arXiv 2407.191362024-07cond-mat.mtrl-sci

具有极端弹性各向异性的平面结构化材料

Planar structured materials with extreme elastic anisotropy

Jagannadh Boddapati, Chiara Daraio

AI总结：

本文通过余弦函数单胞数据库系统估计了单尺度二维结构化材料的各向异性刚度张量范围，并与层级层合板对比确定需层级设计的性能区域，进而提出功能梯度结构构造方法并展示其独特力学行为。

摘要：

通过降低对称性来设计各向异性结构化材料会产生独特的行为，例如在单轴压缩或拉伸下发生剪切。这种方向相关的耦合力学现象对于能量重定向等应用至关重要。虽然已证明诸如层级层合板之类的秩亏材料能够表现出极端的弹性各向异性，但对于单尺度制造技术所能实现的完全各向异性弹性张量，目前的认识仍然有限。在实现极端弹性各向异性的各向异性模量方面，尚不存在类似于各向同性复合材料中Hashin-Shtrikman界限那样的既定上下界。本文估计了单尺度二维结构化材料所能实现的各向异性刚度张量范围。为此，我们首先利用周期性余弦函数的线性组合，建立了一个周期性各向异性单尺度单胞几何数据库。该数据库覆盖了范围广泛的各向异性弹性张量，随后将其与层级层合板的弹性张量进行比较。通过这一比较，我们确定了在性能空间中必须采用层级设计才能实现极端性能的区域。我们展示了一种利用单胞的余弦函数表示来构造各种二维功能梯度结构的方法。这些梯度结构能够在具有不同图案的单胞之间无缝插值，从而允许独立控制多个功能梯度，例如孔隙率、各向异性模量和对称性。当使用位于性能空间极端部位的单胞进行设计时，这些梯度结构表现出独特的力学行为。我们对特定的梯度设计进行了数值研究，以观察诸如选择性应变能局部化、拉伸下的压缩应变以及局部旋转等行为。

英文摘要：

Designing anisotropic structured materials by reducing symmetry results in unique behaviors, such as shearing under uniaxial compression or tension. This direction-dependent coupled mechanical phenomenon is crucial for applications such as energy redirection. While rank-deficient materials such as hierarchical laminates have been shown to exhibit extreme elastic anisotropy, there is limited knowledge about the fully anisotropic elasticity tensors achievable with single-scale fabrication techniques. No established upper and lower bounds on anisotropic moduli achieving extreme elastic anisotropy exist, similar to Hashin-Shtrikman bounds in isotropic composites. In this paper, we estimate the range of anisotropic stiffness tensors achieved by single-scale two-dimensional structured materials. To achieve this, we first develop a database of periodic anisotropic single-scale unit cell geometries using linear combinations of periodic cosine functions. The database covers a wide range of anisotropic elasticity tensors, which are then compared with the elasticity tensors of hierarchical laminates. Through this comparison, we identify the regions in the property space where hierarchical design is necessary to achieve extremal properties. We demonstrate a method to construct various 2D functionally graded structures using this cosine function representation for the unit cells. These graded structures seamlessly interpolate between unit cells with distinct patterns, allowing for independent control of several functional gradients, such as porosity, anisotropic moduli, and symmetry. The graded structures exhibit unique mechanical behaviors when designed with unit cells positioned at extreme parts of the property space. Specific graded designs are numerically studied to observe behaviors such as selective strain energy localization, compressive strains under tension, and localized rotations.

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