On the mechanics of the intrusion of sills

1969 ◽  
Vol 6 (6) ◽  
pp. 1415-1419 ◽  
Author(s):  
P. E. Gretener
Keyword(s):  
Principal Stress ◽  
Upper Mantle ◽  
Poisson’S Ratio ◽  
Vertical Stress ◽  
Poisson's Ratio ◽  
Stress Axis ◽  
Principal Stresses ◽  
State Of Stress ◽  
As Stress

Diabase sills contain material originating from the base of the crust or the upper mantle. As a result they must be fed by dike- or plug-like bodies. The formation of a sill thus represents a major reorientation of the form of the intrusion. Tabular intrusive bodies tend to orient themselves perpendicular to the least compressive principal stress axis as shown by E. M. Anderson. It is suggested that diabase sills form under sedimentary strata in which the two horizontal principal stresses exceed the vertical stress (Sx > Sy > Sz). Such strata act as stress barriers and prevent further ascent of the magma, In order for this situation to occur the sediments must be in compression in the x-direction and confined in the y-direction. The parameter of importance to produce the above state of stress is the effective Poisson's ratio.

scholarly journals Rational modelling of elastic soil behaviour in 3D condition

2019 ◽  
Vol 92 ◽  
pp. 15003
Author(s):  
Teruo Nakai ◽  
Hossain Md. Shahin ◽  
Akira Ishikawa
Keyword(s):  
Principal Stress ◽  
Linear Relation ◽  
Poisson’S Ratio ◽  
Elastic Strain ◽  
Volumetric Strain ◽  
Poisson's Ratio ◽  
Elastic Component ◽  
Principal Stresses ◽  
Strain Relation ◽  
Proposed Model

A simple and rigorous formulation of elastic component of elastoplastic model for geomaterials is presented. Although linear relation between elastic volumetric strain and mean principal stress in log scale is assumed in most of the usual models, linear relation between each principal stress and the corresponding principal elastic strain in log scale is assumed. Incorporating Poisson's ratio, three principal stresses vs. three elastic principal strain relation is obtained. Also, assuming coaxially between stresses and elastic strains, this relation can be transformed to stress- elastic strain relation in general coordinate. The material parameters of the proposed model of the elastic component are the same as those of the usual models, i.e., swelling index κ and Poisson's ratio ν. This proposed model can describe typical unloading behaviour of various shear tests and constant stress ratio unloading tests reported before.

Variability of Poisson's ratio in investigating the state of stress of rubber parts

1971 ◽  
Vol 3 (4) ◽  
pp. 502-504
Author(s):  
B. M. Gorelik ◽  
G. I. Fel'dman ◽  
M. A. Maiskaya
Keyword(s):  
Poisson’S Ratio ◽  
The State ◽  
Poisson's Ratio ◽  
State Of Stress

scholarly journals Relative amplitudes of P and S waves as a mantle reconnaissance tool

1969 ◽  
Vol 59 (3) ◽  
pp. 1189-1200
Author(s):  
John R. McGinley ◽  
Don L. Anderson
Keyword(s):  
Travel Time ◽  
Upper Mantle ◽  
Poisson’S Ratio ◽  
Basin And Range ◽  
The Other ◽  
Poisson's Ratio ◽  
P Waves ◽  
S Waves ◽  
High Attenuation ◽  
Short Period

abstract The unified magnitude, the ratio of the amiplitudes of S to P waves, and travel-time residuals were compiled from published data for the five Seismological Observatories, TFO, UBO, BMO, WMO and CBO. Using one of the stations as a reference, a relative measure of the above quantities was calculated for each of the other stations for each of a number of earthquakes. The stations in the Basin and Range Province are consistent with a markedly higher attentuation of P waves and a high attenuation of S relative to P when compared to the other stations. This latter observation indicates a high Poisson's ratio in the mantle under the Basin and Range. The delay times to these stations are also consistent with the high Poisson's ratio and with a low-velocity upper mantle. The ratio of the amplitudes of long-period S waves to short-period P waves varies by a factor of 4 among these stations. BMO, in eastern Oregon, has a high S/P amplitude ratio compared to other stations and a travel-time residual that is comparable to the observatories in the mid-continent. This may be another example of a seismic “window” into the upper mantle that is generated by underthrusting of the oceanic lithosphere.

The Use of a Mechano-Lattice Analogy for Determining the Abrading Stresses in Sliding Rubber

1971 ◽  
Vol 44 (3) ◽  
pp. 758-770
Author(s):  
W. O. Yandell
Keyword(s):  
Principal Stress ◽  
Poisson’S Ratio ◽  
Sliding Friction ◽  
Poisson's Ratio ◽  
Large Strains ◽  
Damping Factor ◽  
Stress Strain ◽  
Minor Principal Stress

Abstract A rigorous mechano-lattice analogy analysis for calculating the hysteretic sliding friction of and stresses in rubber sliding on variously shaped asperities is presented. The analysis allows large strains and any Poisson's Ratio, rigidity or damping factor of the rubber. The analysis was used to calculate the distributions of minor principal stress in rubber sliding over smooth and frictional prisms with different sharpnesses and over a cylinder. The potentially disruptive stress regions were thus revealed and compared. The effect of changes in the Poisson's Ratio and of the damping factor of the rubber were also examined. It was postulated that the fine texture generates more stress-strain hysteretic heat which may lead to the more rapid abrasion observed by some workers.

Effects of a Change of Poisson’s Ratio Analyzed by Twinned Gradients: Illustrated by Simple Solutions of Boussinesq’s Problem of a Normal Force and Cerruti’s Problem of a Tangential Force Acting on the Surface of a Large Solid, and by a Simple Derivation of the Stresses in a Rotating Thick Disk

1940 ◽  
Vol 7 (3) ◽  
pp. A113-A116
Author(s):  
H. M. Westergaard
Keyword(s):  
Poisson’S Ratio ◽  
Normal Force ◽  
Plane Surface ◽  
Tangential Force ◽  
Thick Disk ◽  
Poisson's Ratio ◽  
Total Force ◽  
Principal Stresses ◽  
Simple Derivation ◽  
Boussinesq’S Problem

Abstract Some problems of elasticity have a simple solution for a particular value of Poisson’s ratio. For example, Boussinesq’s problem of a normal force and Cerruti’s problem of a tangential force, acting on the plane surface of a semi-infinite solid, are solved when Poisson’s ratio is 1/2 by referring to Kelvin’s problem of a force at a point in the interior of an infinite solid. For, when Poisson’s ratio is 1/2, the solution of Kelvin’s problem can be stated in terms of one principal stress at each point, acting along the radial line from the point of the load; the other principal stresses are zero; and one half of the total force may be assigned to one half of the infinite solid. For other values of Poisson’s ratio terms must be added in the formulas for the displacements and stresses. The derivations that have been available are somewhat lengthy, especially for Cerruti’s problem. The difficulties are reduced by a simple analytical device, here called “the twinned gradient.” The displacement to be added by the change of Poisson’s ratio is stated as the gradient of a potential except that one of the components is replaced by its twin, an identical component in reversed direction. This device also lends itself to a simplification of the analysis of stresses in a rotating thick disk.

An Application of the Interferometer Strain Gage in Photoelasticity

1935 ◽  
Vol 2 (3) ◽  
pp. A99-A102
Author(s):  
R. W. Vose
Keyword(s):  
Strain Gage ◽  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Massachusetts Institute ◽  
Massachusetts Institute Of Technology ◽  
Lateral Deformation ◽  
Principal Stresses ◽  
Photoelastic Analysis ◽  
The Difference ◽  
Institute Of Technology

Abstract This paper was written at the suggestion of Mr. Mieth Maeser, in response to numerous inquiries concerning the methods of photoelastic analysis in use at the Massachusetts Institute of Technology. By the use of any of the usual photoelastic methods the difference of the principal stresses and their direction at any point in a suitable loaded specimen are determined, and through a knowledge of Poisson’s ratio their sum is obtained (and a solution made possible) by a measurement of the lateral deformation of the specimen by means of an interferometer strain gage. This instrument, together with its accessories and their use, is illustrated and described in the paper. Examples of the problems solved by the use of the instrument show its accuracy and the consistency of the results obtained by the method.

S-wave observations in the Franciscan terrane, central California

1981 ◽  
Vol 71 (6) ◽  
pp. 1863-1874
Author(s):  
Alan R. Levander ◽  
Robert L. Kovach
Keyword(s):  
Wave Velocity ◽  
Upper Mantle ◽  
Poisson’S Ratio ◽  
San Andreas Fault ◽  
Poisson's Ratio ◽  
S Wave ◽  
Central California ◽  
Wave Velocities ◽  
San Andreas ◽  
Pn Velocity

Abstract We have examined S-wave arrivals from local earthquakes at a three-station seismograph array in the Franciscan terrane of the Diablo Range, California. A single crustal S-wave phase is observed with a velocity of 3.30 km/sec. Poisson's ratio calculated for the crust from a composite Wadati diagram is 0.27. Beyond epicentral distances of 90 km we have tentatively identified an Sn phase with a velocity of 4.35 km/sec. Other investigators have reported a Pn velocity of 8.0 km/sec corresponding to an upper mantle Poisson's ratio of 0.29. The 3.30 km/sec crustal S-wave velocity is intermediate in value between crustal S-wave velocities measured in similar terranes 75 km north at Berkeley and 90 km south at Bear Valley, suggesting a NW-SE crustal S-wave velocity gradient east of the San Andreas fault in the Franciscan terrane. This may be indicative of an increase in crustal rigidity from southeast to northwest, possibly associated with the differing levels of seismic activity observed along portions of the San Andreas fault.

scholarly journals An Extension Failure Criterion for Brittle Rock

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Aizhong Lu ◽  
Ning Zhang ◽  
Guisen Zeng
Keyword(s):  
Principal Stress ◽  
Poisson’S Ratio ◽  
Compressive Strain ◽  
Strength Criterion ◽  
Maximum Principal Stress ◽  
Intermediate Principal Stress ◽  
Brittle Rock ◽  
Poisson's Ratio ◽  
Triaxial Tests ◽  
True Triaxial

Under the triaxial compressive state, the compressive strain is supposed to happen in the direction of the maximum principal stress, but tensile strain happens in the direction of the minimum principal stress. Moreover, as the intermediate principal stress is not too high, the corresponding strain can also be tensile. If the brittle rock is assumed as linear elastic in the prefailure stage, a new strength criterion based on the sum of the two tensile strains was presented. The new criterion considers the differences in mechanical parameters (i.e., elastic modulus and Poisson’s ratio) under tension and compression. The parameters of the criterion only include Poisson’s ratio and uniaxial strength. And the effect of the intermediate principal stress σ 2 can be reflected. Certain featured failure phenomenon of rock material can be explained well by the proposed criterion. The results of conventional and true triaxial tests can verify the criterion well. Finally, the criterion is compared with the Mohr–Coulomb and Drucker–Prager criteria.

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