2.5 Nonslipping Solution for Power-Law-Shaped Indenters

2.5.1 The General Solution

Let us consider in detail the nonslipping contact for punches of monomial shape. In the nonslipping contact problem, the equation for the determination of the derivative of the sought function δ′(t) of displacements under the punch of shape x3 = −f(r) has the form (Mossakovskii, 1963)

f(r)=2π0r1r2x2[0xδ(t)cos(βlnxtx+t)dt]dx.

si127_e  (3.69)

It follows from Eq. (3.69) that if δ′(t) = Kdtd−1 or δ(t) = Kdtd/d, then f(r) = Bdrd, where

Bd=KdCd,Cd=2πI*(d)I**(d),

si128_e  (3.70) ...

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