Energy Loss in Moving Contact Problems

Firstly, it is relevant here and later to relate the stress tensor components on the surface to the applied stresses, with the aid of (1.1.1). Let the half-space occupy jv 0. The contact pressure p r, t) is given by 

Let us denote the contact area by C t). In fact, it generally corresponds to Suit). From (1.1.8), we see that the rate of energy input, by the moving load, is given by 

Consider next the case of horizontal motion, along the x-axis. Frictionless contact will be discussed first. Let the position of the lowest point be ro(t) = (xo(t), 0), where Xo(0 = C/, the punch velocity. In the contact area. 

General Theorems and Methods of Solution of Boundary Value Problems 

This formula was given by Hunter (1961) for the special case of plane strain conditions and a cylindrical punch. For an elastic medium, this force is zero. However, for a viscoelastic medium, we shall see that this is not the case. The deformation caused by the moving load results in mechanical energy loss, which is manifested by the presence of a resisting force. This is the well-known force of hysteretic friction, first demonstrated experimentally by Tabor (1952). 

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