Elasticity

Elasticity is that property of most strained substances by which they may recover their original shape and size when those forces which produce the strain are removed. There are different kinds of strain, such as strain in shape, bulk, or in length, and consequently different kinds of elasticity. Thus, a substance may be changed in shape without having its volume altered; if it possess an elasticity that will bring it back to its original shape when the stress is removed, it is said to possess rigidity or elasticity of form. The characteristic of a fluid is that it possesses no rigidity; any small force may in course of time deform it, and a removal of that force will not necessarily lead to a renewal of the original form. Then a substance may be changed in volume by the application of stress. A sphere of gas, for example, may be compressed into a smaller sphere. If the original conditions of force be obtained. the gas will recover its former size; and it is said to have an elasticity of bulk [Boyle's Law], a property that is possessed by nearly all solids, liquids, and gases to a greater or less extent. If a stress be applied in one direction only to a substance, as when a weight is hung at one end of a steel wire that is supported at the other end, change of dimension in that direction will take place; the wire will be extended. Removal of the weight will cause a more or less complete return to the original length. This is due to an elasticity of length, and it may be studied without regard to the change in the lateral dimensions of the wire or other material so strained. As a matter of fact, the wire will increase in bulk slightly, though it contracts a little laterally. In all cases of solids an excessive strain will so alter the substance that it cannot return to its original shape and size. Thus, copper wire may be permanently extended if the applied forces are sufficiently large. The material is then said to have a permanent set, or to have been stressed beyond the elastic limit. An elastic limit cannot be fixed for a fluid. The numerical measure of elasticity is given by a modulus for each material, i.e. the quotient of stress divided by strain. Stress is generally measured in pounds per square inch, and strain as the ratio of the change in dimension to the original dimension itself. Thus, if a length L is extended to L + l, the strain is l / L. Hooke's law states that up to the elastic limit stress is proportional to the strain it produces. The following are the average moduli of elasticity of length and of rigidity for the more important materials employed in engineering, together with their elastic strengths in tension. All are in pounds per square inch: -

If inelastic bodies impact directly on each other, they will remain together without rebounding. Elastic bodies, on the other hand, exert a mutual force of restitution when they collide, and this produces a separation. [Impact.]