Elastic Instability and Geology

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 thestrength. 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