Elasticity

“ Limits of Elasticity.—A solid body which has been strained by considerable forces does not in general recover its original size and shape completely after the forces cease to act. The strain that is left is called set. If set occurs the elasticity is said to be “imperfect,” and the greatest strain (or the greatest load) of any specified type, for which no set occurs, defines the “limit of perfect elasticity” corresponding to the specified type of strain, or of stress. ”

“ Here, then, out of matter possessing rigidity, but absolutely devoid of elasticity, we have made a perfect model of a spring in the form of a spring balance. Connect millions of millions of particles by pairs of rods such as these of this spring balance, and we have a group of particles constituting an elastic solid; exactly fulfilling the mathematical ideal worked out by Navier, Poisson, and Cauchy, and many other mathematicians, who, following their example, have endeavored to found a theory of the elasticity of solids on mutual attraction and repulsion between a group of material particles. ”

“ The elasticity of all the diameters of any plane perpendicular to the axis of a prism of rock crystal, may be considered as being sensibly the same.
2nd. All the planes parallel to the axis are far from possessing the same elastic state; but if any three of these planes be taken, restricting ourselves only to this condition, that the angles which they form with each other are equal, then their elastic state is the same. ”

“ In some substances the limit is reached with slight distortion, while others are perfectly elastic even when greatly stretched. India rubber is an example of a body having perfect elasticity through wide limits. Glass has great elastic force but its limit of elasticity is soon reached. Substances like India rubber may be said to have great "stretchability," but little elastic force. In physics, elasticity refers to the elastic force rather than to ability to endure stretching. ”

“ Elasticity.
What makes a ball bounce?
How does a springboard help you dive?
Why are automobile and bicycle tires filled with air?
Suppose there were a man who was perfectly elastic, and who made everything he touched perfectly elastic. Fortunately there is no such person, but suppose an elastic man did exist:
He walks with a spring and a bound; his feet bounce up like rubber balls each time they strike the earth; his legs snap back into place after each step as if pulled by a spring. If he stumbles and falls to the ground, he bounces back up into the air without a scar. ”

“ The elastic state of these plates cannot present such remarkable differences as those we have observed in the preceding series; for, being all cut round the axis of greatest elasticity, they can only contain in their plane that of least or that of mean elasticity, or lastly, those intermediate between these limits, which do not vary greatly from each other. ”

“ When the limits of elasticity are not exceeded no injury is done to a material or structure by the action of the forces. The strength or weakness of a material, and the safety or insecurity of a structure, are thus closely related to the elasticity of the material and to the change of size or shape of the structure when subjected to forces. ”

“ Reasoning from this experiment, we might infer that the elasticity of a beam is not affected by a weight which is less than half that which would break it, and that, therefore, it may bear without injury a weight not exceeding this amount. ”

“ It possesses so-called elasticity of bulk. In the case of water having a free surface there is, as we have seen, a resistance to any change of level in the surface. This may be called an elasticity of surface form. Whenever an elastic material is strained or deformed, energy has to be expended on it to create the deformation. Thus to wind up a watch-spring, stretch a piece of indiarubber, compress some air, or bend a bow, requires an energy expenditure. ”

“ It therefore requires energy to bend a bow, just as truly and visibly as it does to raise a weight above the earth, and elasticity is, therefore, as truly a species of force as gravity is. We shall not here attempt to discuss the various ways in which this force may act, or in which a soUd elastic substance will resist all attempts to deform it; but in all cases it is clearly manifest that work must be spent upon the body, and the force of elasticity must be encountered and overcome throughout a certain space before any sensible deformation can take place. ”

“ The behaviour of an elastic solid body, strained within the limits of its elasticity, is entirely determined by the constants and if the body is isotropic, that is to say, if it has the same quality in all directions around any point. ”

“ And accordingly, so long as our purpose is morphological, so long as what we seek to explain is regularity and definiteness of form, it matters little if we should happen, here or there, to confuse surface tension with elasticity, the contractile forces manifested at a liquid surface with those which come into play at the complex internal surfaces of an elastic solid. ”

“ The elasticity is essential in order for the medium to store up energy, and also to enable it to resume its original shape after deformation, while the inertia is necessary in order that the medium may transmit the impulse, and oscillate to and fro until the impulse received has been passed on. ”

“ For any particular mode of stress the limit of elasticity is much more sharply defined in some materials than in others. When well denned it may readily be recognized in the testing of a sample from the fact that after the stress exceeds the limit of elasticity the strain begins to increase in a much more rapid ratio to the stress than before. ”

“ Elasticity is the real origin or indispensable intermediary of all the more important physical phenomena of the universe. . . . In a word, the function of elasticity in nature is at least as important as that of universal gravitation. Indeed gravitation and elasticity should be considered as effects of the same cause, which correlate or connect all the material parts of the [242] universe ”

“ Now this argument from analogy with a solid is rather misleading, for the forces that operate in the case of a solid sphere that flattens itself and rebounds, are due to the bodily elasticity which enables it not only to resist, but also to recover from any distortion of shape or shearing of its internal parts past each other. ”

“ Of all bodies, the air is the most eminent for this property, and it has thence obtained the name of an elastic fluid. Hard bodies are in the next degree elastic; if two ivory, or hardened steel balls are struck together, the parts at which they touch, will be flattened; but their elasticity will make them instantaneously resume their former shape. ”

“ The energy of form is manifested in bodies (solid or rigid bodies) that maintain a definite shape because every change of shape is connected with work or with the expenditure of some other energy. If the changes are small, the bodies are of such a nature that they return to their former condition of their own accord after the force exerted upon them has ceased to act. This property is called elasticity. However, the theory of elasticity, which has been extensively and rationally developed, is regarded as belonging rather to mathematical physics in general than to mechanics in particular. ”

“ Degrees of Elasticity in Different Substances.—Some substances have so very little elasticity that they are practically considered as having none. Lead is one of these. A rod of lead when bent remains so, and a leaden ball does not rebound. While aeriform substances are the most compressible of all, they are also the most elastic. Air compressed returns to its usual condition the moment that it is relieved from the pressure, and with a force proportioned to the amount of the pressure. So it is with steam and the gases. ”

“ If you make a dent in rubber, it springs right back to the shape it had before. Elasticity of volume is the tendency of a substance to go back to its original size, as lead does. If you manage to squeeze lead into a smaller space, it will spring right back to the same size as soon as you stop pressing it on all sides. But a dent in lead will stay there; it has little elasticity of form.
Air and water—all liquids, in fact—have a great deal of elasticity of volume, but practically no elasticity of form. ”

“ The word elastic, in physics, is the name given to the tendency which a body exerts, when distorted, to return to its original shape. Rubber possesses more elasticity than any other material known, it being possible to stretch a piece of rubber cord to eight or nine times its original length without fracture. Rubber also possesses the added requisite of lightness and will store up more energy than any form of steel spring. ”

“ The proper definition of elasticity is the power of recovering the original form after distortion, and matter gradually acquires this power. As life develops, the equilibrium of the compounds that make up the form becomes more and more unstable, while at the same time the general cohesion of the form increases; when we come to the higher forms, such as the body of man, we find a power of maintaining the central position greater than we find in any other form, together with an increased plasticity and elasticity ”

“ Further, as the elasticity of the medium which regulates the pressure is proportional to the density, so the pressure must decrease, as the elasticity decreases--that is, as the electric potential decreases, or the electric density is diminished. ”

“ To represent all the correlated quantities we should have to construct not only a diagram of moments but also a diagram of elastic deflexion and its so-called “curvature”; and the engineer would want to know something more about the material of the ligamentous tension-member—its modulus of elasticity in direct tension, its elastic limit, and its safe working stress.
In various ways our structural problem is beset by “limiting conditions.” Not only must rigidity be associated with flexibility, but also stability must be ensured in various positions and attitudes ”

“ The hypothesis which he thus suggests is, that there is an elastic medium pervading all space, and increasing in elasticity as we proceed from dense bodies outwards: that this “causes the gravity of such dense bodies to each other: every body endeavouring to go from the denser parts of the medium towards the rarer.” ”

“ Elasticity implies susceptibility of compression, and the susceptibility of compression depends upon the porosity of bodies; for were there no pores or spaces between the particles of matter of which a body is composed, it could not be compressed. ”

“ The modulus of the elasticity of any substance is a column of the same substance capable of producing a pressure on its base which is to the weight causing a certain degree of compression as the length of the substance is to the diminution of its length. ”

“ Hooke’s law of proportionality of stress and strain leads to the introduction of important physical constants: the moduluses of elasticity of a body. Let a bar of uniform section (of area ) be stretched with tension which is distributed uniformly over the section, so that the stretching force is and let the bar be unsupported at the sides. The bar will undergo a longitudinal extension of magnitude where is a constant quantity depending upon the material. ”

“ You are quite right; and the return of the ball, after having struck the wall, affords an example of what is termed reflected motion, upon which I shall have to remark when we come to the interesting subject of ‘Compound Forces;’ but at present, my only wish is to render the property of elasticity intelligible to you. It is a force of very extensive application; there is scarcely a machine wherein the elasticity of one or more solids is not essentially concerned. Nature, also, avails herself of this property to accomplish many of her purposes. ”

“ Thus the definition of a solid cannot be drawn from its mechanical properties. It cannot be said, after what we have just seen, that solid bodies retain their form, nor that they have a limited elasticity, for M. Spring has made known a case where the elasticity of solids is without any limit. ”

“ In what has been said above it is assumed that the stress is within the limit of elasticity. When the twisting couple is increased so that this limit is passed, plastic yielding begins in the outermost layer, and a larger proportion of the whole stress falls to be borne by layers nearer the centre. ”

“ Now, the velocity of wave propagation can be seen, without the aid of any mathematical analysis, to depend on the elasticity of the medium and its density; for we can see that if a medium is highly elastic the disturbance would be propagated at a great speed. ”

“ In a body which possesses three unequal axes of elasticity, there are four planes in which the elasticity is so distributed that the two sounds of the plates parallel to these planes become equal, and the two modes of division gradually transform themselves into each other, by turning round two fixed points, which, for this reason, I have called nodal centres. ”

“ When one of the axes of elasticity occurs in the plane of the plate, one of the nodal figures always consists of two straight lines, which intersect each other at right angles, and one of which invariably places itself in the exact direction of this axis ”

“ And yet you know that a bubble made of suds has not only strength, but elasticity. Suppose a bubble of energy floating in space were to be covered to the depth of the thickness of a sheet of tissue paper with the dust of space, would that surprise you? ”

“ Tests of elasticity are made by subjecting wire of different materials but of the same dimensions to the same tension. The one changing least is said to have the greatest elastic force or elasticity. If greater forces are applied to the wire and then removed, one will finally be found that will permanently stretch the wire so that it will not return exactly to the former length. ”