Strong surface elasticity has been only found in nanoscale materials due to their large surface-to-volume ratio. In this paper, at the macroscale, the strong surface elasticity is revealed in thin metamaterial structures. Moreover, the metamaterial structures filled with complex microstructures often need computationally prohibitive resources if the fully-resolved microstructures are modeled using high-fidelity approaches. Based on the revealed surface elasticity, a surface-based efficient yet accurate homogenization method is developed for thin metamaterial structures. This study explores the role that microstructure plays in determining the macroscopic properties of a metamaterial continuum and reveals the occurrence of the size-dependent surface effect that is strictly related to the microstructure configuration. The contribution of surface elasticity to the mechanical properties of thin metamaterial structures cannot be neglected, particularly when the size of microstructures is comparable to their thickness. The coupling effect of intrinsic length determined by microstructure and extrinsic length (the thickness) on surface elasticity is investigated using the homogenization method. The intrinsic length can be calibrated by the size-dependent effective elasticity tensor. The strength of surface elasticity is determined by the intrinsic length with a specific thickness. The contribution of surface elasticity to the effective elasticity tensor can be determined by the difference between intrinsic length and extrinsic length. Finally, a simple yet representative metamaterial truss under tension is used to illustrate the application of the homogenization method. Our findings not only provide mechanical insights into metamaterial structures but also offer a surface-based computational method for metamaterial structures filled with complex microstructures.

中文翻译：

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一种结合表面效应的薄超材料结构均匀化方法


由于纳米级材料的表面积与体积之比较大，因此仅在纳米级材料中发现了强表面弹性。在本文中，在宏观尺度上，揭示了薄超材料结构中的强表面弹性。此外，如果使用高保真方法对完全解析的微结构进行建模，则充满复杂微结构的超材料结构通常需要大量的计算资源。基于所揭示的表面弹性，针对薄超材料结构开发了一种基于表面的高效而精确的均质化方法。这项研究探讨了微观结构在确定超材料连续体宏观特性中所起的作用，并揭示了与微观结构配置严格相关的尺寸相关表面效应的发生。表面弹性对薄超材料结构机械性能的贡献不容忽视，特别是当微结构的尺寸与其厚度相当时。采用均质化方法研究了由微观结构决定的内在长度和外在长度（厚度）对表面弹性的耦合效应。固有长度可以通过尺寸相关的有效弹性张量来校准。表面弹性的强度由特定厚度的固有长度决定。表面弹性对有效弹性张量的贡献可以通过内在长度和外在长度之间的差异来确定。最后，用一个简单但具有代表性的受拉超材​​料桁架来说明均质化方法的应用。 我们的研究结果不仅提供了对超材料结构的机械见解，而且还为充满复杂微结构的超材料结构提供了基于表面的计算方法。