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.

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.

A Novel Constitutive Model for Concrete under Uniaxial Compression

2010 ◽  
Vol 650 ◽  
pp. 47-55 ◽  
Author(s):  
Jin Long Pan ◽  
Jia Jia Zhou ◽  
Zong Jin Li ◽  
Christopher K.Y. Leung
Keyword(s):  
Constitutive Model ◽  
Uniaxial Compression ◽  
Poisson’S Ratio ◽  
Longitudinal Strain ◽  
Polynomial Function ◽  
Poisson's Ratio ◽  
Test Results ◽  
Proposed Model ◽  
Order Polynomial

In this paper, a novel constitutive model of concrete has been proposed by introducing a new parameter, namely, cracking Poisson’s ratio (νcr), to account for the effect of localization due to cracking. By fitting the curve between the dimensionless strain (ε/εpr) and cracking Poisson’s ratio (νcr), νcr can be expressed as an 3rd order polynomial function of dimensionless longitudinal strain (ε/εpr). The constitutive model for the softening regime can then be proposed with the parameters of dimensionless strain and cracking Poisson’s ratio. Finally, Validity of the proposed model is verified by the test results of cylinder specimens of C30.

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.

On the “elastic stiffness” in a high-cycle accumulation model — continued investigations

2013 ◽  
Vol 50 (12) ◽  
pp. 1260-1272 ◽  
Author(s):  
Torsten Wichtmann ◽  
Andrzej Niemunis ◽  
Theodoros Triantafyllidis
Keyword(s):  
Stress Relaxation ◽  
Bulk Modulus ◽  
Poisson’S Ratio ◽  
Volumetric Strain ◽  
Fine Sand ◽  
Elastic Stiffness ◽  
Poisson's Ratio ◽  
Initial Stresses ◽  
Cyclic Test ◽  
Membrane Penetration

The high-cycle accumulation (HCA) model proposed by the authors can be used to predict permanent deformations or stress relaxation due to a large number (e.g., several millions) of load cycles with relative small strain amplitudes (<10−3). The predicted stress relaxation depends on the isotropic “elastic stiffness”, [Formula: see text], used in the HCA model. To calibrate the bulk modulus, K, the rate of pore pressure accumulation obtained from an undrained cyclic test and the rate of volumetric strain accumulation measured in a drained cyclic test are compared. Poisson’s ratio, ν, can be determined from the shape of the stress relaxation path measured in an undrained test with anisotropic consolidation stresses and strain cycles. Unfortunately, the calibration of K shown for a medium coarse sand in a previous paper by Wichtmann et al. in 2010 was affected by membrane penetration effects. Consequently, all further studies have been performed on a fine sand for which membrane penetration is negligible. The present paper reports on the new results. The strong pressure dependence of K and its independence from amplitude found in the previous study could be confirmed by the new tests. In addition, the new experimental results reveal a density dependence of K, while the bulk modulus is rather independent of stress ratio. Furthermore, for the first time Poisson’s ratio, ν, used in the HCA model has been calibrated based on tests performed with different amplitudes, densities, and initial stresses.

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.

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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