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

Abstract

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.