Numerical results have been obtained for a wide range of values of $i and x and may be qualitatively described as follows.
For $, < 1 the sphere sticks at the beginning of the impact, as shown above (condition (44)). As the sphere penetrates the half-space and the contact area grows, successive annuli are laid down in a stress-relieved state and there is no microslip. However, once the midpoint of the impact is passed, the contact area shrinks and the tangential elastic recovery of the surfaces causes an annulus of microslip to be established surrounding a central stuck region. This annulus spreads inwards as the cycle proceeds until eventually the whole contact area slides, i.e. gross slip is established.
(ii) 1 < IL1 < 4x - 1