Abstract
In the present study, we examine the surface shear horizontal (SH) wave in a classical linear elastic half-space covered by a surface layer modeled by the couple stress theory [Mindlin and Tiersten, Arch. Ration. Mech. Anal. 11, 415 (1962)]. The boundary conditions on the surface of the half space are translated into the “body” forces in the surface layer according to the surface elasticity proposed by Gurtin and Murdoch [Arch. Ration. Mech. Anal. 57, 291 (1975)]. Combining the surface elasticity and the couple stress theory, we find that the surface SH waves are only available for a limited range of wavelengths due to the presence of the micro-length in the couple stress theory.
Highlights
The couple stress theory is one of the many attempts to include the microstructure effect into the linear elasticity
We briefly review the key equations of the threedimensional couple stress theory by Mindlin and Tiersten
Combining the concepts of the surface elasticity2 and the couple stress theory,1 we modeled the surface layer with micro-patterns by the couple stress theory in this study of shear horizontal (SH) wave near the surfaces/interfaces
Summary
The couple stress theory is one of the many attempts to include the microstructure effect into the linear elasticity. The development on the couple stress theory can be traced back over a century, intensive research on the topic only started from the 1960s. The couple stress theory has been examined and improvised by many researchers. By setting an extra equilibrium condition, Yang et al. concluded that the couple stress tensor should be symmetric. A derivation by Hadjesfandiari and Dargush differed from Yang et al., claiming that the couple stress should be an anti-symmetric tensor. The consensus on certain aspects of the couple stress theory has not been reached. Study, we will use Mindlin and Tiersten’s original derivation and make simplifications for the anti-plane deformation.
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