Large deformation and collapse analysis of re-entrant auxetic and hexagonal honeycomb lattice structures subjected to tension and compression

TL;DR

The paper investigates large-deformation responses of re-entrant auxetic (RA) and hexagonal honeycomb (HH) lattice structures under tension and compression using 2D plane-strain and 3D analyses. A hyperelastic–plastic constitutive model with multiplicative decomposition ($F=F^eF^p$), Mises–Huber yield and Simo exponential hardening is employed, calibrated against uni-axial PU tests, and stabilized with Polynomial Pressure Projection for the U-P mixed element; contact domain methods capture self-contact and plate interactions. Results show RA maintains a negative Poisson’s ratio in multiple loading directions and exhibits higher energy-absorption efficiency, while HH shows a monotonic increase in stress with strain; 2D results closely match 3D analyses, supporting computational efficiency. The study provides a physics-based framework for designing lattice materials with tunable auxetic behavior and enhanced energy absorption, highlighting the importance of loading direction in achieving desired mechanical performance.

Abstract

Additively manufactured auxetic structures offer desirable qualities like lightweight, good energy absorption, excellent indentation resistance, high shear stiffness and fracture toughness among others. A wide range of materials from polymers to metals can be used to fabricate these structures. In contrast to conventional materials, auxetic structures exhibit negative Poisson's ratios. Hence, unique mechanical properties can be achieved by specific design. In this work, two types of structures, namely re-entrant auxetic and non-auxetic hexagonal honeycomb, are investigated. Large deformation analyses in both 2D plane strain and 3D are conducted using linear triangular and tetrahedral multi-field displacement-pressure elements. Hyperelastic with rate-independent plasticity constitutive models are utilized and calibrated with experimental uni-axial tensile test results. The structures are subjected to compression and tension at both transversal and longitudinal directions. The contact domain method is employed to capture both self-contact and the interaction between the structure and loading plates. The obtained results show consistency with the experimental data. The outcomes of the analyses regarding the re-entrant auxetic structure agree with the expected behavior, showing a negative value of Poisson's ratio and greater efficiency of energy absorption than the hexagonal honeycomb. By understanding the influence of the loading direction on the structural behavior, equivalent Poisson's ratio and energy absorption a reliable theoretical framework for prospective designs of the lattice materials can be established.

Figures (16)

• Figure 1: Various types of auxetic structures.
• Figure 2: Flowchart of the plastic constitutive model.
• Figure 3: The patches constructed between bodies in the contact domain method.
• Figure 4: Linear triangle contact patch in previous (left) and current (right) configuration.
• Figure 5: Geometry of the (a) HH and (b) RA unit cells.