scholarly journals Shear modulus of an elastic solid under external pressure as a function of temperature: The case of helium

2012 ◽  
Vol 85 (6) ◽  
Author(s):  
Felipe Barra ◽  
Fernando Lund ◽  
Nicolás Mujica ◽  
Sergio Rica
Keyword(s):  
Shear Modulus ◽  
Elastic Solid ◽  
External Pressure

The Elastic Coefficients of the Theory of Consolidation

1957 ◽  
Vol 24 (4) ◽  
pp. 594-601
Author(s):  
M. A. Biot ◽  
D. G. Willis
Keyword(s):  
Nonlinear Systems ◽  
Shear Modulus ◽  
Physical Interpretation ◽  
Compressible Fluid ◽  
Elastic Solid ◽  
Fluid Content ◽  
Alternate Forms ◽  
Elastic Coefficients ◽  
Methods Of Measurement

Abstract The theory of the deformation of a porous elastic solid containing a compressible fluid has been established by Biot. In this paper, methods of measurement are described for the determination of the elastic coefficients of the theory. The physical interpretation of the coefficients in various alternate forms is also discussed. Any combination of measurements which is sufficient to fix the properties of the system may be used to determine the coefficients. For an isotropic system, in which there are four coefficients, the four measurements of shear modulus, jacketed and unjacketed compressibility, and coefficient of fluid content, together with a measurement of porosity appear to be the most convenient. The porosity is not required if the variables and coefficients are expressed in the proper way. The coefficient of fluid content is a measure of the volume of fluid entering the pores of a solid sample during an unjacketed compressibility test. The stress-strain relations may be expressed in terms of the stresses and strains produced during the various measurements, to give four expressions relating the measured coefficients to the original coefficients of the consolidation theory. The same method is easily extended to cases of anisotropy. The theory is directly applicable to linear systems but also may be applied to incremental variations in nonlinear systems provided the stresses are defined properly.

Buckling of Externally Pressurized Composite Torispherical Domes

1989 ◽  
Vol 203 (1) ◽  
pp. 41-56 ◽  
Author(s):  
G D Galletly ◽  
A Muc
Keyword(s):  
Shear Modulus ◽  
Failure Mode ◽  
Young Modulus ◽  
External Pressure ◽  
Limited Extent ◽  
Woven Composite ◽  
Plane Shear ◽  
Buckling Strength ◽  
Shell Buckling ◽  
Theory And Experiment

The results of external pressure buckling tests on 0.25 m diameter woven composite (mainly CFRP) domes are given in the paper and they are compared with the predictions of the shell buckling program BOSOR 4. The agreement between theory and experiment was satisfactory. The tests also show that the buckling strength of CFRP torispheres is good. They could replace steel torispheres and would be considerably lighter. The buckling pressures of the woven composite domes are a function of the Young modulus E but the relation is not a simple linear one (the in-plane shear modulus G12 also needs to be taken into account). Results of some tests on CFRP and GFRP domes lend support to this statement. The provisions of BS 4994, when applied to these domes, predict that buckling is the controlling failure mode. While this is correct, the buckling pressures predicted by BS 4994 seem rather low. The effect of dome thickness on the buckling pressures was expected to vary as (t/R)2. This was confirmed herein, to a limited extent, by a few tests on shallow CFRP domes.

scholarly journals Analytical solutions for cosmological perturbations in a one-component universe with shear stress

2015 ◽  
Vol 24 (08) ◽  
pp. 1550063 ◽  
Author(s):  
Matej Škovran
Keyword(s):  
Shear Stress ◽  
Energy Density ◽  
Shear Modulus ◽  
Ideal Fluid ◽  
Analytical Solutions ◽  
Elastic Solid ◽  
Explicit Solutions ◽  
Cosmological Perturbations ◽  
Flat Universe ◽  
Tensor Perturbations

We construct explicit solutions for scalar, vector and tensor perturbations in a less known setting, a flat universe filled by an isotropic elastic solid with pressure and shear modulus proportional to energy density. The solutions generalize the well-known formulas for cosmological perturbations in a universe filled by ideal fluid.

scholarly journals The effect of arbitrarily small rigidity on the free oscillations of the Earth

1997 ◽  
Vol 40 (5) ◽  
Author(s):  
F. Gilbert
Keyword(s):  
Shear Modulus ◽  
Singular Perturbation ◽  
Rayleigh Waves ◽  
Elastic Solid ◽  
Free Oscillations ◽  
Approximate Methods ◽  
Fluid State ◽  
The Earth ◽  
Elastic Interface ◽  
Small Shear

The system of propagator equations for an elastic solid becomes singular as the shear modulus becomes vanishingly small. In computational applications there is severe loss of precision as the limit of zero shear modulus is approached. The use of perturbation theory to address the effect of very small shear modulus, using the fluid state as a basis, is unsatisfactory because certain phenomena, e.g., Rayleigh waves, cannot be represented. Two approximate methods are presented to account for the singular perturbation. Since most of the Earth is nearly neutrally stratified, in which case the motion is nearly irrotational, one can impose the irrotational constraint and obtain a modified and reduced system of propagator equations. This system does not have the singular perturbation. In the second method the transition zone between a fluid and a solid is represented as an infinitesimally thin, Massive, Elastic Interface (MEI). The boundary conditions across the MEI are dispersive and algebraic. The limit of zero shear modulus is non-singular.

Elastic Instability and Geology

1932 ◽  
Vol 69 (7) ◽  
pp. 321-324 ◽  
Author(s):  
Harold Jeffreys
Keyword(s):  
Permanent Deformation ◽  
Elastic Solid ◽  
External Pressure ◽  
Considerable Change ◽  
Engineering Practice ◽  
Elastic Instability ◽  
Finite Radius ◽  
Steady Rotation ◽  
All Speeds ◽  
Great Stress

IN the February number of the Geological Magazine, Mr. A. J. Bull illustrates an interesting experiment on a type of deformation in a sheet of elastic material subject to a contraction. The inferences he draws from it, however, need further discussion. An elastic solid, under sufficiently great stress, will develop a permanent deformation either by continuous yield or by fracture, according to the nature of the material. The stress needed to produce such deformation may conveniently be called the strength. But in certain circumstances it is possible for a stress to produce a considerable change of shape before the strength is reached, and such phenomena are common in engineering practice. A simple example is provided when a rod of india-rubber is compressed longitudinally. So long as the force applied is not too great the rod remains straight; but at a certain critical value of the compression it suddenly buckles sideways into an arc. The straight form is still a possible position of equilibrium, but it is no longer stable, and the slightest disturbance grows until the rod has become strongly bent, giving a new and stable position of equilibrium. It is easy to verify in this case that the strength has not been reached; we need only remove the thrust on the ends, when the rod returns to its original straight form. Another example is provided by a flywheel on a long shaft. Steady rotation is possible at all speeds; but there is a critical speed at which instability develops. Then it becomes possible for the rod to bend and to carry the centre of the flywheel around a circle of finite radius; the tendency of the rod to recover its form provides just enough force to keep the centre of the wheel moving in a circle. Any further increase of the speed of rotation will make the shaft bend through a considerable angle, with disastrous consequences. Other known cases arise in the collapse of tubes under external pressure or longitudinal thrust.1

scholarly journals Microstructure and Pressure Driven Electrodeposition Stability in Solid-State Batteries

2020 ◽  
Author(s):  
Ankit Verma ◽  
Hiroki Kawkami ◽  
Hiroyuki Wada ◽  
Anna Hirowatari ◽  
Nobuhisa Ikeda ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Solid State ◽  
Shear Modulus ◽  
Solid Electrolyte ◽  
Current Density ◽  
High Current Density ◽  
External Pressure ◽  
Operating Conditions ◽  
Solid State Batteries ◽  
The Impact

Interfacial deposition stability at the lithium metal-solid electrolyte interface in all solid-state batteries (ASSB) is governed by the stress-transport-electrochemistry coupling in conjunction with the polycrystalline/amorphous solid electrolyte architecture. In this work, we delineate the optimal solid electrolyte microstructure comprising of grains, grain boundary and voids possessing desirable ionic conductivity and elastic modulus for superior transport and strength. An analytical formalism is provided to discern the impact of external “stack” pressure induced mechanical stress on electrodeposition stability; stress magnitude obtained are in the megapascal range considerably diminishing the stress-kinetics effects. For experimental stack pressures ranging up to 10 MPa, the impact of stress on reaction kinetics is negligibly small and electrolyte transport overpotentials dictate electrodeposition stability. We detail the deposition stability phase map as a function of solid electrolyte to Li metal shear modulus and molar volume ratios under varying operating conditions including external pressure, surface roughness, applied current density and ambient temperature. High current density operation with stable deposition can be ensured with ample external pressure, high temperature and low surface roughness operation for low shear modulus ratio of the solid electrolyte to Li metal. <br>

Determining the Sub-Surface Stresses in a Graded-Elastic Solid Using Fourier Series Decomposition

2011 ◽  
Author(s):  
Stewart Chidlow ◽  
Mircea Teodorescu ◽  
Nick Vaughan
Keyword(s):  
Fourier Series ◽  
Shear Modulus ◽  
Solution Method ◽  
Analytic Solution ◽  
Elastic Solid ◽  
Local Deformation ◽  
Elastic Substrate ◽  
Micro Scale ◽  
Surface Stresses ◽  
Layered Solid

This paper describes a fully analytic solution method for the displacements and sub-surface stresses within a graded elastic layered solid. This method can be utilised to predict the local deformation of nano or micro-scale depositions under contacting conditions. The solid consists of two distinct layers which are considered to be perfectly bonded and comprise of a graded elastic coating whose shear modulus varies exponentially with the depth coordinate and an infinitely deep homogeneously elastic substrate. The solution given in this paper is generic and easily utilised to solve real problems as it requires only known physical characteristics of the solid under study and an applied surface pressure. As a result, this model is very cheap to use and can be easily integrated into tribological codes to predict local deflections.

scholarly journals Microstructure and Pressure Driven Electrodeposition Stability in Solid-State Batteries

2020 ◽  
Author(s):  
Ankit Verma ◽  
Hiroki Kawkami ◽  
Hiroyuki Wada ◽  
Anna Hirowatari ◽  
Nobuhisa Ikeda ◽  
...  
Keyword(s):  
Surface Roughness ◽  
Solid State ◽  
Shear Modulus ◽  
Solid Electrolyte ◽  
Current Density ◽  
High Current Density ◽  
External Pressure ◽  
Operating Conditions ◽  
Solid State Batteries ◽  
The Impact

Interfacial deposition stability at the lithium metal-solid electrolyte interface in all solid-state batteries (ASSB) is governed by the stress-transport-electrochemistry coupling in conjunction with the polycrystalline/amorphous solid electrolyte architecture. In this work, we delineate the optimal solid electrolyte microstructure comprising of grains, grain boundary and voids possessing desirable ionic conductivity and elastic modulus for superior transport and strength. An analytical formalism is provided to discern the impact of external “stack” pressure induced mechanical stress on electrodeposition stability; stress magnitude obtained are in the megapascal range considerably diminishing the stress-kinetics effects. For experimental stack pressures ranging up to 10 MPa, the impact of stress on reaction kinetics is negligibly small and electrolyte transport overpotentials dictate electrodeposition stability. We detail the deposition stability phase map as a function of solid electrolyte to Li metal shear modulus and molar volume ratios under varying operating conditions including external pressure, surface roughness, applied current density and ambient temperature. High current density operation with stable deposition can be ensured with ample external pressure, high temperature and low surface roughness operation for low shear modulus ratio of the solid electrolyte to Li metal. <br>

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