A general analytical framework for the mechanics of heterogeneous hexagonal lattices

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