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.

中文翻译：

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极弹性材料的瑞利表面波


这里的极弹性材料是指一类特定的弹性材料，其弹性矩阵表现出一个或多个零特征值，从而产生原则上不消耗能量的软变形模式。它们可以通过人工设计的固体微结构进行近似。由于软模式，极弹性材料具有传统固体所不具备的奇特的体波特性，为操纵体波提供了前所未有的机会，例如，充当弹性波的声子偏振器或水声波的隐形斗篷。尽管瑞利表面波具有潜力，但与这种极端弹性材料的体波行为密切相关，到目前为止，它们在很大程度上仍未得到探索。在本文中，我们基于连续介质理论从理论上研究了瑞利波在极端弹性材料中的传播，并用基于受电弓结构设计的微观结构超材料验证了我们的发现。推导了极弹性材料中瑞利波的色散关系和极化，并利用应变梯度理论研究了高阶梯度效应的影响。本研究为探索极弹性材料中的表面波提供了一个连续体模型，并可能激发极弹性材料在控制表面波中的应用。