Symmetrical frictionless indentation over a uniformly expanding contact region—I. Basic analysis

The study of two-dimensional wave propagation in a half-space due to indentation by a rigid smooth indentor of a general shape at a non-uniform velocity is approached by assuming that the indentor shape and displacement history can be represented by polynomial curves in, respectively, a spatial variable and the time. As a first step symmetric indentation over a contact region expanding at a constant sub-Rayleigh wave speed is considered. Since superposition will yield more general forms attention is confined to polynomials homogeneous of degree $\text{n ? 1}$ with n + 1 terms and arbitrary coefficients. By homogeneous function techniques all the field variables in the half-space for any $\text{n}$ are obtained as single integrals. Conditions for the existence of singularities in the stresses and particle velocities are examined and some general results with bearing on the indentation problem are discussed.