Experimental study of auxetic behavior of re-entrant honeycomb with curvilinear elements

R. Goldstein1, D. Lisovenko1, A. Chentsov1, S. Lavrentyev1
1Institute for Problems in Mechanics RAS, prospect Vernadskogo 101, b1, Moscow, 119526
Abstract
The mechanical behavior of a two-dimensional structure with negative Poisson`s ratio (auxetic structure) was experimentally studied. The concave hexagon (re-entrant honeycomb) with straight sides is often an element of auxetic structures. In this paper, a new design of a concave hexagon in which a part of straight elements is replaced with curvilinear elements is suggested. The sample (110 × 20 × 0.7 mm plate with the central part of 26.2 × 20 × 0.7 mm) was made by the laser cutting method from nonauxetic polyethyleneterephthalate (PET-a amorphous) plates. The transverse size of elements of hexagons is equal to sample thickness. The sample was subjected to a monotonous uniaxial tension until the last moment when it still maintained its planarity. As a result of experimental data processing the tensile force — displacement diagram was calculated. Variability of Poisson`s ratio depending on engineering deformations was studied. The analysis showed that auxetic structure at tension attained the maximum longitudinal deformation (before loss of stability) of 99 %, and the maximum transverse deformation of 59 %. Elastic deformations reached 2 %. Poisson`s ratio defined by analogy with elastic small deformations varies in the range from –0.19 to –0.60 with an increase of longitudinal and transverse deformations.
Received: 07 March 2017   Revised: 27 March 2017   Accepted: 29 March 2017
Views: 48   Downloads: 18
References
1.
R. Lakes. Science 235 (4792), 1038 (1987). DOI: 10.1126 / science.235.4792.1038
2.
R. F. Almgren. J. Elasticity 15 (4), 427 (1985). DOI: 10.1007 / BF00042531
3.
A. G. Kolpakov, Prikl. Mat. Mekh. 59, 969 (1985).
4.
D. Y. Fozdar, P. Soman, J. W. Lee, L.‑H. Han, S. Chen, Adv. Func. Mater. 21 (14), 2712 (2011). DOI: 10.1002 / adfm.201002022
5.
L. J. Gibson, M. F. Ashby, G. S. Schajer, C. I. Robertson. Proc. Royal Soc. London A 382, 25 (1982). DOI: 10.1098 / rspa.1982.0087
6.
T.‑C. Lim, Auxetic Materials and Structures. Springer Singapore. (2015) 588 p. DOI: 10.1007 / 978‑981‑287‑275‑3
7.
H. M. A. Kolken, A. A. Zadpoor, RSC Adv. 7 (9), 5111 (2017). DOI: 10.1039 / C6RA27333E
8.
M. Bilski, K. W. Wojciechowski. Phys. Status Solidi B 253 (7), 1318 (2016). DOI: 10.1002 / pssb.201600140
9.
L. Zhou, L. Jiang, H. Phys. Status Solidi B 253 (7), 1331 (2016). DOI: 10.1002 / pssb.201552768
10.
H. Jopek. Phys. Status Solidi B 253 (7), 1369 (2016) DOI: 10.1002 / pssb.201600117
11.
R. V. Goldstein, V. A. Gorodtsov, D. S. Lisovenko. Eur. J. Mech. A Solids 63, 122 (2017). DOI: 10.1016 / j.euromechsol.2017.01.001
12.
A. Alderson, Chem. Ind. 17, 384 (1999).
13.
K. E. Evans, A. Alderson, Adv. Mater. 12 (9), 617 (2000). DOI: 10.1002 / (SICI) 1521 – 4095 (200005) 12:9<617::AID-ADMA617>3.0. CO;2 – 3
14.
K. L. Alderson, V. R. Simkins, V. L. Coenen, P. J. Davies, A. Alderson, K. E. Evans, Phys. Status Solidi B, 242 (3), 509 (2005). DOI: 10.1002 / pssb.200460371
15.
A. C. Branka, D. M. Heyes, Sz.Mackowiak, S. Pieprzyk, K. W. Wojciechowski, Phys. Status Solidi B 249 (7), 1373 (2012). DOI: 10.1002 / pssb.201084222
16.
R. V. Goldstein, V. A. Gorodtsov, D. S. Lisovenko. Mech. Solids, 45 (4), 529 (2010). DOI: 10.3103 / S0025654410040047
17.
R. V. Goldstein, V. A. Gorodtsov, D. S. Lisovenko. Phys. Status Solidi B, 250 (10), 2038 (2013). DOI: 10.1002 / pssb.201384233
18.
R. V. Goldstein, V. A. Gorodtsov, D. S. Lisovenko. Letters on Materials, 3 (1), 7 (2013). DOI: 10.22226 / 2410‑3535‑2013‑1‑7‑11
19.
R. H. Baughman, J. M. Shacklette, A. A. Zakhidov, S. Stafström, Nature 392 (6674), 362 (1998). DOI: 10.1038 / 32842
20.
V. V. Krasavin, A. V. Krasavin, Phys. Status Solidi B 251 (11), 2314 (2014). DOI: 10.1002 / pssb.201451129
21.
R. V. Goldstein, V. A. Gorodtsov, D. S. Lisovenko. Dokl. Phys., 58 (9), 400 (2013). DOI: 10.1134 / S1028335813090097
22.
R. V. Goldstein, V. A. Gorodtsov, D. S. Lisovenko, M. A. Volkov. Dokl. Phys. 61 (12), 604 (2016). DOI: 10.1134 / S1028335816120016
23.
D. Attard, J. N. Grima. Phys. Status Solidi B 245 (11), 2395 (2008). DOI: 10.1002 / pssb.200880269
24.
J. N. Grima, P.‑S. Farrugia, R. Gatt, D. Attard. Phys. Status Solidi B, 245 (3), 521 (2008). DOI: 10.1002 / pssb.200777705
25.
J. W. Narojczyk, K. W. Wojciechowski. J. Non-Cryst. Solids 356 (37-40), 2026 (2010). DOI: 10.1016 / j.jnoncrysol.2010.05.080
26.
V. V. Novikov, K. W. Wojciechowski. Phys. Solid State 41 (12), 1970 (1999). DOI: 10.1134 / 1.1131137
27.
K. W. Wojciechowski, Mol. Phys. Rep. 10, 129 (1995).
28.
R. V. Goldstein, V. A. Gorodtsov, D. S. Lisovenko. Phys. Status Solidi B 253 (7), 1261 (2016). DOI: 10.1002 / pssb.201600054
29.
S. V. Dmitriev, E. A. Korznikova, D. I. Bokij, K. Zhou. Phys. Status Solidi B 253 (7), 1310 (2016). DOI: 10.1002 / pssb.201600086