  The existence of torsional and SH surface waves in a half-space of a
homogeneous and isotropic material is shown to be possible in the context of
the complete Toupin-Mindlin theory of gradient elasticity. This finding is in
marked contrast with the well-known result of the classical theory, where such
waves do not exist in a homogeneous (isotropic or anisotropic) half-space. In
the context of the classical theory, this weakness is usually circumvented by
modeling the half-space as a layered structure or as having non-homogeneous
properties. On the other hand, employing a simplified version of gradient
elasticity (including only one microstructural parameter and an additional
surface-energy term), Vardoulakis and Georgiadis (1997), and Georgiadis et al.
(2000), showed that such surface waves may exist in a homogeneous half-space
only if a certain type of gradient anisotropy is included in the formulation.
On the contrary, in the present work, we prove that the complete Toupin-Mindlin
theory of isotropic gradient elasticity (with five microstructural parameters)
is capable of predicting torsional and SH surface waves in a purely isotropic
and homogeneous material. In fact, it is shown that torsional and SH surface
waves are dispersive and can propagate at any frequency (i.e. no cut-off
frequencies appear). The character of the dispersion (either normal or
anomalous) depends strongly upon the microstructural characteristics.
