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Non-linear properties of metallic cellular materials with a negative Poisson's ratio

Negative Poisson's ratio copper foam was prepared and characterized experimentally. The transformation into re-entrant foam was accomplished by applying sequential permanent compressions above the yield point to achieve a triaxial compression. The Poisson's ratio of the re-entrant foam depended on strain and attained a relative minimum at strains near zero. Poisson's ratio as small as -0.8 was achieved. The strain dependence of properties occurred over a narrower range of strain than in the polymer foams studied earlier. Annealing of the foam resulted in a slightly greater magnitude of negative Poisson's ratio and greater toughness at the expense of a decrease in the Young's modulus.

Choi, J. B.↗

Saint-Venant end effects for materials with negative Poisson's ratios

Results are presented from an analysis of Saint-Venant end effects for materials with negative Poisson's ratio. Examples are presented showing that slow decay of end stress occurs in circular cylinders of negative Poisson's ratio, whereas 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 ratios approaching 0.5). In sand panels with stiff but not perfectly rigid face sheets, a negative Poisson's ratio results in end stress decay, which is faster than it would be otherwise. It is suggested that the slow decay previously predicted for sandwich strips in plane deformation as a result of the geometry can be mitigated by the use of a negative Poisson's ratio material for the core.

Lakes, R. S.↗

Holographic study of conventional and negative Poisson's ratio metallic foams - Elasticity, yield and micro-deformation

An experimental study by holographic interferometry is reported of the following material properties of conventional and negative Poisson's ratio copper foams: Young's moduli, Poisson's ratios, yield strengths and characteristic lengths associated with inhomogeneous deformation. The Young's modulus and yield strength of the conventional copper foam were comparable to those predicted by microstructural modeling on the basis of cellular rib bending. The reentrant copper foam exhibited a negative Poisson's ratio, as indicated by the elliptical contour fringes on the specimen surface in the bending tests. Inhomogeneous, non-affine deformation was observed holographically in both foam materials.

Chen, C. P.↗

Deformation mechanisms in negative Poisson's ratio materials - Structural aspects

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. Several structural models are examined. The non-affine kinematics are seen to be essential for the production of negative Poisson's ratios for isotropic materials containing central force linkages of positive stiffness. Non-central forces combined with pre-load can also give rise to a negative Poisson's ratio in isotropic materials. A chiral microstructure with non-central force interaction or non-affine deformation can also exhibit a negative Poisson's ratio. Toughness and damage resistance in these materials may be affected by the Poisson's ratio itself, as well as by generalized continuum aspects associated with the microstructure.

Lakes, R.↗

Indentability of conventional and negative Poisson's ratio foams

The indentation resistance of foams, both of conventional structure and of reentrant structure giving rise to negative Poisson's ratio, is studied using holographic interferometry. In holographic indentation tests, reentrant foams had higher yield strength and lower stiffness than conventional foams of the same original relative density. Calculated energy absorption for dynamic impact is considerably higher for reentrant foam than conventional foam.

Lakes, R. S.↗

Indentability of conventional and negative Poisson's ratio foams

The indentation resistance of foams, both of conventional structure and of re-entrant structure giving rise to negative Poisson's ratio, is studied using holographic interferometry. In holographic indentation tests, re-entrant foams had higher yield strengths sigma(sub y) and lower stiffness E than conventional foams of the same original relative density. Calculated energy absorption for dynamic impact is considerably higher for re-entrant foam than conventional foam.

Lakes, R. S.↗

Holographic study of non-affine deformation in copper foam with a negative Poisson's ratio of -0.8

While conventional foams have positive Poisson's ratios (become smaller in cross-section when stretched and larger when compressed), foam materials have recently been defined which possess 'reentrant' cellular architectures; in these, inwardly-protruding cell ribs are responsible for negative Poisson's ratio behavior, yielding greater resilience than conventional foams. Double-exposure holographic interferometry is presently used to examine the microdeformation of a reentrant copper foam. Attention is given to the nonaffine (inhomogeneous) deformation of this foam.

Chen, C. P.↗

Experimental micro mechanics methods for conventional and negative Poisson's ratio cellular solids as Cosserat continua

Continuum representations of micromechanical phenomena in structured materials are described, with emphasis on cellular solids. These phenomena are interpreted in light of Cosserat elasticity, a generalized continuum theory which admits degrees of freedom not present in classical elasticity. These are the rotation of points in the material, and a couple per unit area or couple stress. Experimental work in this area is reviewed, and other interpretation schemes are discussed. The applicability of Cosserat elasticity to cellular solids and fibrous composite materials is considered as is the application of related generalized continuum theories. New experimental results are presented for foam materials with negative Poisson's ratios.

Lakes, R.↗

Auxetic Thermo-Responsive Shape-Memory Polyurethane Aerogels

Shape memory polymer aerogels are stimuli-responsive aerogel materials that incorporate polymer aerogel characteristics such as flexibility at low density, and high porosity with shape-changing capabilities upon exposure to external stimuli. By designing the structure of these materials at meso- to macroscale, their shape memory response can be efficiently engineered to show an auxetic response such as a negative Poisson’s ratio, leading to an active and tunable metamaterial. We present a material technology based on a shape memory polyurethane aerogel derived from aliphatic triisocyanate and triethylene glycol, which demonstrates and remembers an auxetic shape change through a thermomechanical cycle first below, and then back again above the glass transition temperature of the polyurethane. Our auxetic shape memory polyurethane aerogels exhibit a significant auxetic response with a negative Poisson’s ratio of approximately -0.8 at 15% compressive strain. This technology is expected to impact multiple areas of interest in relation to commercial, aeronautic, and aerospace industries. Potential applications include minimally invasive medical technologies, soft robotics, and self-deployable structures and habitats. Structure-property relationships of the auxetic shape memory polymer aerogels will be discussed.

Sadeq Malakooti↗

The Constitutive Modeling of Thin Films with Randon Material Wrinkles

Material wrinkles drastically alter the structural constitutive properties of thin films. Normally linear elastic materials, when wrinkled, become highly nonlinear and initially inelastic. Stiffness' reduced by 99% and negative Poisson's ratios are typically observed. This paper presents an effective continuum constitutive model for the elastic effects of material wrinkles in thin films. The model considers general two-dimensional stress and strain states (simultaneous bi-axial and shear stress/strain) and neglects out of plane bending. The constitutive model is derived from a traditional mechanics analysis of an idealized physical model of random material wrinkles. Model parameters are the directly measurable wrinkle characteristics of amplitude and wavelength. For these reasons, the equations are mechanistic and deterministic. The model is compared with bi-axial tensile test data for wrinkled Kaptong(Registered Trademark) HN and is shown to deterministically predict strain as a function of stress with an average RMS error of 22%. On average, fitting the model to test data yields an RMS error of 1.2%

Murphey, Thomas W.↗

Meta-aerogels: Auxetic Shape-memory Polyurethane Aerogels

Shape-memory poly(isocyanurate-urethane) (PIR-PUR) aerogels are low-density monolithic nanoporous solids that remember and return to their permanent shape through a heating actuation step. Herein, through structural design at the macro scale, the shape-memory response is augmented with an auxetic effect manifested by a negative Poisson’s ratio of approximately -0.8 at 15% compressive strain. Thus, auxetic shape-memory PIR-PUR monoliths experience volume contraction upon compression at a temperature above the glass transition temperature of the base polymer (Tg ~ 30 °C), and they can be stowed indefinitely in that temporary shape by cooling below Tg. By heating back above Tg, the compressed/shrunk form expands back to their original shape/size. This technology is relevant to a broad range of industries spanning the commercial, aeronautical, and aerospace sectors. The materials are referred to as meta-aerogels and their potential applications include minimally invasive medical devices, soft robotics, and in situations where volume is at a premium, as for example for storage of deployable space structures and planetary habitats during transport to the point of service.

Sadeq Malakooti↗

Composite laminates with negative through-the-thickness Poisson's ratios

A simple analysis using two dimensional lamination theory combined with the appropriate three dimensional anisotropic constitutive equation is presented to show some rather surprising results for the range of values of the through-the-thickness effective Poisson's ratio nu sub xz for angle ply laminates. Results for graphite-epoxy show that the through-the-thickness effective Poisson's ratio can range from a high of 0.49 for a 90 laminate to a low of -0.21 for a + or - 25s laminate. It is shown that negative values of nu sub xz are also possible for other laminates.

Carl T. Herakovich↗

Composite laminates with negative through-the-thickness Poisson's ratios

A simple analysis using two-dimensional lamination theory combined with the appropriate three-dimensional anisotropic constitutive equation is presented to show some rather surprising results for the range of values of the through-the-thickness effective Poisson's ratio nu sub xz for angle ply laminates. Results for graphite-epoxy show that the through-the-thickness effective Poisson's ratio can range from a high of 0.49 for a 90 laminate to a low of -0.21 for a + or - 25s laminate. It is shown that negative values of nu sub xz are also possible for other laminates.

Herakovich, C. T.↗

Structure of the lunar mantle

The structure of the lunar mantle is examined by using data on the decay of shear wave amplitude with distance and the relative arrival times of P and S waves. The new analysis confirms a previous lunar model based primarily upon travel times and more closely defines certain properties of the lunar mantle. A negative shear wave velocity gradient of 0.0013 (km/s)/km, shear wave Q of 4000, and Poisson's ratio of 0.250 plus or minus 0.025 are found for the upper mantle, which lies between the depths of 60 and 300 km. A rapid decrease of shear wave velocity with increasing depth is observed starting at around a 300-km depth, associated with a lower Q for shear waves. Poisson's ratio in the lower part of the middle mantle, which extends to a depth of about 1000 km, is estimated to be 0.36 plus or minus 0.02.

Nakamura, Y.↗