Contact Mechanics - Hertzian Theory of Non-adhesive Elastic Contact

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:

P_z = \int_S p(x,y)~ \mathrm{d}A ~;~~ Q_x = \int_S q_x(x,y)~ \mathrm{d}A ~;~~ Q_y = \int_S q_y(x,y)~ \mathrm{d}A

must be equal and opposite to the forces established in the other body. The moments corresponding to these forces:

M_x = \int_S y~p(x,y)~ \mathrm{d}A ~;~~ M_y = \int_S x~p(x,y)~ \mathrm{d}A ~;~~ M_z = \int_S ~ \mathrm{d}A

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:

    “A theory if you hold it hard enough
    And long enough gets rated as a creed....”
    —Robert Frost (1874–1963)

    “bodies wrapped in elastic bands,
    bodies cased in wood or used like telephones,
    bodies crucified up onto their crutches,
    bodies wearing rubber bags between their legs,
    bodies vomiting up their juice like detergent,
    bodies smooth and bare as darning eggs.”
    —Anne Sexton (1928–1974)

    “For those parents from lower-class and minority communities ... [who] have had minimal experience in negotiating dominant, external institutions or have had negative and hostile contact with social service agencies, their initial approaches to the school are often overwhelming and difficult. Not only does the school feel like an alien environment with incomprehensible norms and structures, but the families often do not feel entitled to make demands or force disagreements.”
    —Sara Lawrence Lightfoot (20th century)