scholarly journals Large elastic deformations of isotropic materials. I. Fundamental concepts

1948 ◽  
Vol 240 (822) ◽  
pp. 459-490 ◽  
Keyword(s):  
The Body ◽  
Elastic Behaviour ◽  
Stress And Strain ◽  
Elastic Deformations ◽  
Hooke’S Law ◽  
Widespread Agreement ◽  
Wide Range ◽  
Hooke's Law ◽  
High Degree

The mathematical theory of small elastic deformations has been developed to a high degree of sophistication on certain fundamental assumptions regarding the stress-strain relationships which are obeyed by the materials considered. The relationships taken are, in effect, a generalization of Hooke’s law— ut tensio, sic vis . The justification for these assumptions lies in the widespread agreement of experiment with the predictions of the theory and in the interpretation of the elastic behaviour of the materials in terms of their known structure. The same factors have contributed to our appreciation of the limitations of these assumptions. The principal problems, which the theory seeks to solve, are the determination of the deformation which a body undergoes and the distribution of stresses in it, when certain forces are applied to it, and when certain points of the body are subjected to specified displacements. These problems are always dealt with on the assumption that the generalization of Hooke’s law is obeyed by the material of the body and that the deformation is small, i.e. the change of length, in any linear element in the material, is small compared with the length of the element in the undeformed state. Apart from the fact that the generalization of Hooke’s law is obeyed accurately by a very wide range of materials, under a considerable variety of stress and strain conditions, it has the further advantage that it leads to a mathematically tractable theory.

scholarly journals Breakdown of Hooke’s law of elasticity at the Mott critical endpoint in an organic conductor

2016 ◽  
Vol 2 (12) ◽  
pp. e1601646 ◽  
Author(s):  
Elena Gati ◽  
Markus Garst ◽  
Rudra S. Manna ◽  
Ulrich Tutsch ◽  
Bernd Wolf ◽  
...  
Keyword(s):  
Degrees Of Freedom ◽  
Relative Length ◽  
Mott Transition ◽  
Organic Conductor ◽  
Strong Electron ◽  
Hooke’S Law ◽  
Wide Range ◽  
Hooke's Law ◽  
Length Changes ◽  
Universal Properties

The Mott metal-insulator transition, a paradigm of strong electron-electron correlations, has been considered as a source of intriguing phenomena. Despite its importance for a wide range of materials, fundamental aspects of the transition, such as its universal properties, are still under debate. We report detailed measurements of relative length changes ΔL/Las a function of continuously controlled helium-gas pressurePfor the organic conductor κ-(BEDT-TTF)2Cu[N(CN)2]Cl across the pressure-induced Mott transition. We observe strongly nonlinear variations of ΔL/Lwith pressure around the Mott critical endpoint, highlighting a breakdown of Hooke’s law of elasticity. We assign these nonlinear strain-stress relations to an intimate, nonperturbative coupling of the critical electronic system to the lattice degrees of freedom. Our results are fully consistent with mean-field criticality, predicted for electrons in a compressible lattice with finite shear moduli. We argue that the Mott transition for all systems that are amenable to pressure tuning shows the universal properties of an isostructural solid-solid transition.

Badania zastosowania chlorków poliglinu w procesie koagulacji zanieczyszczeń w wodach złożowych o szerokim zakresie pH

Nafta-Gaz ◽  
2020 ◽  
Vol 76 (11) ◽  
pp. 807-815
Author(s):  
Piotr Jakubowicz ◽  
Keyword(s):  
High Efficiency ◽  
Total Alkalinity ◽  
Degree Of Hydrolysis ◽  
Reservoir Water ◽  
Rapid Reduction ◽  
Coagulant Activity ◽  
Wide Range ◽  
Oil And Natural Gas ◽  
High Degree

Reservoir waters extracted during exploitation of crude oil and natural gas are a serious threat to the environment. The reason is high content of dissolved salts, mainly chlorides, as well as toxic components, such as: petroleum substances with aromatic hydrocarbons, and various chemicals applied during hydrocarbons production, e.g. corrosion, hydrates and paraffin inhibitors, surfactants, methanol etc. For this reason, the extracted reservoir water should be managed in a way that is least harmful to the environment. One of the methods of management that meets this requirement is injection of reservoir water into the absorptive horizon. In order to provide failure-free injection, with maximum use of the capabilities of an absorptive horizon, it is necessary to prepare the water properly by removing the components (solids, deposits and suspensions) that cause damage of the injection well. One of the most effective methods of water treatment is coagulation. Aluminum(III) sulfate(VI), commonly used in coagulation, requires a neutral pH of water. Exceeding this level results in rapid reduction in coagulation efficiency, and even in increase in the content of suspended solids in purified water. Extracted reservoir waters drastically change their properties from strongly reducing to oxidizing, due to methane removal after pressure reduction and oxygenation in contact with air. Moreover, while changing the electrochemical potential to positive, presence of iron and manganese ions in the water causes precipitation of oxides and hydroxides in the form of suspensions and the pH decreases due to their hydrolysis. Due to the dynamic course of these processes, as well as the additional acidification of water by addition of the coagulant (aluminum(III) sulfate(VI)), adjustment of the pH to the level appropriate for effective coagulation is often a serious problem. The solution could be application of properly selected modern coagulants of much greater efficiency, enabling a decrease of the agent dose as well as reduction of volume and improvement of the structure of post-coagulation sediments. Additionally, they are highly efficient in a wide range of water reactions. The article describes laboratory tests on a selected coagulant (polyaluminium chloride), which allow for determination of the range of deposit water reaction in which this agent can be used. For the tests, Flokor 1ASW was selected due to its high degree of hydrolysis and slight acidity (pH ~3.5) compared with other polyaluminium chlorides, which means low consumption of total alkalinity of purified water. The results obtained show a wide range of water reaction (pH from 8.0 to 4.0), in which the effectiveness of coagulant activity ensures the correct level of purification. In addition, the use of Flokor 1ASW with effective Stabpol K flocculant allows for production of big and quickly settled flocs. Post-coagulation sediments have much smaller volume than when using aluminum(III) sulfate(VI). The results of industrial tests, carried out in order to prepare reservoir water for injection, without pH correction, have been presented in the article. They confirmed the high efficiency of the selected chemicals.

A Ternary Solution for Independent Acoustic Impedance and Speed of Sound Matching to Biological Tissues

1982 ◽  
Vol 4 (2) ◽  
pp. 163-170 ◽  
Author(s):  
Jonathan Ophir ◽  
Paul Jaeger
Keyword(s):  
Speed Of Sound ◽  
Acoustic Impedance ◽  
Soft Tissues ◽  
Sound Propagation ◽  
Biological Tissues ◽  
Liquid System ◽  
The Body ◽  
Acoustic Parameters ◽  
Wide Range

In applications requiring a liquid which is acoustically well matched to biological tissues, it is often difficult to find a material which is matched well in terms of both the acoustic impedance and speed of sound propagation in it; changing one parameter invariably affects the other. A three component liquid system is described, which allows independent adjustment of these two acoustic parameters over a wide range. This range encompasses the soft tissues of the body. Results of parameter measurements are presented in the form which allows simple determination of the mixture required to match any combination of acoustic impedance and speed of sound propagation over a given range.

Gel Structure. VI. Preparation of Gels and Globular Structures from Rubbers by Vulcanization of Solutions

1956 ◽  
Vol 29 (1) ◽  
pp. 296-301
Author(s):  
P. I. Zubov ◽  
Z. N. Zhurkina ◽  
V. A. Kargin
Keyword(s):  
Mechanical Properties ◽  
Natural Rubber ◽  
Gel Structure ◽  
Hooke’S Law ◽  
Sulfur Monochloride ◽  
Synthetic Rubber ◽  
Wide Range ◽  
Polybutadiene Rubber ◽  
Hooke's Law

Abstract 1. The mechanical properties of gels prepared from solutions of natural rubber and synthetic rubber were studied. 2. It was established that gels of synthetic rubber (polybutadiene rubber) have a wide range of relaxation periods. Gels of natural rubber (smoked sheet) behave like ideally elastic substances, following Hooke's law in the change of rate of deformation by 1000 times. 3. The viscosity of solutions of natural rubber and of polybutiadiene rubber in the presence of sulfur monochloride was studied. 4. We observed that sulfur monochloride sharply decreases the viscosity of natural rubber solutions and has almost no influence on the viscosity of synthetic rubber solutions.

scholarly journals An Evaluation of the Potential of Heparin to Inhibit the Viral Entry of SARS-CoV-2

2021 ◽  
Keyword(s):  
Viral Entry ◽  
The Body ◽  
Ligand Docking ◽  
Binding Potential ◽  
Docking Simulations ◽  
Binding Domains ◽  
Wide Range ◽  
Novel Coronavirus ◽  
Viral Components ◽  
High Degree

Heparin is an anticoagulant medicine that prevents the formation of harmful blood clots in the vessels. Following the outbreak of the novel coronavirus disease 2019 (COVID-19), heparin has helped to improve the health of affected patients beyond its anticoagulant effects. The potential antiviral activity of heparin has attracted speculation due to its highly sulfated profile, which allows it to have a high binding affinity to a wide range of viral components. Heparin’s successful binding to the ZIKA virus, human immunodeficiency virus, as well as the SARS CoV and MERS CoV spike proteins have demonstrated its potential to inhibit the entry of SARS-CoV-2 into the body. A high degree of sequence homology also enables heparin to have inhibitory binding potential on viral components. The SARS-CoV-2 virus exhibits significant differences in its spike glycoprotein (SGP) sequence compared to other coronaviruses. The SGP sequence in SARS-CoV-2 contains additional potential glycosaminoglycan (GAG) binding domains that may drive differences in the attachment and entry process of the virus. Findings from unbiased computational ligand docking simulations, pseudotyped spike protein experiments, and cell to cell fusion assays have also opened possibilities to investigate the antiviral properties of heparin in clinical trials

scholarly journals A focus on homocysteine in autism.

2013 ◽  
Vol 60 (2) ◽  
Author(s):  
Joanna Kałużna-Czaplińska ◽  
Ewa Żurawicz ◽  
Monika Michalska ◽  
Jacek Rynkowski
Keyword(s):  
Human Physiology ◽  
Folic Acid ◽  
Dietary Habits ◽  
Biological Fluids ◽  
Body Fluids ◽  
The Body ◽  
Autistic Children ◽  
Pathological Conditions ◽  
Wide Range

Homocysteine is an amino acid, which plays several important roles in human physiology. A wide range of disorders, including neuropsychiatric disorders and autism, are associated with increased homocysteine levels in biological fluids. Various B vitamins: B6 (pyridoxine), B12 (cobalamin), and B9 (folic acid) are required as co-factors by the enzymes involved in homocysteine metabolism. Therefore, monitoring of homocysteine levels in body fluids of autistic children can provide information on genetic and physiological diseases, improper lifestyle (including dietary habits), as well as a variety of pathological conditions. This review presents information on homocysteine metabolism, determination of homocysteine in biological fluids, and shows abnormalities in the levels of homocysteine in the body fluids of autistic children.

Effects of Stress

1996 ◽  
Author(s):  
Gerhard Oertel
Keyword(s):  
Yield Stress ◽  
Elastic Strain ◽  
Elastic Response ◽  
Stress And Strain ◽  
Crystalline Materials ◽  
Hooke’S Law ◽  
Permanent Strain ◽  
Compliance Tensor ◽  
Hooke's Law ◽  
Critical Yield

The simplest relationship between stress and strain is Hooke’s law, describing the linear elastic response of solids to stress. Elastic strain (almost in all cases small) is proportional to the applied stress, with one proportionality factor expressing the relationship between normal, and another that between tangential stress and strain. An ideally elastic strain is completely reversed upon removal of the stress that has caused it. Most materials obey Hooke’s law somewhat imperfectly, and that only up to a critical yield stress beyond which they begin to flow and to acquire, in addition to the elastic strain, a permanent strain that does not revert upon stress release. Hooke’s law in this form is applied to materials that are elastically isotropic, or can be assumed to be approximately so. Crystals, however, never are elastically isotropic, nor are crystalline materials consisting of constituent grains with a distribution of crystallographic orientations that departs from being uniform. The response of a crystal to a stress (at a level below the yield stress) consists of a strain determined by a matter tensor of the fourth rank, the compliance tensor s i j k l : . . . ɛij = s i j k l σkl, (7.1) . . . the 81 components of which are constants. Any tensor that describes the linear relationship between two tensors of the second rank is necessarily of the fourth rank, and like other tensors of the fourth rank, the compliance tensor can be referred to a new set of reference coordinates by means of a rotation matrix aij: s i j k l = aimajnakoalp smnop. (7.2) . . . The components of the compliance tensor are highly redundant, first because both the stress and the strain tensors are symmetric, and second because the tensor itself is symmetric. The number of independent components for crystals of the lowest, triclinic (both classes) symmetry is 21, and with increasing crystal symmetry the redundancies become more numerous; only three independent compliances are needed to describe the elastic properties of a cubic crystal.

scholarly journals A robust microbalance of high sensitivity. Suitable for weighing sorbed films

1929 ◽  
Vol 125 (799) ◽  
pp. 579-586 ◽  
Keyword(s):  
Plane Surface ◽  
Horizontal Tube ◽  
High Sensitivity ◽  
Null Point ◽  
Monomolecular Film ◽  
Wide Range ◽  
Beam Type ◽  
High Degree ◽  
Two Sides

The sorption balance of McBain and Baker may be made of high degree of sensitivity, but the total weight which it will then support is correspondingly diminished. For weighing a monomolecular film on a comparatively heavy plane surface it is necessary to use a balance of beam type. A balance sensitive to 4 x 10 -9 grams can be made sufficiently compact to be placed in a horizontal tube so that it may be used over a wide range of temperatures and pressures including the conditions necessary for freeing from sorbed material the surfaces to be weighed. such a balance may be so designed that the volumes of the two sides of the balance are equal and unaffected by buoyancy. If, likewise, there be placed upon the two sides of the balance equal volumes of the same substance but of different area of surface, the differential change of weight caused by adsorption will be measured directly. A final desideratum is that the balance should be of null point type and free from any bind of hysteresis. Steele and Grant described a microbalance made of fused quartz which was sensitive to 4 x 10 -9 grams and was capable of weighing 0.1 gram with an accuracy of 1 x 10 -7 gram, added improvements were described by Gray and Ramsay .Aston simplified the design of the beam and made a balance specially adapted to the determination of gas densities. Stock and Ritter made a further modification by replacing the fused charts bulks-edge with a pair of needle points. They also described a null-point balance in which a magnetised steel needle was sealed horizontally within the beam. The magnetic held from a bar magnet held vertically over the centre of the balance was used to compensate changes in level of the beam. The intensity of this controlling magnetic field was varied either by altering the distance between the bar magnet and the balance, or by increasing the held of the bar magnet electrically.

On determination of material parameters from loading and unloading responses in nanoindentation with a single sharp indenter

2006 ◽  
Vol 21 (4) ◽  
pp. 995-1011 ◽  
Author(s):  
Lugen Wang ◽  
S.I. Rokhlin
Keyword(s):  
Finite Element ◽  
Strain Hardening ◽  
Yield Stress ◽  
Finite Element Simulations ◽  
Strain Hardening Exponent ◽  
Scaling Functions ◽  
Stress And Strain ◽  
Wide Range ◽  
Loading And Unloading

This paper quantitatively describes the loading-unloading response in nanoindentation with sharp indenters using scaling analyses and finite element simulations. Explicit forward and inverse scaling functions for an indentation unloading have been obtained and related to those functions for the loading response [L. Wang et al., J. Material Res.20(4), 987–1001 (2005)]. The scaling functions have been obtained by fitting the large deformation finite element simulations and are valid from the elastic to the full plastic indentation regimes. Using the explicit forward functions for loading and unloading, full indentation responses for a wide range of materials can be obtained without use of finite element calculations. The corresponding inverse scaling functions allow one to obtain material properties from the indentation measurements. The relation between the work of indentation and the ratio between hardness and modulus has also been studied. Using these scaling functions, the issue of nonuniqueness of the determination of material modulus, yield stress, and strain-hardening exponent from nanoindentation measurements with a single sharp indenter has been further investigated. It is shown that a limited material parameter range in the elastoplastic regime can be defined where the material modulus, yield stress, and strain-hardening exponent may be determined from only one full indentation response. The error of such property determination from scattering in experimental measurements is determined.

Electron Heat Transfer in a Quiescent Nonequilibrium Plasma

1970 ◽  
Vol 92 (3) ◽  
pp. 447-455 ◽  
Author(s):  
E. V. McAssey ◽  
Hsuan Yeh
Keyword(s):  
Heat Transfer ◽  
Nonequilibrium Plasma ◽  
Spherical Body ◽  
Operating Conditions ◽  
The Body ◽  
Electron Heat ◽  
Wide Range ◽  
Weakly Ionized ◽  
Body Potential

An asymptotic solution has been obtained for the electron heat transfer to a spherical body immersed in a weakly ionized, quiescent plasma. Dimensional analysis of the governing equations shows that the problem can be divided into two regions: charge-separated and quasi-neutral. For the charge-separated region, the equations must be solved numerically, whereas the quasi-neutral solution can be expressed in closed form. From these studies it was found that the extent of the charge-separated region (i.e, sheath) is of the order of Λ2/3. Within the sheath the effects of ionization and recombination are of the order of Λ4/3. The results include the variation of electron flux, electron heat transfer, and current as a function of body potential. The results are presented in a form to permit the easy determination of the electron heat transfer to a body immersed in a quiescent, weakly ionized plasma over a wide range of operating conditions. Furthermore, the electrical characteristics presented here can be used in conjunction with electron heating data to treat the body as a probe for diagnostic purposes.

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