4) or in three dimensions [21]. Structural mechanisms are also of interest in connection with the fabrication [5] R. F. Almgren, "An isotropic three dimensional structure with Poisson's ratio = -1", J. Elasticity, 1985, 15, 427-430. Evans, and B.D. The relationship between shear modulus G, bulk modulus K, and Poisson's ratio [[nu]] for isotropic materials is. Several rare earth alloys (Sm1-xYxS) exhibit negative Poisson's ratios in the vicinity of a valence transition, for certain concentration values [30]; experiments disclose values as small as -0.7. 6. For the structure in Fig. [49] J. The convex shapes are more appropriate than saddle shapes for sandwich panels for aircraft or automobiles. 6 Poisson's ratio vs rotatable node size r divided by lattice spacing d, for non-central force it would increase the cross sectional area). Such materials may also find use in sandwich panels. D., Appl. As for forces which do not depend on distance but instead connect only selected pairs of particles, the corresponding kinematical deformation is a non-affine one. Advances in negative Poisson's ratio materials [13] K.E. 35 0 obj
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It remains to be determined by experiment which structural mechanisms are most important in generating the effects in real materials such as the above. [4] A.G. Kolpakov, "On the determination of the averaged moduli of elastic gridworks", Prikl. As for toughness and damage 5 Behavior of structure shown in Fig. Evans, "Microporous materials with negative Poisson's ratio: I. Microstructure and mechanical properties, J. Phys. occurs. Microcracks in a material can be viewed as flattened pores with minimal volume. Structures of the above type require some form of individual Cosserat elasticity allows the effects of chirality to be incorporated in a natural way; new effects are predicted such as the untwisting of a bar under tensile force, and size effects in Poisson's ratio above are the simplest examples. Lakes, "Negative Poisson's ratio materials, reply", Science, 238, (1987) 551, 35 Lakes, R.S., "Experimental microelasticity of two porous solids", International Journal of Solids and Structures, 22 (1986) 55-, 36 R.S. A Poisson's ratio approaching -1 requires constituents which differ even more in stiffnesses, so that one phase is very soft, tending to 'empty space' in its properties. Royal Society London, 1982, A382, 25-42. In some laminates composed of fibrous layers it is theoretically possible to achieve a negative Poisson's ratio as small as -0.21 in the direction perpendicular to the layers by control of the stacking sequence [18]. [10] Choi, J. Poisson's ratios differing from 1/4 can arise from deviations from the above assumptions, specifically (i) non-central forces between particles in the solid, (ii) forces which do not depend on distance alone, or (iii) anisotropy, including noncentrosymmetry. Macroscopic structures in two or three dimensions consisting of rods, springs, and sliders, were devised to give a negative Poisson's ratio [5]; these structures have an inverted characteristic similar to the honeycombs. Solid squares, k3/k1 = 1, f =1. Sci & Geomech. Phys. Abstr. Macroscopic structures of sliders, hinges, and springs can also exhibit negative Poisson's ratio [18]. [7] L.J. [11] Choi, J. Diagrams at bottom. Pyrolytic graphite [28] intended for thermal protection in aerospace uses was found to have a negative Poisson's ratio of -0.21 in one crystallographic direction. A solid with [[nu]] close to -1 would be the opposite of rubber: difficult to shear but easy to deform volumetrically: G much greater than K. Therefore it may be called anti-rubber. Phys. the materials originally reported [1] were polymer foams of relatively low Caddock, and K.E. 37 Pt. Moreover, many relationships for deformation in the theory of elasticity contain terms (1 - [[nu]]^2) Stress distribution in a flexible pad such as a wrestling mat is more favorable to reducing impact forces upon both small objects such as an elbow and large objects such as a leg or back, if Poisson's ratio is as small as possible [48]. Not all solids which behave as generalized continua will have a negative Poisson's ratio, however all negative Poisson's ratio materials will be describable as generalized continua. The polyethylene was mechanically 14, p. 758-763, Proceedings, 20th Midwest Mechanics Conference, Purdue University, Aug. 31-Sept. 2, 1987, 4 A. W. Lipsett and A. I. Beltzer, "Reexamination of dynamic problems of elasticity for negative Poisson's ratio", J. Acoust. [43] C.P. Herakovich, "Composite laminates with negative through-the -thickness Poisson's ratio", J. Non-central forces can also be introduced by endowing the lattice's connecting ligaments with bending and torsional rigidity. 6.1 Applications The non-affine, rotational and noncentrosymmetric degrees of freedom considered above in a structural sense can also be viewed in the context of continuum A chiral microstructure with non-central force interaction or non-affine deformation can also exhibit a negative Poisson's ratio. Poisson's ratio in materials is governed by the following aspects of the microstructure: the presence of rotational degrees of freedom, non-affine deformation kinematics, or anisotropic structure. The effect of microcracks would also appear to have a non-affine character. It remains to be seen whether materials with negative Poisson's ratios can be made in a controlled way based on 35]. The material was created by compacting powdered polymer, sintering, and extrusion. [3] L. J. Gibson, M. F. Ashby, G. S. Schajer, and C. I. Robertson, "The mechanics of two dimensional cellular solids", Proc. As for dynamical aspects, Lakes, "Negative Poisson's ratio materials", Science, 238, (1987) 551. Auxetics may be useful in applications such as body armor, packing material, knee and elbow pads, robust shock absorbing material, and sponge mops. In the case of [[alpha]]-cristobalite, an isotropic solid made of randomly oriented crystals would exhibit a negative Poisson's ratio. They have several potential applications in medical, sports, automobile, defense, etc.Design and modeling of auxetic materials is still in progress. Soc. This can also be done in a structured way and lead to new aspects in material design as for mechanical metamaterials. Caddock, "Microporous materials with negative Poisson's ratio: II. To that end, we consider several microstructures with the aim of distinguishing which kinds of interaction are most important to achieve a negative Poisson's ratio. A more recent (2017) review is available. The corresponding prestrain is then determined for the ligaments k3 based on equilibrium considerations. [18] C.T. A honeycomb composed of regular hexagonal cells (Fig.1) has a Poisson's ratio of +1 [7,25].

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