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The existence of torsional and SH surface waves in a half-space of ahomogeneous and isotropic material is shown to be possible in the context ofthe complete Toupin-Mindlin theory of gradient elasticity. This finding is inmarked contrast with the well-known result of the classical theory, where suchwaves do not exist in a homogeneous (isotropic or anisotropic) half-space. Inthe context of the classical theory, this weakness is usually circumvented bymodeling the half-space as a layered structure or as having non-homogeneousproperties. On the other hand, employing a simplified version of gradientelasticity (including only one microstructural parameter and an additionalsurface-energy term), Vardoulakis and Georgiadis (1997), and Georgiadis et al.(2000), showed that such surface waves may exist in a homogeneous half-spaceonly 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-Mindlintheory of isotropic gradient elasticity (with five microstructural parameters)is capable of predicting torsional and SH surface waves in a purely isotropicand homogeneous material. In fact, it is shown that torsional and SH surfacewaves are dispersive and can propagate at any frequency (i.e. no cut-offfrequencies appear). The character of the dispersion (either normal oranomalous) depends strongly upon the microstructural characteristics.

Torsional and SH surface waves in an isotropic and homogenous elastic half-space characterized by the Toupin-Mindlin gradient theory