A novel foam structure is presented, which exhibits a negative Poisson's ratio. Such a material expands laterally when stretched, in contrast to ordinary materials.
Virtually all common materials undergo a transverse contraction when stretched in one direction and a transverse expansion when compressed. The magnitude of this transverse deformation is governed by a material property known as Poisson's ratio. Poisson's ratio is defined as minus the transverse strain divided by the axial strain in the direction of stretching force. Since ordinary materials contract laterally when stretched and expand laterally when compressed, Poisson's ratio for such materials is positive. Poisson's ratios for various materials are approximately 0.5 for rubbers and for soft biological tissues, 0.45 for lead, 0.33 for aluminum, 0.27 for common steels, 0.1 to 0.4 for cellular solids such as typical polymer foams, and nearly zero for cork.
Negative Poisson's ratios are theoretically permissible but have not, with few exceptions, been observed in real materials. Specifically, in an isotropic material (a material which does not have a preferred orientation) the allowable range of Poisson's ratio is from -1.0 to +0.5, based on thermodynamic considerations of strain energy in the theory of elasticity. It is believed by many that materials with negative values of Poisson's ratio are unknown; however Love presents a single example of cubic 'single crystal' pyrite as having a Poisson's ratio of -0.14; he suggests the effect may result from a twinned crystal. Analysis of the tensorial elastic constants of anisotropic single crystal cadmium suggests Poisson's ratio may attain negative values in some directions. Anisotropic, macroscopic two-dimensional flexible models of certain honeycomb structures (not materials) have exhibited negative Poisson's ratios in some directions. These known examples of negative Poisson's ratios all depend on the presence of a high degree of anisotropy; the effect only occurs in some directions and may be dominated by coupling between stretching force and shear deformation. The materials described in the following, by contrast, need not be anisotropic.
Foams with negative Poisson's ratios were produced from conventional low density open-cell polymer foams by causing the ribs of each cell to permanently protrude inward, resulting in a re-entrant structure. A polyester foam was used as a starting material and was found to have a density of 0.03 gm/cubic cm, a Young's modulus of 71 kPa (10 psi), a cell size of 1.2 mm, and a Poisson's ratio of 0.4. The method used to create the re-entrant structure is as follows. Specimens of conventional foam were compressed triaxially, i.e. in three orthogonal directions, and were placed in a mold. The mold was heated to a temperature slightly above the softening temperature of the foam material, 163 deg.C to 171 deg.C in this case. The mold was then cooled to room temperature and the foam was extracted. Specimens which were given a permanent volumetric compression of a factor of 1.4 to a factor of 4 during this transformation process were found to exhibit negative Poisson's ratios. For example, a foam subjected to a permanent volumetric compression of a factor of two had a Young's modulus of 72 kPa, and a Poisson's ratio of -0.7. Polyester foams of similar structure and properties but different cell sizes (0.3 mm, 0.4 mm, 2.5 mm) transformed by the above procedure were also found to exhibit negative Poisson's ratios. Reticulated metal foams were transformed by the alternate procedure of plastically deforming the material at room temperature. Permanent compressions were performed sequentially in each of three orthogonal directions. Foams transformed in this way were also found to exhibit re-entrant structures.
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