Rayleigh surface waves of extremal elastic materials

TL;DR

This paper investigates Rayleigh surface waves in extremal elastic materials, revealing their unique properties and potential for advanced wave manipulation, supported by theoretical models and microstructure metamaterial verification.

Contribution

It introduces a continuum model for Rayleigh waves in extremal elastic materials and explores their properties using strain gradient theory and microstructure design.

Findings

Derived dispersion relations and polarizations of Rayleigh waves.

Identified effects of higher order gradient terms on surface wave behavior.

Validated theoretical predictions with pantographic microstructure metamaterials.

Abstract

Extremal elastic materials here refer to a specific class of elastic materials whose elastic matrices exhibit one or more zero eigenvalues, resulting in soft deformation modes that, in principle, cost no energy. They can be approximated through artificially designed solid microstructures. Extremal elastic materials have exotic bulk wave properties unavailable with conventional solids due to the soft modes, offering unprecedented opportunities for manipulating bulk waves, e.g., acting as phonon polarizers for elastic waves or invisibility cloaks for underwater acoustic waves. Despite their potential, Rayleigh surface waves, crucially linked to bulk wave behaviors of such extremal elastic materials, have largely remained unexplored so far. In this paper, we theoretically investigate the propagation of Rayleigh waves in extremal elastic materials based on continuum theory and verify our findings with designed microstructure metamaterials based on pantographic structures. Dispersion relations and polarizations of Rayleigh waves in extremal elastic materials are derived, and the impact of higher order gradient effects is also investigated by using strain gradient theory. This study provides a continuum model for exploring surface waves in extremal elastic materials and may stimulate applications of extremal elastic materials for controlling surface waves.