VAM-based equivalent-homogenization model for 3D re-entrant auxetic honeycomb structures

Abstract

The integration of two vertically crossed re-entrant honeycombs gives rise to a 3D re-entrant honeycomb (3D-RH), which displays intricate three-dimensional auxeticity. To simplify the modeling complexity, this study employs asymptotic analysis of the energy functional stored in the unit cell of the 3D-RH to develop unified constitutive models for 3D structures and panels with multiple length scales. Based on this, an equivalent 3D Cauchy continuum model is established for multi-layer 3D-RH, while a 2D equivalent plate model is developed for sandwich panel with single-layer 3D-RH (SP-3D-RH). The accuracy and effectiveness of these equivalent models are subsequently confirmed through investigations of the X-shaped compressive deformation of multi-layer 3D-RH, as well as the in-plane auxetic deformation and out-of-plane dome-shaped deformation of single-layer 3D-RH. Compared to traditional hexagonal and re-entrant honeycomb sandwich panels, the SP-3D-RH exhibited enhanced equivalent tensile stiffness while effectively mitigating maximum deformation and strain energy under bending and tension conditions. However, due to its relatively low equivalent shear stiffness, the SP-3D-RH exhibited significant deformation and strain energy when subjected to torsional loads, resulting in local stress concentration in the connect region between adjacent facesheets. Parameter analysis shows that the facesheet-to-strut thickness ratio had a substantial impact on the equivalent stiffness and in-plane behavior of the SP-3D-RH, while adjusting the horizontal strut length, strut depth, and re-entrant angle of the 3D-RH can improve the out-of-plane behavior.