Hertzian Theory of Non-adhesive Elastic Contact
The classical theory of contact focused primarily on non-adhesive contact where no tension force is allowed to occur within the contact area, i.e., contacting bodies can be separated without adhesion forces. Several analytical and numerical approaches have been used to solve contact problems that satisfy the no-adhesion condition. Complex forces and moments are transmitted between the bodies where they touch, so problems in contact mechanics can become quite sophisticated. In addition, the contact stresses are usually a nonlinear function of the deformation. To simplify the solution procedure, a frame of reference is usually defined in which the objects (possibly in motion relative to one another) are static. They interact through surface tractions (or pressures/stresses) at their interface.
As an example, consider two objects which meet at some surface in the (,)-plane with the -axis assumed normal to the surface. One of the bodies will experience a normally-directed pressure distribution and in-plane surface traction distributions and over the region . In terms of a Newtonian force balance, the forces:
must be equal and opposite to the forces established in the other body. The moments corresponding to these forces:
are also required to cancel between bodies so that they are kinematically immobile.
Read more about this topic: Contact Mechanics
Famous quotes containing the words theory, elastic and/or contact:
“The whole theory of modern education is radically unsound. Fortunately in England, at any rate, education produces no effect whatsoever. If it did, it would prove a serious danger to the upper classes, and probably lead to acts of violence in Grosvenor Square.”
—Oscar Wilde (1854–1900)
“We want some coat woven of elastic steel, stout as the first, and limber as the second. We want a ship in these billows we inhabit. An angular, dogmatic house would be rent to chips and splinters, in this storm of many elements. No, it must be tight, and fit to the form of man, to live at all; as a shell is the architecture of a house founded on the sea.”
—Ralph Waldo Emerson (1803–1882)
“No contact with savage Indian tribes has ever daunted me more than the morning I spent with an old lady swathed in woolies who compared herself to a rotten herring encased in a block of ice.”
—Claude Lévi-Strauss (b. 1908)