The present work studies the propagation and reflection of plane waves in an elastic
2D half-space. The material microstructure is taken into account assuming the
validity of the complete Toupin–Mindlin theory of isotropic gradient elasticity. This
theory involves five additional microstructural material constants besides the two
standard Lamé constants of elasticity. Our study builds upon the earlier work of
Gourgiotis et al. (2013), which considered a simplified version of the Toupin–Mindlin
theory with only one microstructural constant, in wave reflection. Our aim here is to
consider the most general material response in the isotropic setting of the strain
gradient theory, providing, thus, more general results as compared with those
of the earlier work. More specifically, we study the effect of the gradient
parameters upon the amplitudes, reflection angles and phase shift of the reflected
waves, which proved to be four in the context of gradient elasticity (i.e.,
two waves propagating in the material volume and two surface waves with
exponential decay from the surface), due to an incident either dilatational or
distortional wave at the free surface of a 2D half-space. In addition, special
emphasis is given here in the Rayleigh waves arising along the surface of the
half-space.