Fig. 1 Natural bee honeycomb-inspired RH-FP: ( a ) conventional manmade honeycomb; ( b ) natural bee honeycomb with folding partition; ( c ) unit cell of the ( ⅰ ) main reentrant honeycomb, ( ⅱ ) folding partition, ( ⅲ ) RH-FP, and its ( ⅳ ) NPR behavior under compression in y direction; ( d ) t... More about this image found in Natural bee honeycomb-inspired RH-FP: ( a ) conventional manmade honeycomb;...

Fig. 2 Mechanical properties of the RH-FP: ( a ) stress–strain curves of the RH-FP with t / l = 0.05; ( b ) normalized Young's modulus E / E s and normalized yield strength σ / σ s of the RH-FP; ( c ) Poisson's ratio of the RH-FP. Deformation process of RH-FP specime... More about this image found in Mechanical properties of the RH-FP: ( a ) stress–strain curves of the RH-FP...

Fig. 3 NPR of the 3D plate-based metamaterials with general structures: ( a ) design of the 3D plate-based NPR metamaterials with ( ⅰ ), ( ⅱ ) RH-RH1, ( ⅲ ), ( ⅳ ) RH-RH2, and ( ⅴ ), ( ⅵ ) RH-HH structures; ( b ) displacement distribution and deformation of ( ⅰ ) RH-RH1, ( ⅱ ) RH-RH2, ( ⅲ ) RH-RH2... More about this image found in NPR of the 3D plate-based metamaterials with general structures: ( a ) desi...

Fig. 4 Normalized Young's modulus, yield strength, and load-bearing performance of 3D plate-based NPR metamaterials: ( a ) ( E / E s ) / ( ρ / ρ s ) versus ρ / ρ s , ( b ) E / E s versus ρ / ρ s , ( c ) σ / σ s versus ρ / ρ ... More about this image found in Normalized Young's modulus, yield strength, and load-bearing performance of...

Fig. 5 Stress distribution and Young's modulus of different structures: stress distribution of ( a ) main reentrant honeycomb with x direction free, ( b ) main reentrant honeycomb with x direction fixed, ( c ) RH-FP with x direction free, ( d ) reentrant part in RH-FP, ( e ) folding partitio... More about this image found in Stress distribution and Young's modulus of different structures: stress dis...

Fig. 1 ( a ) An irregular re-entrant honeycomb (RHc) lattice structure and ( b ) an irregular honeycomb (Hc) lattice structure. The dashed quadrilateral denotes the RVE of the lattice. More about this image found in ( a ) An irregular re-entrant honeycomb (RHc) lattice structure and ...

Fig. 2 ( a ) A periodic unit cell of irregular RHc ( θ 1 and θ 2 are both positive for RHc and negative for Hc). For a regular lattice, θ 1 = θ 2 and L 1 = L 2 . ( b ) FBD of a unit cell of an irregular RHc. More about this image found in ( a ) A periodic unit cell of irregular RHc ( θ 1 and θ 2...

Fig. 3 Comparison of the variation with θ of the effective elastic properties of a regular lattice structure obtained from the proposed AM with the existing model results of Gibson and Ashby [ 59 ], Evans and Masters [ 45 ], Grima et al. [ 49 ], and the FE models. Inset figures show the deta... More about this image found in Comparison of the variation with θ of the effective elastic propertie...

Fig. 4 Effective elastic properties of lattice versus θ , with H = 0.6 m, L = 0.4 m, and cross section = 0.02 m × 0.005 m : ( a ) Poisson’s ratios (insets show the corresponding lattices) and ( b ) Young’s modulus. At angles θ = 41.821 d... More about this image found in Effective elastic properties of lattice versus θ , with H = 0.6 ...

Fig. 5 The parameter design space α – θ * at which the regular RHc lattice has an L 4 symmetry axis. The area under the curve α = 2 sin θ * is the interference region where parts of two adjacent unit cells come in contact. More about this image found in The parameter design space α – θ * at which the regular RHc la...

Fig. 6 Effective elastic properties of the irregular lattice versus θ 1 , with H = 0.6 m, L 1 = 2 H / 3 m, cross section = 0.02 m × 0.005 m, and θ 2 = 45 deg sgn ( θ 1 ): ( a ) Poisson’s ratio, ( b ) Young’s modulus (i... More about this image found in Effective elastic properties of the irregular lattice versus θ 1 , ...

Fig. 7 Effective elastic properties of the irregular lattice versus θ 1 , with H = 0.6 m, L 1 = 2 H / 3 m, cross section = 0.02 m × 0.005 m , and θ 2 = 10 deg sgn ( θ 1 ) : ( a ) Poisson’s ratio, ( b ) Young’s mo... More about this image found in Effective elastic properties of the irregular lattice versus θ 1 , ...