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Journal articles on the topic 'Negative Poissons Ratio'

Author: Grafiati

Published: 11 December 2022

Last updated: 26 January 2023

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1

Lim, Teik Cheng. "Rotating Disks Made from Materials with Negative Poisson's Ratio." Advanced Materials Research 804 (September 2013): 347–52. http://dx.doi.org/10.4028/www.scientific.net/amr.804.347.

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Auxetic materials are those that exhibit negative Poissons ratio. In spite of their rarity, auxetic materials have been artificially produced and also found to exist are known to exist naturally. Arising from their anomalous behavior, research on auxetic materials has been carried out for possible applications in fields as diverse as biomechanics and aero-structures. This paper investigates the effect of auxeticity on the maximum stress in thin and thick rotating disks. The obtained results show that maximum stresses are lower in rotating thin disks that are made from negative Poissons ratio materials. It is also revealed that the maximum stresses in thick rotating disks can be reasonably approximated by rotating thin disk theory if the thick disk material possesses negative Poissons ratio.

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2

Ali, Imran, and Jing Jun Yu. "Zero Poisson’s Ratio Honeycomb Structures-An FEA Study." Applied Mechanics and Materials 446-447 (November 2013): 329–34. http://dx.doi.org/10.4028/www.scientific.net/amm.446-447.329.

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Conventional honeycomb structures show positive Poissons ratio under in-plane loading while Auxetic honeycombs show negative Poissons ratio. Accordion, Hybrid and Semi re-entrant honeycomb structures show zero Poissons ratio, i.e. they show zero or negligible deformation in lateral direction under longitudinal loadings. In this paper an FEA analysis of these three types of structures is made using commercial software ANSYSR14 using 8 node 281 shell elements. Cell wall thickness and cell angle is varied to analyze their effect on elastic modulus Exand global strains along X direction under X-direction loadings. Eyis also analyzed to measure lateral stiffness and deformation behavior of structure for its potential application as flexures.

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3

Zhou, Ming, and Zhao Qun Du. "Effects of Structural Parameters and Performance on Poisson's Ratio of Auxetic Yarn." Advanced Materials Research 821-822 (September 2013): 252–58. http://dx.doi.org/10.4028/www.scientific.net/amr.821-822.252.

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Auxetic yarn is designed by ourselves by wrap-core structure, which has special physical properties and geometrical structure different from traditional yarn. The wrap-core auxetic yarn will expand transversely under tension. Therefore, the tensile tests were conducted to analyze effects of structural parameters and performance on lateral deformation of yarn. The experimental results show that yarn with negative Poissons ratio as low as-4.31 is produced successfully. Moreover, effects of structure and performance, including the wrap angle, the diameter ratio, the tension modulus of the wrap yarn and the twist of the core yarn, on poissons ratio of yarn are analyzed. It is found that the negative Poissons ratio effect becomes more observable with the higher diameter ratio or lower wrap angle, and it becomes much more observable when the twist degree of the core yarn is higher or the wrap yarns modulus is lower.

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4

Lim, Teik Cheng. "Stress Concentration Factors in Auxetic Rods and Plates." Applied Mechanics and Materials 394 (September 2013): 134–39. http://dx.doi.org/10.4028/www.scientific.net/amm.394.134.

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Auxetic materials are solids that possess negative Poissons ratio. Although rare, such materials do occur naturally and also have been artificially produced. Due to their unique properties, auxetic materials have been extensively investigated for load bearing applications including in biomedical engineering and aircraft structures. This paper considers the effect of Poissons ratio on the stress concentration factors on rods with hyperbolic groove and large thin plates with circular holes and rigid inclusions. Results reveal that the use of auxetic materials is useful for reducing stress concentration in the maximum circumferential stress of the rods with grooves, and in plates with circular holes and rigid inclusions. However, the use of auxetic materials increases the stress concentration in the axial direction of the rod. Therefore a procedure to accurately select and/or design materials with precise negative Poissons ratio for optimal design is suggested for future work.

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5

Ge, Zhao Yang, and Hong Hu. "Design and Compression Deformation Analysis of an Innovational Structure with Auxetic Effect." Applied Mechanics and Materials 427-429 (September 2013): 99–103. http://dx.doi.org/10.4028/www.scientific.net/amm.427-429.99.

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An innovational structure with auxetic effect was designed from inspiration of a re-entrant honeycomb structure firstly proposed by Gibson et.al. In the newly designed structure, yarns were used to replace the straight and tilted ribs of re-entrant honeycomb structure in order to achieve negative Poissons ratio. The compression testing was carried out in the vertical direction of the structure using an INSTRON 5566 tester to understand its deformation behavior. The results show that the difference in bending stiffness between the warp and weft yarns is the main reason for getting negative Poissons ratio of the structure.

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6

Mardling, Paul, Andrew Alderson, Nicola Jordan-Mahy, and Christine Lyn Le Maitre. "The use of auxetic materials in tissue engineering." Biomaterials Science 8, no. 8 (2020): 2074–83. http://dx.doi.org/10.1039/c9bm01928f.

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A number of biological tissues have been shown to behave in an auxetic manner, defined by having a negative poissons ratio. Thus mimicking this environment has a number of potential applications especially in tissue engineering.

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7

Lim, Teik Cheng. "Spherical Auxetic Shells." Advanced Materials Research 804 (September 2013): 146–50. http://dx.doi.org/10.4028/www.scientific.net/amr.804.146.

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Materials that exhibit negative Poissons ratio are called auxetic materials. Although such materials are quite rare, they nevertheless exist as naturally occurring materials and artificially made materials. Due to their unique material properties, auxetic materials have been intensively investigated for the past 20 years. This paper studies the effect of auxeticity on the maximum stresses in spherical shells. The results suggest that auxetic materials are not suitable for shells with built-in edge, but highly suitable for shells that are simply supported. For the latter boundary condition, it was found that the ratio of maximum bending stress to the maximum membrane stress diminishes as the Poissons ratio of the shell material approaches-1. This means that under the boundary condition of simple supports, a geometrically thick shell is mechanically equivalent to a thin or membrane shell, and therefore the use of membrane shell theory suffices even for a reasonably thick shell if the shell material is highly auxetic.

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8

Phan-Thien, N., and B. L. Karihaloo. "Materials With Negative Poisson’s Ratio: A Qualitative Microstructural Model." Journal of Applied Mechanics 61, no. 4 (1994): 1001–4. http://dx.doi.org/10.1115/1.2901547.

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Materials with negative Poisson ’s ratio are peculiar in that they expand laterally when stretched. Examples of such type of behavior have been discovered with foams by Lakes (1987); however, it is only recently that isotropic materials with negative Poisson’s ratio have been shown by Milton (1992) to exist within the framework of classical theory of elasticity. In this Note, we demonstrate qualitatively that a composite material with a reentrant microstructure can also have a negative Poisson’s ratio, even though the composite may be isotropic owing to a completely random distribution of the microstructure.

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9

Sorohan, Stefan, Dan Mihai Constantinescu, Marin Sandu, and Adriana Sandu. "Evaluation of Thermal Stresses in Sandwich Panels with Chiral Cellular Cores." Key Engineering Materials 601 (March 2014): 242–45. http://dx.doi.org/10.4028/www.scientific.net/kem.601.242.

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Sandwich panels are important components of advanced structures used in aerospace, automotive, railway, civil engineering etc. They are subjected to high and repeated variations of temperature which induce additional stresses as the core and the face sheets are from different materials having different coefficients of thermal expansion and moduli of elasticity. Therefore it is important to evaluate both mechanical and thermal stresses. In the literature one can find thermo-mechanical analyses of sandwich panels with metallic or composite face sheets and having a honeycomb or compact core made from polyurethane foam. In this paper was analysed a plane sandwich panel made from a cellular rigid polyurethane core, having a chiral configuration and auxetic properties (negative Poissons ratio) exposed to a stationary temperature field with a linear variation from +25 °C on one sheet to-50 °C on the opposite sheet. Two boundary conditions were considered in the thermo-mechanical evaluation: the free panel and the panel simply supported around the edges.

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10

Wang, Wenrui, Chenwei He, Lu Xie, and Qing Peng. "The Temperature-Sensitive Anisotropic Negative Poisson’s Ratio of Carbon Honeycomb." Nanomaterials 9, no. 4 (2019): 487. http://dx.doi.org/10.3390/nano9040487.

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We report that carbon honeycomb, a new three-dimension carbon allotrope, exhibits large negative Poisson’s ratio, as large as −0.32, in tensile revealed via molecular dynamics simulations. The Poisson’s ratio of carbon honeycomb is anisotropic, and sensitive to temperature. The carbon honeycomb has phase transformation from normal to auxetic by tensile, along both zigzag and armchair directions. The critical strain for the normal-auxetic transition along the cell-axis direction reduces with respect to an increase in temperature. Combined with high strength of 50 GPa, such a unique and adjustable negative Poisson ratio suggests broad engineering applications of carbon honeycomb.

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11

Pan, Kun, Jieyu Ding, Wei Zhang, and Shengdong Zhao. "The Negative Poisson’s Ratio Ship Base Design and Vibration Isolation Performance Analysis." Applied Sciences 11, no. 23 (2021): 11167. http://dx.doi.org/10.3390/app112311167.

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This paper mainly studies the vibration isolation of negative Poisson’s ratio structure in the honeycomb base of ships. Based on the structure of the negative Poisson’s ratio structure, different laying methods and different cell structure are used to construct the honeycomb base with the re-entrant hexagonal cell, the mathematical expression of Poisson’s ratio of a single re-entrant hexagonal cell structure is obtained through theoretical analysis. The negative Poisson ratio and relative density could be got by changing the angle and side thickness of the cell structure. Based on the different energy band of the re-entrant hexagonal cell structure, the different negative Poisson’s ratio re-entrant hexagonal honeycomb base was got, the energy band and the frequency response curve of the ship base are analyzed by COMSOL software. The energy band diagram and the frequency response of the structure are obtained to analyze the vibration isolation performance of the honeycomb base. By comparing the experimental results, the following conclusions can be gotten: (1) Compared with the traditional base, the negative Poisson’s ratio base has better vibration isolation effect on external excitation; (2) Different laying method and Poisson ratios can get different isolation effect. The combined base structure can provide better isolation effect to the external excitation in a larger frequency band; (3) By adding different mass blocks to the inner or peripheral angles of the basic re-entrant hexagonal cell, the vibration isolation performance of the structure can be changed to better.

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12

Burns, Stephen. "Negative Poisson's Ratio Materials." Science 238, no. 4826 (1987): 551. http://dx.doi.org/10.1126/science.238.4826.551.a.

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13

BURNS, S. "Negative Poisson's Ratio Materials." Science 238, no. 4826 (1987): 551. http://dx.doi.org/10.1126/science.238.4826.551.

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14

Lakes, R. S. "Saint-Venant End Effects for Materials With Negative Poisson’s Ratios." Journal of Applied Mechanics 59, no. 4 (1992): 744–46. http://dx.doi.org/10.1115/1.2894037.

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In this paper we analyze Saint-Venant end effects for materials with negative Poisson ’s ratios. We present an example of slow decay of stress arising from selfequilibrated stress at the end of a circular cylinder of elastic material with a negative Poisson’s ratio. By contrast, a sandwich panel containing rigid face sheets and a compliant core exhibits no anomalous effects for negative Poisson’s ratio, but exhibits slow stress decay for core Poisson’s ratio approaching 0.5. In sandwich panels with stiff but not perfectly rigid face sheets, slow decay of stress is known to occur; a negative Poisson’s ratio results in end stress decay, which is faster than it would be otherwise.

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15

Lakes, Rod, and K. W. Wojciechowski. "Negative compressibility, negative Poisson's ratio, and stability." physica status solidi (b) 245, no. 3 (2008): 545–51. http://dx.doi.org/10.1002/pssb.200777708.

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16

Ravirala, Naveen, Kim L. Alderson, Philip J. Davies, Virginia R. Simkins, and Andrew Alderson. "Negative Poisson’s Ratio Polyester Fibers." Textile Research Journal 76, no. 7 (2006): 540–46. http://dx.doi.org/10.1177/0040517506065255.

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17

Brandel, B., and R. S. Lakes. "Negative Poisson's ratio polyethylene foams." Journal of Materials Science 36, no. 24 (2001): 5885–93. http://dx.doi.org/10.1023/a:1012928726952.

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18

LAKES, R. "Response: Negative Poisson's Ratio Materials." Science 238, no. 4826 (1987): 551. http://dx.doi.org/10.1126/science.238.4826.551-a.

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19

Miller, W., Z. Ren, C. W. Smith, and K. E. Evans. "A negative Poisson’s ratio carbon fibre composite using a negative Poisson’s ratio yarn reinforcement." Composites Science and Technology 72, no. 7 (2012): 761–66. http://dx.doi.org/10.1016/j.compscitech.2012.01.025.

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20

Choi, J. B., and R. S. Lakes. "Nonlinear Analysis of the Poisson's Ratio of Negative Poisson's Ratio Foams." Journal of Composite Materials 29, no. 1 (1995): 113–28. http://dx.doi.org/10.1177/002199839502900106.

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21

Chen, Ke, Haoran Wan, Xiang Fang, and Hongyu Chen. "Laser Additive Manufacturing of Anti-Tetrachiral Endovascular Stents with Negative Poisson’s Ratio and Favorable Cytocompatibility." Micromachines 13, no. 7 (2022): 1135. http://dx.doi.org/10.3390/mi13071135.

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Laser additive manufacturing (LAM) of complex-shaped metallic components offers great potential for fabricating customized endovascular stents. In this study, anti-tetrachiral auxetic stents with negative Poisson ratios (NPR) were designed and fabricated via LAM. Poisson’s ratios of models with different diameters of circular node (DCN) were calculated using finite element analysis (FEA). The experimental method was conducted with the LAM-fabricated anti-tetrachiral stents to validate their NPR effect and the simulation results. The results show that, with the increase in DCN from 0.6 to 1.5 mm, the Poisson ratios of anti-tetrachiral stents varied from −1.03 to −1.12, which is in line with the simulation results. The interrelationship between structural parameters of anti-tetrachiral stents, their mechanical properties and biocompatibility was demonstrated. The anti-tetrachiral stents with a DCN of 0.9 mm showed the highest absolute value of negative Poisson’s ratio, combined with good cytocompatibility. The cytocompatibility tests indicate the envisaged cell viability and adhesion of the vascular endothelial cell on the LAM-fabricated anti-tetrachiral auxetic stents. The manufactured stents exhibit great superiority in the application of endovascular stent implantation due to their high flexibility for easy maneuverability during deployment and enough strength for arterial support.

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22

Gong, Xiaobo, Chengwei Ren, Yuhong Liu, Jian Sun, and Fang Xie. "Impact Response of the Honeycomb Sandwich Structure with Different Poisson’s Ratios." Materials 15, no. 19 (2022): 6982. http://dx.doi.org/10.3390/ma15196982.

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The honeycomb sandwich structure is widely used in energy-absorbing facilities because it is lightweight, has a high specific stiffness and high specific strength, and is easy to process. It also has dynamic mechanical characteristics such as a high impact resistance and high energy absorption. To explore the influence of the Poisson’s ratio on the local impact resistance, this paper compares and analyzes the local impact resistance of a series of honeycomb cores with different Poisson’s ratios under the impact of a spherical projectile at different speeds. Three typical honeycombs with negative/zero/positive Poisson ratios (re-entrant hexagon, semi-re-entrant hexagon, and hexagon) are selected to change the geometric parameters in order to have the same relative density and different Poisson ratios (−2.76–3.63). The relative magnitude of the rear face sheet displacement is in the order of negative Poisson’s ratio > zero Poisson’s ratio > positive Poisson’s ratio, which reveals that the honeycomb structure with the positive Poisson’s ratio has better protection ability than the others. Finally, a dual-wall hexagonal honeycomb is proposed. The rear face sheet displacement of the dual-wall hexagonal honeycomb sandwich structure is reduced by 34.4% at 25 m/s compared with the hexagonal honeycomb, which has a better local impact resistance.

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23

Lakes, Roderic S. "Negative-Poisson's-Ratio Materials: Auxetic Solids." Annual Review of Materials Research 47, no. 1 (2017): 63–81. http://dx.doi.org/10.1146/annurev-matsci-070616-124118.

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24

HIMENO, Mamoru, Takehiro MORITA, Yoshinori SAWAE, and Tetsuo YAMAGUCHI. "Negative Poisson's ratio and stress distribution." Proceedings of Mechanical Engineering Congress, Japan 2018 (2018): J0420204. http://dx.doi.org/10.1299/jsmemecj.2018.j0420204.

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25

Yanping Liu, Hong Hu, Jimmy K. C. Lam, and Su Liu. "Negative Poisson’s Ratio Weft-knitted Fabrics." Textile Research Journal 80, no. 9 (2009): 856–63. http://dx.doi.org/10.1177/0040517509349788.

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26

Qin, Huasong, Yu Sun, Jefferson Zhe Liu, Mengjie Li, and Yilun Liu. "Negative Poisson's ratio in rippled graphene." Nanoscale 9, no. 12 (2017): 4135–42. http://dx.doi.org/10.1039/c6nr07911c.

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27

Wan, Jing, Jin-Wu Jiang, and Harold S. Park. "Negative Poisson's ratio in graphene oxide." Nanoscale 9, no. 11 (2017): 4007–12. http://dx.doi.org/10.1039/c6nr08657h.

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28

Lakes, Roderic. "Advances in negative Poisson's ratio materials." Advanced Materials 5, no. 4 (1993): 293–96. http://dx.doi.org/10.1002/adma.19930050416.

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29

Liu, Gang, Qimiao Zeng, Pengfei Zhu, Ruge Quhe, and Pengfei Lu. "Negative Poisson's ratio in monolayer PdSe2." Computational Materials Science 160 (April 2019): 309–14. http://dx.doi.org/10.1016/j.commatsci.2019.01.024.

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30

Lee, Moon Kyu, Jae Bong Choi, Kui Won Choi, and H. N. Lim. "Design of Rotational Particle Structure with Negative Poisson’s Ratio Using Numerical Method." Materials Science Forum 544-545 (May 2007): 43–46. http://dx.doi.org/10.4028/www.scientific.net/msf.544-545.43.

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In the area of biomaterials, the structures with negative Poisson’s ratio are able to be applied to the polymer component of prosthesis, artificial blood-vessel and catheter. To induce its characteristic, previous studies postulated many structural shapes such as non-convex shape with reentrant corners and re-entrant honeycomb. In this study, we proposed the rotational particle structures and investigated the Poisson’s ratio and the ratio (Ee/E) of the elastic modulus of these structures based on structural design variables using finite element method. The auto-meshing preprocessor was coded using MATLAB in order to construct numerical models as design variables and perform finite element analysis (FEA) effectively. Three selected design variables were the ratio of fibril’s length to particle’s diameter (0.2~2.0), the ratio of fibril’s length to its width (0.02~0.2) and the angle of fibril about horizontal axis (0 degree ~ tangential angle). Finite element model has 2D plain stress quadratic element and composed of 515 particles and 6-linked fibrils per each particle. For all of 213 cases, one side of each model is applied a tension, 0.1% strain and analyze Poisson’s ratio and the ratio (Ee/E) of the elastic modulus. As the ratio of fibril’s length to particle’s diameter increased and the ratio of fibril’s diameter to fibril’s length decreased fixing the fibril’s angle with 45 degree, the negative Poisson effect of rotational particle structures increased. The ratio of elastic modulus of these structures decreased with Poisson’s ratio. The results show the reasonable values as compared with the previous analytical results.

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31

Park, Yeong Jun, and Jeong Koo Kim. "The Effect of Negative Poisson’s Ratio Polyurethane Scaffolds for Articular Cartilage Tissue Engineering Applications." Advances in Materials Science and Engineering 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/853289.

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An auxetic polyurethane (PU) scaffold was prepared to investigate chondrocyte proliferation under compressive stimulation for cartilage regeneration. To give a negative Poisson’s ratio to the PU scaffold, volumetric compression with a 3 : 1 ratio was applied during heat treatment. For the control PU scaffold, the Poisson’s ratio was 0.9 ± 0.25 with elongation at 20% of the strain range. Poisson’s ratio for experimental specimens was approximately −0.4 ± 0.12 under the same conditions. In cell proliferation tests, cells were cultivated within the prepared scaffold under compression with a 20% strain range. With a 20% strain range elongation, the compressive load was approximately 0.3 N. The experimental group showed a 1.3 times higher cellular proliferation rate than that of the control group after 3 days in culture. At day 5 of culture, however, the rate of proliferation of the control group increased so that there was no significant difference between groups. However, collagen content (produced by the cells) in the cell-proliferated medium was 1.5 times higher in the experimental group after 5 days in culture. This may have been due to the effectiveness of the auxetic structure of the scaffold. An isotropic compressive load was transmitted to the cells due to the negative Poisson ratio of the scaffold.

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32

Muslov, S. A., A. I. Lotkov, and V. N. Timkin. "Poisson ratio of TiNi." Perspektivnye Materialy 12 (2021): 5–20. http://dx.doi.org/10.30791/1028-978x-2021-12-5-20.

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A review of the literature data and methods for calculating the Poisson coefficient of the TiNi intermetallic compound in the poly- and single-crystal state is performed. The results of our own research are also presented. Significant variability of the presented data is noted, due to differences in the thermomechanical processing of the alloys and the measurement and calculation methods used. By averaging the matrices of elastic constants and compliance coefficients using the Voigt, Reuss, and Hill approximations, we obtained the values of the parameters of the effective elastic properties of TiNi polycrystals and calculated the Poisson’s ratio. Using analytical expressions to calculate the values of the extreme values, the extrema of the Poisson’s ratio of cubic TiNi crystals are determined for standard orientations. Based on a number of data, TiNi crystals are auxetics (materials having negative Poisson’s ratio values), on the basis of others they are not. We found that TiNi crystals belong to the so-called partial auxetics, in this case the signs of the inequalities (s12 < 0, s = s11 + s12 − s44/2 > 0 or s12 > 0, s = s11 + s12 − s44/2 < 0) are opposite. The values of the Poisson’s ratio TiNi averaged over the transverse directions of deformation are analyzed. Isosurfaces of the Poisson’s ratio and their sections are presented using the ELATE computational graphic package and the MATHCAD computer algebra program. Aspects of TiNi elastic anisotropy, its parameters, and their relationship with martensitic transformations in TiNi and alloys based on it are discussed.

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33

Xie, Fang, and Zuo Min Liu. "Effect of Negative Poisson's Ratios of Auxetic UHMWPE on the Contact Mechanics in Artificial Hip Joint Replacement." Advanced Materials Research 399-401 (November 2011): 1559–63. http://dx.doi.org/10.4028/www.scientific.net/amr.399-401.1559.

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With the development of functional and structural materials, increasing interests have been shown in the field of biomaterials with a negative Poisson’s ratio (auxetic), which exhibit the unusual property of becoming thinner when compressed. This unusual property makes it potentially a synthetic replacement biomaterial with adequate mechanical property and wear resistance. In this study, the potential of applying the auxetic ultra-high molecular weight polyethylene (UHMWPE) for the artificial hip joint was discussed. The contact mechanics characteristics in artificial hip joint replacement under different Poisson's ratios of -1<μ≤0.5 were investigated and compared using the finite element method. The results show that Poisson’s ratio had great effect on the contact mechanics in artificial hip joint replacement. Therefore, the future work should focus on tailoring an auxetic UHMWPE with a suitable Poisson’s ratio for artificial hip joint replacements.

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34

Meng, Fanchao, Shuying Chen, Wenyan Zhang, et al. "Negative Poisson's ratio in graphene Miura origami." Mechanics of Materials 155 (April 2021): 103774. http://dx.doi.org/10.1016/j.mechmat.2021.103774.

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35

Lakes, Roderic. "Response : Negative Poisson's Ratio Materials." Science 238, no. 4826 (1987): 551. http://dx.doi.org/10.1126/science.238.4826.551.b.

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36

Lakes, R. S., and R. Witt. "Making and Characterizing Negative Poisson's Ratio Materials." International Journal of Mechanical Engineering Education 30, no. 1 (2002): 50–58. http://dx.doi.org/10.7227/ijmee.30.1.5.

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37

Tokmakova, Svetlana. "Directions with negative Poisson’s ratio in crystals." Journal of the Acoustical Society of America 110, no. 5 (2001): 2702. http://dx.doi.org/10.1121/1.4777317.

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38

Hao, Feng, Xiangbiao Liao, Mingjia Li, Hang Xiao, and Xi Chen. "Oxidation-induced negative Poisson’s ratio of phosphorene." Journal of Physics: Condensed Matter 30, no. 31 (2018): 315302. http://dx.doi.org/10.1088/1361-648x/aacfd1.

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39

Openov, L. A., and A. I. Podlivaev. "Negative Poisson’s ratio in a nonplanar phagraphene." Physics of the Solid State 59, no. 6 (2017): 1267–69. http://dx.doi.org/10.1134/s106378341706018x.

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40

Wang, Yuanlong, Liangmo Wang, Zheng-dong Ma, and Tao Wang. "A negative Poisson's ratio suspension jounce bumper." Materials & Design 103 (August 2016): 90–99. http://dx.doi.org/10.1016/j.matdes.2016.04.041.

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41

Shufrin, Igor, Elena Pasternak, and Arcady V. Dyskin. "Planar isotropic structures with negative Poisson’s ratio." International Journal of Solids and Structures 49, no. 17 (2012): 2239–53. http://dx.doi.org/10.1016/j.ijsolstr.2012.04.022.

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42

Shufrin, Igor, Elena Pasternak, and Arcady V. Dyskin. "Negative Poisson’s ratio in hollow sphere materials." International Journal of Solids and Structures 54 (February 2015): 192–214. http://dx.doi.org/10.1016/j.ijsolstr.2014.10.014.

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43

Shufrin, Igor, Elena Pasternak, and Arcady V. Dyskin. "Hybrid materials with negative Poisson’s ratio inclusions." International Journal of Engineering Science 89 (April 2015): 100–120. http://dx.doi.org/10.1016/j.ijengsci.2014.12.006.

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44

Steffens, Fernanda, Fernando Ribeiro Oliveira, Carlos Mota, and Raul Fangueiro. "High-performance composite with negative Poisson’s ratio." Journal of Materials Research 32, no. 18 (2017): 3477–84. http://dx.doi.org/10.1557/jmr.2017.340.

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45

LAKES, R. "Foam Structures with a Negative Poisson's Ratio." Science 235, no. 4792 (1987): 1038–40. http://dx.doi.org/10.1126/science.235.4792.1038.

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46

Jiang, Jin-Wu, Tienchong Chang, and Xingming Guo. "Tunable negative Poisson's ratio in hydrogenated graphene." Nanoscale 8, no. 35 (2016): 15948–53. http://dx.doi.org/10.1039/c6nr04976a.

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Friis, E. A., R. S. Lakes, and J. B. Park. "Negative Poisson's ratio polymeric and metallic foams." Journal of Materials Science 23, no. 12 (1988): 4406–14. http://dx.doi.org/10.1007/bf00551939.

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Babaee, Sahab, Jongmin Shim, James C. Weaver, Elizabeth R. Chen, Nikita Patel, and Katia Bertoldi. "3D Soft Metamaterials with Negative Poisson's Ratio." Advanced Materials 25, no. 36 (2013): 5044–49. http://dx.doi.org/10.1002/adma.201301986.

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Huang, Chuanwei, and Lang Chen. "Negative Poisson's Ratio in Modern Functional Materials." Advanced Materials 28, no. 37 (2016): 8079–96. http://dx.doi.org/10.1002/adma.201601363.

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Khokhlov, A. V. "NON-MONOTONICITY, SIGN CHANGES AND OTHER FEATURES OF POISSON'S RATIO EVOLUTION FOR ISOTROPIC LINEAR VISCOELASTIC MATERIALS UNDER TENSION AT CONSTANT STRESS RATES." Problems of strenght and plasticity 81, no. 3 (2019): 271–91. http://dx.doi.org/10.32326/1814-9146-2019-81-3-271-291.

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Abstract:

We study analytically the Boltzmann - Volterra linear constitutive equation for isotropic non-aging viscoelastic media in order to elucidate its capabilities to provide a qualitative simulation of rheological phenomena related to different types of evolution of triaxial strain state and of the lateral contraction ratio (the Poisson ratio) observed in uni-axial tests of viscoelastic materials under tension or compression at constant stress rate. In particular, we consider such effects as increasing, decreasing or non-monotone dependences of lateral strain and Poisson's ratio on time, sign changes and negativity of Poisson's ratio (auxeticity effect) and its stabilization at large times. The viscoelasticity equation implies that the hydrostatic and deviatoric parts of stress and strain tensors don't depend on each other. It is governed by two material functions of a positive real argument (that is shear and bulk creep compliances). Assuming both creep compliances are arbitrary positive, differentiable, increasing and convex up functions on time semi-axis, we analyze general expressions for the Poisson ratio and strain triaxiality ratio (which is equal to volumetric strain divided by deviatoric strain) generated by the viscoelasticity relation under uni-axial tension or compression. We investigate qualitative properties and peculiarities of their evolution in time and their dependences on material functions characteristics. We obtain the universal accurate two-sided bound for the Poisson ratio range and criteria for the Poisson ratio increase or decrease and for extrema existence. We derive necessary and sufficient restrictions on shear and bulk creep compliances providing sign changes of the Poisson ratio and negative values of Poisson's ratio on some interval of time. The properties of the Poisson ratio under tension at constant stress rates found in the study we compare to properties the Poisson ratio evolution under constant stress (in virtual creep tests) and illustrate them using popular classical and fractal models with shear and bulk creep functions each one controlled by three parameters. The analysis carried out let us to conclude that the linear viscoelasticity theory (supplied with common creep functions which are non-exotic from any point of view) is able to simulate qualitatively the main effects associated with different types of the Poisson ratio evolution under tension or compression at constant stress rate except for dependence of Poisson's ratio on stress rate. It is proved that the linear theory can reproduce increasing, decreasing or non-monotone and convex up or down dependences of lateral strain and Poisson's ratio on time and it can provide existence of minimum, maximum or inflection points and sign changes from minus to plus and vice versa and asymptotic stabilization at large times.

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