# Elasticity

## Stress, Strain, And Elastic Modulus

The simplest description of elasticity is Hooke's law, which states, "The stress is proportional to the strain." This relation was first expressed by the British scientist, Robert Hooke (1635-1702). He arrived at it through studies in which he placed weights on metal springs and measured how far the springs stretched in response. Hooke noted that the added length was always proportional to the weight; that is, doubling the weight doubled the added length.

In the modern statement of Hooke's law, the terms "stress" and "strain" have precise mathematical definitions. Stress is the applied force divided by the area the force acts on. Strain is the added length divided by the original length.

To understand why these special definitions are needed, first consider two bars of the same length, made of the same material. One bar is twice as thick as the other. Experiments have shown that both bars can be stretched to the same additional length only if twice as much weight is placed on the bar that is twice as thick. Thus, they both carry the same stress, as defined above.

The special definition of strain is required because, when an object is stretched, the stretch occurs along its entire length, not just at the end to which the weight is applied. The same stress applied to a long rod and a short rod will cause a greater extension of the long rod. The strain, however, will be the same on both rods.

The amount of stress required to produce a given amount of strain also depends on the material being stretched. Therefore, the ratio of stress to strain is a unique property of materials, different for each substance. It is called the elastic modulus (plural: moduli). It is also known as Young's modulus, after Thomas Young (1773-1829) who first described it. It has been measured for thousands of materials. The greater the elastic modulus, the stiffer the material is. For example, the elastic modulus of rubber is about six hundred psi (pounds per square inch). That of steel is about 30 million psi.