Equivalent Elastic Modulus of Multi-material Auxetic Honeycomb Under Bending, Axial, and Shear Effects: An Analytical Approach

An analytical approach is proposed for evaluating the elastic properties of auxetic multi-material hexagonal lattices. The axial, bending, and shear effect of the cell walls under the application of in-plane tensile/compressive stresses is taken into consideration. The numerical study shows that the consideration of axial and shear deformation of cell walls along with the bending of walls is a must for the accurate prediction of equivalent elastic properties of multi-material lattice. The conventional uniform thickness and mono-material homogeneous lattices are also analyzed under bending, shear, and axial stress as a special case of the heterogeneous case considered here. In addition, the variations of constitutive in-plane constants, (C11–C12) are presented for benchmark purposes under the intrinsic materials ratio, (q) input parameter. The present study shows that the properties of the hexagonal lattice can be tailored efficiently by introducing the proper material disparity ratio (MDR) between cell walls which mainly governed by cell angles (θ) and H/L ratio. The generalized analytical approach and multi-material design proposed in this paper open the opportunity to parametric studies  and the design of next-generation heterogeneous lattices with highly tailored effective elastic properties.