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The in-plane mechanical properties of highly compressible and stretchable 2D lattices

机译：高度可压缩和可拉伸的2D格子的面内机械性能

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摘要

Highly compressible and stretchable lattice materials are perfectly suitable to be exploited in a range of cutting edge engineering applications such as low band-gap acoustic metamaterials, vibration absorbers, soft robotics, stretchable electronics and stent devices. Physics-based understanding and efficient computational methods are of paramount importance for the analysis and design of such cellular metamaterials. This paper develops the analytical framework to understand the nonlinear mechanics of hexagonal lattices subject to in-plane compressive and tensile stresses. Nonlinear equivalent elastic moduli and Poisson's ratios of the stressed lattice are expressed through the coefficients of the stiffness matrices of the constitutive beam elements. The stiffness coefficients, in turn, are derived from the transcendental displacement function which is the exact solution of the corresponding governing ordinary differential equation with appropriate boundary conditions. The closed-form analytical expressions of the equivalent elastic properties of the lattice are expressed in terms of trigonometric functions for the case of compressive stress and hyperbolic functions for the case of tensile stress. The general expressions are then used to investigate three special cases of wide interest, namely, auxetic hexagonal lattices, rhombus-shaped lattices and rectangular lattices. Analytical expressions are validated using independent nonlinear finite element simulation results. Numerical results are displayed for applied compressions and tensions in both directions separately and together. The equivalent elastic moduli show a softening effect under compression and a stiffening effect under tension. The Poisson's ratios are not significantly affected by the applied stresses. The proposed analytical approach and the new closed-form expressions provide a computationally efficient and physically intuitive framework for the analysis and parametric design of lattice materials under external stresses.
机译：高可压缩和可伸缩的晶格材料完全适合于在一系列切削刃工程应用中开采，例如低带间隙声学超材料，减振器，软机器人，可伸展电子和支架器件。基于物理的理解和有效的计算方法对于这种细胞超材料的分析和设计至关重要。本文开发了分析框架，了解受面内压缩和拉伸应力的六边形格子的非线性力学。应应力晶格的非线性等同弹性模和泊松比通过构成梁元件的刚度矩阵的系数表示。逆变系数又源自超趋势位移函数，其是具有适当边界条件的相应控制常微分方程的精确解。晶格的等效弹性特性的闭合形式分析表达式以三角函数表示用于拉伸应力的压缩应力和双曲线功能的情况。然后使用一般表达来调查三种特殊情况，即辅助六角形格子，菱形格格和矩形格子。使用独立非线性有限元模拟结果验证分析表达式。显示数值结果，用于分别并在一起两个方向上的施加压缩和张力。等效弹性模量显示出在压缩下的软化效果和张力下的加强效果。泊松的比率不会受到施加的应力的显着影响。所提出的分析方法和新的闭合形式表达为外部应力下的晶格材料的分析和参数设计提供了一种计算有效和物理直观的框架。

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