Computation of the homogenized linear elastic response of 2D microcellular re-entrant auxetic honeycombs based on modified strain gradient theory

摘要

In this study, the mechanical properties of microcellular re-entrant auxetic honeycombs are investigated. Modified strain gradient theory (MSGT) is applied to consider microscale analysis. The mechanical properties of microcellular re-entrant auxetic honeycombs are derived from Hamilton's principle and Euler-Bernoulli beam theory. According to this method, the cell walls of the cellular re-entrant auxetic structure are treated as beams. The mechanical properties of microcellular re-entrant auxetic honeycombs are obtained by linear elastic deformation and the mechanical behavior of the base material. The results show that decreasing cell wall angle (theta), Young's modulus in X-2 direction (E lowast;(2)), Poisson's ratio magnitude (nu lowast;(21)) and shear modulus (G lowast;(12)) increase, also Young's modulus in X-1 direction (E lowast;(1)) decreases. In addition, microscale analysis plays a great role in the characterization of microcellular re-entrant auxetic honeycombs' mechanical properties, therefore, it affects their natural frequencies and critical buckling loads. The present theory is checked and compared with the results in the literature. The proposed microscale method can be used for manufacturing process design and optimization of microcellular structures, and it is a theoretical background for more investigation and further experimental works in the field of auxetic microstructures such as microsensors, microbots, and microfilters.