Comparison of anti-plane surface waves in strain-gradient materials and materials with surface stresses

Abstract

Here we discuss the similarities and differences in anti-plane surface wave propagation in an elastic half-space within the framework of the theories of Gurtin–Murdoch surface elasticity and Toupin–Mindlin strain-gradient elasticity. The qualitative behaviour of the dispersion curves and the decay of the obtained solutions are quite similar. On the other hand, we show that the solutions relating to the surface elasticity model are more localised near the free surface. For the strain-gradient elasticity model there is a range of wavenumbers where the amplitude of displacements decays very slowly.