lateral strain rate is extensive, with an average value of 1.1 × 10−3 a−1 which agreed with the angle between the divergent flow lines observed on a Landsat image. Peaks in the lateral strain rate, corresponding to longitudinal bands of thicker ice, showed that these thicker bands were spreading more rapidly at the expense of thinner areas. The two velocity gradient components of the shear rate tensor also reflected differences in ice thickness.

scholarly journals Surface strain rate colour map of the Tatra Mountains region (Slovakia) based on GNSS data

2016 ◽  
Vol 67 (6) ◽  
pp. 509-524 ◽  
Author(s):  
Martin Bednárik ◽  
Juraj Papčo ◽  
Vladimír Pohánka ◽  
Vladimír Bezák ◽  
Igor Kohút ◽  
...  
Keyword(s):  
Strain Rate ◽  
Stress Tensor ◽  
Surface Deformation ◽  
Interpolation Method ◽  
Surface Strain ◽  
Strain Rate Tensor ◽  
Complex Data ◽  
Shape Descriptors ◽  
Tatra Mountains ◽  
The Tatra Mountains

AbstractThe surface deformation of the Tatra Mountains region in Western Carpathians can nowadays be studied directly thanks to precise geodetic measurements using the GNSS. The strain or stress tensor field is, however, a rather complex “data structure” difficult to present legibly and with sufficient resolution in the form of a classical map. A novel and promising approach to the solution of this problem is coding the three principal strain or stress values into the three colour channels (red, green, blue) of an RGB colour. In our previous study, the colour depended on the stress tensor shape descriptors. In the current study, the adapted colouring scheme uses a subset of shape descriptors common to stress and strain, which differ only in the scaling factor. In this manner, we generate the colour map of the surface strain rate field, where the colour of each grid point carries the information about the shape of the strain rate tensor at that point. The resulting strain rate colour map can be displayed simultaneously with the map of the faults or elevations and be easily checked for the data or interpolation method errors and incompatibility with the geophysical and geological expectations.

scholarly journals Rate-dependent ductile fracture under plane strain tension: experiments and simulations

2018 ◽  
Vol 183 ◽  
pp. 02022
Author(s):  
Vincent Grolleau ◽  
Vincent Lafilé ◽  
Christian C. Roth ◽  
Bertrand Galpin ◽  
Laurent Mahéo ◽  
...  
Keyword(s):  
High Strain Rate ◽  
Strain Rate ◽  
Plane Strain ◽  
Static Loading ◽  
High Strain ◽  
Fracture Initiation ◽  
Surface Strain ◽  
Experimental Program ◽  
Loading Conditions ◽  
Plane Strain Tension

Among all other stress states achievable under plane stress conditions, the lowest ductility is consistently observed for plane strain tension. For static loading conditions, V-bending of small sheet coupons is the most reliable way of characterising the strain to fracture for plane strain tension. Different from conventional notched tension specimens, necking is suppressed during V-bending which results in a remarkably constant stress state all the way until fracture initiation. The present DYMAT talk is concerned with the extension of the V-bending technique from low to high strain rate experiments. A new technique is designed with the help of finite element simulations. It makes use of modified Nakazima specimens that are subjected to V-bending. Irrespective of the loading velocity, plane strain tension conditions are maintained throughout the entire loading history up to fracture initiation. Experiments are performed on specimens extracted from aluminum 2024-T3 and dual phase DP450 steel sheets. The experimental program includes quasi static loading conditions which are achieved on a universal testing machine. In addition, high strain rate experiments are performed using a specially-designed drop tower system. In all experiments, images are acquired with two cameras to determine the surface strain history through stereo Digital Image Correlation (DIC). The experimental observations are discussed in detail and also compared with the numerical simulations to validate the proposed experimental technique

LES Investigation of Boussinesq Constitutive Relation Validity in a Corner Separation Flow

2018 ◽  
Author(s):  
Jean-François Monier ◽  
Nicolas Poujol ◽  
Mathieu Laurent ◽  
Feng Gao ◽  
Jérôme Boudet ◽  
...  
Keyword(s):  
Strain Rate ◽  
Stress Tensor ◽  
Reynolds Stress ◽  
Constitutive Relation ◽  
Strain Rate Tensor ◽  
Separation Flow ◽  
Compressor Cascade ◽  
Corner Separation ◽  
Reynolds Stress Tensor ◽  
Mean Strain

The present study aims at analysing the Boussinesq constitutive relation validity in a corner separation flow of a compressor cascade. The Boussinesq constitutive relation is commonly used in Reynolds-averaged Navier-Stokes (RANS) simulations for turbomachinery design. It assumes an alignment between the Reynolds stress tensor and the zero-trace mean strain-rate tensor. An indicator that measures the alignment between these tensors is used to test the validity of this assumption in a high fidelity large-eddy simulation. Eddy-viscosities are also computed using the LES database and compared. A large-eddy simulation (LES) of a LMFA-NACA65 compressor cascade, in which a corner separation is present, is considered as reference. With LES, both the Reynolds stress tensor and the mean strain-rate tensor are known, which allows the construction of the indicator and the eddy-viscosities. Two constitutive relations are evaluated. The first one is the Boussinesq constitutive relation, while the second one is the quadratic constitutive relation (QCR), expected to render more anisotropy, thus to present a better alignment between the tensors. The Boussinesq constitutive relation is rarely valid, but the QCR tends to improve the alignment. The improvement is mainly present at the inlet, upstream of the corner separation. At the outlet, the correction is milder. The eddy-viscosity built with the LES results are of the same order of magnitude as those built as the ratio of the turbulent kinetic energy k and the turbulence specific dissipation rate ω. They also show that the main impact of the QCR is to rotate the mean strain-rate tensor in order to realign it with the Reynolds stress tensor, without dilating it.

scholarly journals Monstars on Glaciers

1983 ◽  
Vol 29 (101) ◽  
pp. 70-77 ◽  
Author(s):  
J. F. Nye
Keyword(s):  
Numerical Simulation ◽  
Strain Rate ◽  
Tensor Field ◽  
Pure Shear ◽  
Glacier Surface ◽  
Isotropic Point ◽  
Different Types ◽  
Isolated Points ◽  
Principal Directions ◽  
Structurally Stable

AbstractIsotropic points are structurally stable features of any complicated field of stress or strain-rate, and therefore will almost always be present on the surface of a glacier. A given isotropic point for strain-rate will belong to one of six different classes, depending on the pattern (lemon, star, or monstar) of principal directions and the contours (ellipses or hyperbolas) of constant principal strain-rate values in its neighbourhood. The central isotropic point on a glacier should theoretically have a monstar pattern, but the contours around it may sometimes be elliptic and sometimes hyperbolic. Nearby, but not coincident with it there will be an isotropic point for stress. This will also have a monstar pattern but, in contrast to the strain-rate point, the contours around it must be hyperbolic. Published examples are consistent with these conclusions. In addition to isotropic points for strain-rate a glacier surface will contain isolated points of pure shear; these also can be classified into six different types. Stable features of this kind give information about the essential structure of a tensor field and form useful points of comparison between observation and numerical simulation.

scholarly journals Seismic deformation at the Alban Hills volcano during the 1989-1990 seismic sequence

1998 ◽  
Vol 41 (2) ◽  
Author(s):  
G. Selvaggi ◽  
F. D'Ajello Caracciolo
Keyword(s):  
Strain Rate ◽  
Fluid Pressure ◽  
Strain Rate Tensor ◽  
Seismic Structure ◽  
Fault Plane Solutions ◽  
Alban Hills ◽  
Shear Failures ◽  
One Year ◽  
The One ◽  
Seismic Moment Release

We analysed the one-year-long seismic swarm at the Alban Hills volcano which occurred during 1989-1990. We portray spatial distribution of seismic moment release, better delineating the activated volume during the swarm. The seismic structure is imaged as a 7-km long, 3-km wide, and 3-km thick volume, located between 2 and 5 km depth, and NW-SE striking. Fault plane solutions and scalar seismic moments for the largest earthquakes provide the description of the average strain rate tensor. The principal strain rate axes show a dominant extension in NE-SW direction, a SE-NW direction of compression and a negligible thickening rate. P and T axes direction of the smaller earthquakes suggests that the same mode of deformation is distributed all over the activated volume. These results are discussed in terms of seismic deforming processes active at the Alban Hills volcano, in the frame of magmatic inflation recently invoked to explain the rapid vertical uplift affecting part of the volcano. The observed average deformation is consistent with shear failures occurring on faults connecting stress-oriented dykes in response to an increasing fluid pressure.

scholarly journals How to Realize Volume Conservation During Finite Plastic Deformation

2017 ◽  
Vol 84 (11) ◽  
Author(s):  
Heling Wang ◽  
Dong-Jie Jiang ◽  
Li-Yuan Zhang ◽  
Bin Liu
Keyword(s):  
Plastic Deformation ◽  
Plastic Strain ◽  
Strain Rate ◽  
Plastic Strain Rate ◽  
Strain Rate Tensor ◽  
Cauchy Stress ◽  
Volume Conservation ◽  
Tangential Stiffness ◽  
Manufacture Process ◽  
Universal Approach

Volume conservation during plastic deformation is the most important feature and should be realized in elastoplastic theories. However, it is found in this paper that an elastoplastic theory is not volume conserved if it improperly sets an arbitrary plastic strain rate tensor to be deviatoric. We discuss how to rigorously realize volume conservation in finite strain regime, especially when the unloading stress free configuration is not adopted in the elastoplastic theories. An accurate condition of volume conservation is first clarified and used in this paper that the density of a volume element after the applied loads are completely removed should be identical to that of the initial stress free states. For the elastoplastic theories that adopt the unloading stress free configuration (i.e., the intermediate configuration), the accurate condition of volume conservation is satisfied only if specific definitions of the plastic strain rate are used among many other different definitions. For the elastoplastic theories that do not adopt the unloading stress free configuration, it is even more difficult to realize volume conservation as the information of the stress free configuration lacks. To find a universal approach of realizing volume conservation for elastoplastic theories whether or not adopt the unloading stress free configuration, we propose a single assumption that the density of material only depends on the trace of the Cauchy stress by using their objectivities. Two strategies are further discussed to satisfy the accurate condition of volume conservation: directly and slightly revising the tangential stiffness tensor or using a properly chosen stress/strain measure and elastic compliance tensor. They are implemented into existing elastoplastic theories, and the volume conservation is demonstrated by both theoretical proof and numerical examples. The potential application of the proposed theories is a better simulation of manufacture process such as metal forming.

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