Out-of-plane compressive properties of a butterfly-shaped auxetic metamaterial

Inspired by butterfly, a bio butterfly-shaped auxetic metamaterial (BSAM) was recently proposed in which the unite cell of BSAM was designed based on silhouette of a butterfly. The distinguished in-plane mechanical properties made the BSAM a potential absorber to be used in a broad range of applications. The aim of this study is to examine the out-of-plane mechanical properties under quasi-static compression. Using the validated FE models, a comparison was carried out between BSAM and two popular auxetic honeycombs, namely, re-entrant (RE) and modified re-entrant (MRE). Results showed that the nominal stress–strain curves of the BSAM were significantly higher than those of auxetic honeycombs (RE and MRE). However, the MRE revealed the highest Young’s modulus. The plateau stresses were 10.5 MPa, 7.5 MPa and 3.3 MPa for the compressed BSAM, MRE and RE, respectively. Furthermore, the calculated values of the specific energy absorption per volume (Wv) of the three structures indicated that the percentage of the absorbed energy by the BSAM was 182% and 456% higher than those absorbed by the MRE and RE, respectively. Based on the determined values of ideal Wv (11.4 J cm⁻³ ‘BSAM’, 5.2 J cm⁻³ ‘MRE’ and 2.3 J cm⁻³ ‘RE’), the energy efficiency of the three structures was 64%, 79% and 69% of the total energy in the case BSAM, MRE and RE, respectively. Moreover, the influence of the in-plane thickness (t₁) and the thickness of cylinders (t₂) on the mechanical performance of the BSAM were examined through a parametric study. Findings of the parametric study indicated that the mechanical properties as a function of t₁ were considerably affected, while moderate influence was resulted as a function of t₂.