The superseismic stage of contact between a rigid punch and a linearly elastic medium is studied by the self-similar potential technique. It is shown that the instantaneous values of contact force, contact area, and the rate of penetration of the punch are given by simple algebraic expressions. The stress fields for the mathematical idealization of a velocity distribution “concentrated” in a manner analogous to the integrable singular stress field beneath a point load is given. Using these stresses as influence functions permits the stress field beneath any punch to be computed once the time and spatial variation of the velocity imposed within the contact region has been determined.

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