The in-plane mechanics of two-dimensional heterogeneous hexagonal lattices are investigated. The heterogeneity originates from two physically realistic considerations: different constituent materials and different wall thicknesses. Through the combination of multi-material and multi-thickness elements, the most general form of 2D heterogeneous hexagonal lattices is proposed in this paper. By exploiting the mechanics of a unit cell with multi-material and multi-thickness characteristics, exact closed-form analytical expressions of equivalent elastic properties of the general heterogeneous lattice have been derived. The equivalent elastic properties of the 2D heterogeneous lattice are Young’s modulli and Poisson’s ratios in both directions and the shear modulus. Two distinct cases, namely lattices with thin and thick constituent members, are considered. Euler–Bernoulli beam theory is employed for the thin-wall case, and Timoshenko beam theory is employed for the thick-wall case. The closed-form expressions are validated by independent finite element simulation results. The generalized expressions can be considered as benchmark solutions for validating future numerical and experimental investigations. The conventional single-material and single-thickness homogeneous lattice appears as a special case of the heterogeneous considered here. By introducing the Material Disparity Ratio (MDR) and Geometric Disparity Ratio (GDR), variability in the equivalent elastic properties has been graphically demonstrated. As opposed to classical homogeneous lattices, heterogeneous lattices significantly expand the design space for 2D lattices. Orders-of-magnitude of variability in the equivalent elastic properties is possible by suitably selecting material and geometric disparities within the lattices. The general closed-form expressions proposed in this paper open up the opportunity to design next-generation heterogeneous lattices with highly tailored effective elastic properties.

研究了二维异质六方晶格的面内力学。异质性源于两个物理现实的考虑：不同的构成材料和不同的壁厚。本文通过多材料和多厚度元素的组合，提出了二维异质六边形晶格的最一般形式。通过利用具有多材料和多厚度特性的晶胞的力学特性，推导出了一般异质晶格等效弹性特性的精确闭式解析表达式。二维异质晶格的等效弹性特性是两个方向的杨氏模量和泊松比以及剪切模量。两种不同的情况，即具有薄和厚组成成员的格子，被考虑。薄壁情况采用 Euler-Bernoulli 梁理论，厚壁情况采用 Timoshenko 梁理论。封闭形式的表达式通过独立的有限元仿真结果进行验证。可以将广义表达式视为验证未来数值和实验研究的基准解决方案。传统的单一材料和单一厚度的均质晶格是这里考虑的异质晶格的特例。通过引入材料视差比 (MDR) 和几何视差比 (GDR)，以图形方式证明了等效弹性属性的可变性。与经典的同质晶格相反，异质晶格显着扩展了二维晶格的设计空间。Orders-of-magnitude of variability in the equivalent elastic properties is possible by suitably selecting material and geometric disparities within the lattices. 本文中提出的一般闭式表达式为设计具有高度定制的有效弹性特性的下一代异质晶格提供了机会。