The determination of surface elastic moduli is discussed in the context of a recently proposed strongly anisotropic surface elasticity model. The aim of the model was to describe deformations of solids with thin elastic coatings associated with so-called hyperbolic metasurfaces. These metasurfaces can exhibit a quite unusual behaviour and concurrently a very promising wave propagation behaviour. In the model of strongly anisotropic surface elasticity, strain energy as a function of the first and second deformation gradients has been introduced in addition to the constitutive relations in the bulk. In order to obtain values of surface elastic moduli, we compare dispersion relations for anti-plane surface waves obtained using the two-dimensional (2D) model and three-dimensional (3D) straightforward calculations for microstructured coatings of finite thickness. We show that with derived effective surface moduli, the 2D model can correctly describe the wave propagation.

中文翻译：

---

微结构强各向异性涂层的有效表面弹性模量


在最近提出的强各向异性表面弹性模型的背景下讨论了表面弹性模量的确定。该模型的目的是描述具有与所谓的双曲超表面相关的薄弹性涂层的固体的变形。这些超表面可以表现出非常不寻常的行为，同时也表现出非常有前途的波传播行为。在强各向异性表面弹性模型中，除了本体本构关系之外，还引入了作为第一和第二变形梯度函数的应变能。为了获得表面弹性模量值，我们比较了使用二维 (2D) 模型获得的反平面表面波的色散关系和有限厚度微结构涂层的三维 (3D) 直接计算。我们证明，通过推导的有效表面模量，二维模型可以正确描述波传播。