Graphical Abstract Figure
Abstract
Transformation between saddle- and dome-like bending shapes of regular and reentrant hexagonal honeycomb panels are explored. An analytical model is proposed to uncover the underlying mechanisms and identify the controlling parameter when the cell walls are slender beams. Then, 3D finite element simulations are performed to examine the architecture dependence of bending shape and construct the phase diagrams of anticlastic and synclastic curvatures when the cell walls have a general geometry. The results are believed helpful to the design and application of related honeycomb structures.
References
1.
Gibson
, L. J.
, and Ashby
, M. F.
, 1997
, Cellular Solids: Structure and Properties
, Cambridge University Press
, Cambridge, UK
.2.
Gibson
, L. J.
, Ashby
, M. F.
, Schajer
, G. S.
, and Robertson
, C. I.
, 1982
, “The Mechanics of Two-Dimensional Cellular Materials
,” Proc. R. Soc. A
, 382
(1782
), pp. 25
–42
. 3.
Lakes
, R.
, 1987
, “Foam Structures With a Negative Poisson's Ratio
,” Science
, 235
(4792
), pp. 1038
–1040
. 4.
Evans
, K. E.
, 1991
, “The Design of Doubly-Curved Sandwich Panels With Honeycomb Cores
,” Comps. Struct.
, 17
(2
), pp. 95
–111
. 5.
Masters
, I. G.
, and Evans
, K. E.
, 1996
, “Models for the Elastic Deformation of Honeycombs
,” Compos. Struct.
, 35
(4
), pp. 403
–422
. 6.
Burke
, M.
, 1997
, “A Stretch of the Imagination
,” New Scientist
, 154
(2085
), pp. 36
–39
.7.
Evans
, K. E.
, and Alderson
, A.
, 2000
, “Auxetic Materials: Functional Materials and Structures From Lateral Thinking
,” Adv. Mater.
, 12
(9
), pp. 617
–628
. 8.
Lakes
, R. S.
, and Witt
, R.
, 2002
, “Making and Characterizing Negative Poisson's Ratio Materials
,” Int. J. Mech. Eng. Edu.
, 30
(1
), pp. 50
–58
. 9.
Alderson
, A.
, and Alderson
, K. L.
, 2007
, “Auxetic Materials
,” Proc. Inst. Mech. Eng., Part G, J. Aero. Eng.
, 221
(4
), pp. 565
–575
. 10.
Yao
, Y.
, Ni
, Y.
, and He
, L. H.
, 2023
, “Unexpected Bending Behavior of Architected 2D Lattice Materials
,” Sci. Adv.
, 9
(25
), p. eadg3499
. 11.
Timoshenko
, S. P.
, and Goodier
, J. N.
, 1951
, Theory of Elasticity
, McGraw-Hill
, New York
.12.
Lim
, T. C.
, 2007
, “On Simultaneous Positive and Negative Poisson's Ratio Laminates
,” Phys. Status Solidi B
, 244
(3
), pp. 910
–918
. 13.
McInerney
, J.
, Paulino
, G. H.
, and Rocklin
, D. Z.
, 2022
, “Discrete Symmetries Control Geometric Mechanics in Parallelogram-Based Origami
,” Proc. Natl. Acad. Sci. USA
, 119
(32
), p. e2202777119
. 14.
Vasudevan
, S. P.
, and Pratapa
, P. P.
, 2024
, “Homogenization of Non-Rigid Origami Metamaterials as Kirchhoff–Love Plates
,” Int. J. Solids Struct.
, 300
, p. 112929
. 15.
Nassar
, H.
, 2024
, “How Periodic Surfaces Bend
,” Phil. Trans. R. Soc. A
, 382
(2283
), p. 20240016
. 
