Patil Ganesh U, Matlack Kathryn H
Department of Mechanical Science and Engineering, University of Illinois Urbana-Champaign, Urbana, Illinois 61801, USA.
J Acoust Soc Am. 2019 Mar;145(3):1259. doi: 10.1121/1.5091690.
Periodic lattices offer enhanced mechanical and dynamic properties per unit mass, and the ability to engineer the material response by optimizing the unit cell. Characterizing the effective properties of these lattice materials through experiments can be a time consuming and costly process, so analytical and numerical methods are crucial. Specifically, the Bloch-wave homogenization approach allows one to characterize the effective static properties of the lattice while simultaneously analyzing wave propagation properties such as band gaps, propagating modes, and wave directionality. While this analysis has been used for some time, a thorough study of this approach on three-dimensional (3D) lattice materials with different symmetries and geometries is presented here. Bloch-wave homogenization is applied to extract the effective stiffness tensor of 3D periodic lattices and confirmed with elastostatic homogenization, both within a finite element framework. Multiple periodic lattices with cubic, transversely isotropic, and tetragonal symmetry, including an auxetic geometry, over a wide range of relative densities are analyzed. Further, this approach is used to analyze 3D periodic composite structures, and a way to tailor their overall anisotropy is demonstrated. This work can serve as the basis for nondestructive evaluation of metamaterials properties using ultrasonic velocity measurements.
周期性晶格具有单位质量下增强的力学和动力学性能，以及通过优化单胞来设计材料响应的能力。通过实验表征这些晶格材料的有效性能可能是一个耗时且成本高昂的过程，因此分析和数值方法至关重要。具体而言，布洛赫波均匀化方法能够在表征晶格有效静态性能的同时，分析诸如带隙、传播模式和波方向性等波传播特性。虽然这种分析已经使用了一段时间，但本文在此对具有不同对称性和几何形状的三维（3D）晶格材料的这种方法进行了全面研究。在有限元框架内，应用布洛赫波均匀化来提取3D周期性晶格的有效刚度张量，并通过弹性静力学均匀化进行了验证。分析了多种具有立方、横观各向同性和四方对称性的周期性晶格，包括一种负泊松比几何形状，其相对密度范围很广。此外，该方法用于分析3D周期性复合结构，并展示了一种调整其整体各向异性的方法。这项工作可作为使用超声速度测量对超材料性能进行无损评估的基础。
