Rapid indentation of transversely isotropic or orthotropic half-spaces

The canonical problems of rapid indentation by, respectively, a rigid smooth wedge and a rigid smooth cylinder, are examined for a transversely isotropic or orthotropic halfspace in plane strain. An exact transient analysis based on integral transforms is carried out for the case of contact zone expansion at a constant subcritical rate. Certain functions in the transform space can be factored in such a manner that the resulting solutions, despite anisotropy, have rather simple forms. This factorization is also exploited to obtain a compact exact formula for the Rayleigh wave speed, which serves as the critical contact zone expansion rate. Aspects of contact zone behavior for the two problems are illustrated for five specific materials.