A three-dimensional rotating rigid units network exhibiting negative Poisson's ratios

2012 ◽  
Vol 249 (7) ◽  
pp. 1330-1338 ◽  
Author(s):  
Daphne Attard ◽  
Joseph N. Grima
Keyword(s):  
Three Dimensional ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

scholarly journals Non-Auxetic Mechanical Metamaterials

Materials ◽  
2019 ◽  
Vol 12 (4) ◽  
pp. 635 ◽  
Author(s):  
Christa de Jonge ◽  
Helena Kolken ◽  
Amir Zadpoor
Keyword(s):  
Mechanical Properties ◽  
Yield Stress ◽  
Fatigue Behavior ◽  
Analytical Data ◽  
Three Dimensional ◽  
Mechanical Metamaterials ◽  
Macro Scale ◽  
Unit Cells ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

The concept of “mechanical metamaterials” has become increasingly popular, since their macro-scale characteristics can be designed to exhibit unusual combinations of mechanical properties on the micro-scale. The advances in additive manufacturing (AM, three-dimensional printing) techniques have boosted the fabrication of these mechanical metamaterials by facilitating a precise control over their micro-architecture. Although mechanical metamaterials with negative Poisson’s ratios (i.e., auxetic metamaterials) have received much attention before and have been reviewed multiple times, no comparable review exists for architected materials with positive Poisson’s ratios. Therefore, this review will focus on the topology-property relationships of non-auxetic mechanical metamaterials in general and five topological designs in particular. These include the designs based on the diamond, cube, truncated cube, rhombic dodecahedron, and the truncated cuboctahedron unit cells. We reviewed the mechanical properties and fatigue behavior of these architected materials, while considering the effects of other factors such as those of the AM process. In addition, we systematically analyzed the experimental, computational, and analytical data and solutions available in the literature for the titanium alloy Ti-6Al-4V. Compression dominated lattices, such as the (truncated) cube, showed the highest mechanical properties. All of the proposed unit cells showed a normalized fatigue strength below that of solid titanium (i.e., 40% of the yield stress), in the range of 12–36% of their yield stress. The unit cells discussed in this review could potentially be applied in bone-mimicking porous structures.

scholarly journals Regularly configured structures with polygonal prisms for three-dimensional auxetic behaviour

2017 ◽  
Vol 473 (2202) ◽  
pp. 20160926 ◽  
Author(s):  
Junhyun Kim ◽  
Dongheok Shin ◽  
Do-Sik Yoo ◽  
Kyoungsik Kim
Keyword(s):  
Poisson’S Ratio ◽  
Three Dimensional ◽  
Unit Cell ◽  
Poisson's Ratio ◽  
Numerical Verification ◽  
Geometric Conditions ◽  
Unit Cells ◽  
Negative Poisson's Ratio ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

We report here structures, constructed with regular polygonal prisms, that exhibit negative Poisson’s ratios. In particular, we show how we can construct such a structure with regular n -gonal prism-shaped unit cells that are again built with regular n -gonal component prisms. First, we show that the only three possible values for n are 3, 4 and 6 and then discuss how we construct the unit cell again with regular n -gonal component prisms. Then, we derive Poisson’s ratio formula for each of the three structures and show, by analysis and numerical verification, that the structures possess negative Poisson’s ratio under certain geometric conditions.

Three-Dimensional Compliant Cellular Materials: A Mechanism Based Material Design

2014 ◽  
Author(s):  
Kwangwon Kim ◽  
Jaehyung Ju ◽  
Doo-Man Kim
Keyword(s):  
Three Dimensional ◽  
Material Design ◽  
Longitudinal Direction ◽  
Materials Design ◽  
Cellular Materials ◽  
Yield Strain ◽  
Lateral Direction ◽  
Large Rotation ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

Cellular materials have two important properties: structures and mechanisms. These properties have important applications in materials design; in particular, they’re used to determine the modulus and yield strain. The objective of this study is to gain a better understanding of these two properties and to explore the synthesis of three-dimensional (3D) compliant cellular materials (CCMs) with compliant porous structures (CPSes) generated from modified hexagonal honeycombs. An orthotropic constitutive CCM model in the Cartesian coordinate system is constructed using the strain energy method, which uses the deformation of hinges around holes and the rotation of links. A finite element (FE) based simulation is conducted to validate the analytical model. The moduli and yield strains of the 3D CCMs with an aluminum alloy are about 1.2GPa and 0.4% in the longitudinal direction and about 0.08MPa and 30% in the lateral direction. The CCMs have extremely high positive and negative Poisson’s ratios νxy*∼±30 due to the large rotation of the link member in the transverse direction caused by an input displacement in the longitudinal direction. This paper demonstrates that compliant me so structures can be used for next generation materials design in tailoring mechanical properties such as moduli, strength, strain, and Poisson’s ratios.

Three-Dimensional Constraint Effects on the Slitting Method for Measuring Residual Stress

2013 ◽  
Vol 135 (3) ◽  
Author(s):  
C. Can Aydıner ◽  
Michael B. Prime
Keyword(s):  
Residual Stress ◽  
Plane Strain ◽  
Plane Stress ◽  
Three Dimensional ◽  
Poisson's Ratio ◽  
Out Of Plane ◽  
Sample Width ◽  
Poisson's Ratios ◽  
Poisson’S Ratios ◽  
Calibration Coefficients

The incremental slitting or crack compliance method determines a residual stress profile from strain measurements taken as a slit is incrementally extended into the material. To date, the inverse calculation of residual stress from strain data conveniently adopts a two-dimensional, plane strain approximation for the calibration coefficients. This study provides the first characterization of the errors caused by the 2D approximation, which is a concern since inverse analyses tend to magnify such errors. Three-dimensional finite element calculations are used to study the effect of the out-of-plane dimension through a large scale parametric study over the sample width, Poisson's ratio, and strain gauge width. Energy and strain response to point loads at every slit depth is calculated giving pointwise measures of the out-of-plane constraint level (the scale between plane strain and plane stress). It is shown that the pointwise level of constraint varies with slit depth, a factor that makes the effective constraint a function of the residual stress to be measured. Using a series expansion inverse solution, the 3D simulated data of a representative set of residual stress profiles are reduced with 2D calibration coefficients to yield the error in stress. The sample width below which it is better to use plane stress compliances than plane strain is shown to be about 0.7 times the sample thickness; however, even using the better approximation, the rms stress errors sometimes still exceed 3% with peak errors exceeding 6% for Poisson's ratio 0.3, and errors increase sharply for larger Poisson's ratios. The error is significant, yet, error magnification from the inverse analysis in this case is mild compared to, e.g., plasticity based errors. Finally, a scalar correction (effective constraint) over the plane-strain coefficients is derived to minimize the root-mean-square (rms) stress error. Using the posed scalar correction, the error can be further cut in half for all widths and Poisson's ratios.

scholarly journals Giant negative Poisson’s ratio in two-dimensional V-shaped materials

2021 ◽  
Author(s):  
Xikui Ma ◽  
Jian Liu ◽  
Yingcai Fan ◽  
Weifeng Li ◽  
Jifan Hu ◽  
...  
Keyword(s):  
Poisson’S Ratio ◽  
Poisson's Ratio ◽  
Negative Poisson’S Ratio ◽  
Two Dimensional ◽  
Auxetic Materials ◽  
Negative Poisson's Ratio ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

Two-dimensional (2D) auxetic materials with exceptional negative Poisson’s ratios (NPR) are drawing increasing interest due to the potentials in medicine, fasteners, tougher composites and many other applications. Improving the auxetic...

Continuum Description of the Time- and Strain-Dependent Poisson’s Ratio of Ligament Under Finite Deformation

2013 ◽  
Author(s):  
Aaron M. Swedberg ◽  
Shawn P. Reese ◽  
Steve A. Maas ◽  
Benjamin J. Ellis ◽  
Jeffrey A. Weiss
Keyword(s):  
Large Scale ◽  
Mechanical Response ◽  
Tensile Deformation ◽  
Large Strain ◽  
Fiber Direction ◽  
Strain Behavior ◽  
Nonlinear Stress ◽  
Poisson's Ratios ◽  
Poisson’S Ratios ◽  
Strain Dependent

Ligament volumetric behavior controls fluid and thus nutrient movement as well as the mechanical response of the tissue to applied loads. The reported Poisson’s ratios for tendon and ligament subjected to tensile deformation loading along the fiber direction are large, ranging from 0.8 ± 0.3 in rat tail tendon fascicles [1] to 2.98 ± 2.59 in bovine flexor tendon [2]. These Poisson’s ratios are indicative of volume loss and thus fluid exudation [3,4]. We have developed micromechanical finite element models that can reproduce both the characteristic nonlinear stress-strain behavior and large, strain-dependent Poisson’s ratios seen in tendons and ligaments [5], but these models are computationally expensive and unfeasible for large scale, whole joint models. The objectives of this research were to develop an anisotropic, continuum based constitutive model for ligaments and tendons that can describe strain-dependent Poisson’s ratios much larger than the isotropic limit of 0.5. Further, we sought to demonstrate the ability of the model to describe experimental data, and to show that the model can be combined with biphasic theory to describe the rate- and time-dependent behavior of ligament and tendon.

Carbon nanotube films change Poisson’s ratios from negative to positive

2010 ◽  
Vol 97 (6) ◽  
pp. 061909 ◽  
Author(s):  
Yin Ji Ma ◽  
Xue Feng Yao ◽  
Quan Shui Zheng ◽  
Ya Jun Yin ◽  
Dong Jie Jiang ◽  
...  
Keyword(s):  
Carbon Nanotube ◽  
Poisson's Ratios ◽  
Poisson’S Ratios ◽  
Nanotube Films

scholarly journals Theoretical and practical differences between creep and relaxation Poisson’s ratios in linear viscoelasticity

2015 ◽  
Vol 19 (4) ◽  
pp. 537-555 ◽  
Author(s):  
Abudushalamu Aili ◽  
Matthieu Vandamme ◽  
Jean-Michel Torrenti ◽  
Benoit Masson
Keyword(s):  
Linear Viscoelasticity ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

Testing and Simulation of Stress-Stiffening Extreme Poisson’s Ratio Twisted Fiber-Reinforced Elastomer Composites

2008 ◽  
Author(s):  
Larry D. Peel ◽  
Madhuri Lingala
Keyword(s):  
Double Helix ◽  
Fiber Bundles ◽  
Fiber Reinforced ◽  
Element Analysis ◽  
Morphing Aircraft ◽  
Active Vibration ◽  
Elastomer Composites ◽  
Poisson's Ratios ◽  
Poisson’S Ratios ◽  
Twisted Fiber

Laminates that exhibit high and negative Poisson’s ratios can be used as solid-state actuators, passive and active vibration dampers, and for morphing aircraft structures. Recently, fiber-reinforced elastomer (FRE) laminates have been fabricated that exhibit extreme (high and negative) Poisson’s ratios [1]. The current research explores twisted fiber bundle elastomeric laminates (both single and double helix) which are being investigated using experimentation, linear and non-linear finite element analysis (FEA). Twisted fiber bundles can be made from carbon fibers, fiberglass, etc, but for simplicity the current work uses twisted cotton string. It is observed that uniaxial fiber-reinforced elastomer laminates, where the fibers are twisted as shown in Figure 1, exhibit stress stiffening. Negative Poisson’s ratios may be produced if the fiber bundles have a double helical path as simulated by a series of laminated tubes. Future auxetic FRE laminates may be developed that do experience extreme shear.

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