Mechanical properties of 3D re-entrant auxetic cellular structures

In this work, an analytical model of a 3D re-entrant auxetic cellular structure has been established based on energy method. In the model the overlapping of the struts as well as axial extension or compression (mostly neglected in former studies) were taken into consideration to make the model applicable when the struts are relative stubby which is common in engineering designs. Analytical solutions for the modulus and Poisson's ratios of the cellular structure in all principal directions were deduced. To validate the analytical model in present study, numerical calculations using brick elements were performed on unit cell models with periodic boundary conditions, and comparisons of the present model with analytical formulae and experimental results available in former literatures were also conducted. The results show that when the struts are slender enough, the bending of the struts play decisive role on the deformation of the structure and other mechanisms can be ignored; while when the struts become relative stubby, all the mechanisms including bending, shearing and axial loading need to be considered; The often-ignored axial extension or compression term may even play decisive role on determining the lateral Poisson's ratio of the structure when the struts are relative stubby. (C) 2017 Elsevier Ltd. All rights reserved.