A homogenization method incorporating surface effect for thin metamaterial structure

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.