Negative Poisson's ratios for extreme states of matter

Anomalous mechanical materials squeezing three-dimensional volume compressibility into one dimension

Anomalous mechanical materials, with counterintuitive stress-strain responding behaviors, have emerged as novel type of functional materials with highly enhanced performances. Here we demonstrate that the materials with coexisting negative, zero and positive linear compressibilities can squeeze three-dimensional volume compressibility into one dimension, and provide a general and effective way to precisely stabilize the transmission processes under high pressure. We propose a "corrugated-graphite-like" structural model and discover lithium metaborate (LiBO2) to be the first material with such a mechanical behavior. The capability to keep the flux density stability under pressure in LiBO2 is at least two orders higher than that in conventional materials. Our study opens a way to the design and search of ultrastable transmission materials under extreme conditions.

Giant Poisson's Effect for Wrinkle-Free Stretchable Transparent Electrodes

The next generation of flexible electronics will require highly stretchable and transparent electrodes, many of which consist of a relatively stiff metal network (or carbon materials) and an underlying soft substrate. Typically, such a stiff-soft bilayer suffers from wrinkling or folding when subjected to strains, causing high surface roughness and seriously deteriorated optical transparency. In this work, a network with a giant effective Poisson's ratio on a soft substrate is found to be under biaxial tension upon deformation, and thus does not wrinkle or fold, but maintains smooth surfaces and high transparency. Soft tactile sensors employing such network electrodes exhibit high transparency and low fatigue over many stretching cycles. Such a giant Poisson's ratio has the same effect in other systems. This work offers a new understanding of surface instabilities and a general strategy to prevent them not only in flexible electronics, but also in other materials and mechanical structures that require flat surfaces.

Metal-organic framework based on hinged cube tessellation as transformable mechanical metamaterial

Mechanical metamaterials exhibit unusual properties, such as negative Poisson's ratio, which are difficult to achieve in conventional materials. Rational design of mechanical metamaterials at the microscale is becoming popular partly because of the advance in three-dimensional printing technologies. However, incorporating movable building blocks inside solids, thereby enabling us to manipulate mechanical movement at the molecular scale, has been a difficult task. Here, we report a metal-organic framework, self-assembled from a porphyrin linker and a new type of Zn-based secondary building unit, serving as a joint in a hinged cube tessellation. Detailed structural analysis and theoretical calculation show that this material is a mechanical metamaterial exhibiting auxetic behavior. This work demonstrates that the topology of the framework and flexible hinges inside the structure are intimately related to the mechanical properties of the material, providing a guideline for the rational design of mechanically responsive metal-organic frameworks.

A near-zero Poisson's ratio of Si with ordered nanopores

Significant reduction in the Poisson's ratio is predicted for Si with cylindrical nanopores through first-principles DFT calculations.

Tuning the Poisson's Ratio of Biomaterials for Investigating Cellular Response

Cells sense and respond to mechanical forces, regardless of whether the source is from a normal tissue matrix, an adjacent cell or a synthetic substrate. In recent years, cell response to surface rigidity has been extensively studied by modulating the elastic modulus of poly(ethylene glycol) (PEG)-based hydrogels. In the context of biomaterials, Poisson's ratio, another fundamental material property parameter has not been explored, primarily because of challenges involved in tuning the Poisson's ratio in biological scaffolds. Two-photon polymerization is used to fabricate suspended web structures that exhibit positive and negative Poisson's ratio (NPR), based on analytical models. NPR webs demonstrate biaxial expansion/compression behavior, as one or multiple cells apply local forces and move the structures. Unusual cell division on NPR structures is also demonstrated. This methodology can be used to tune the Poisson's ratio of several photocurable biomaterials and could have potential implications in the field of mechanobiology.

Finite auxetic deformations of plane tessellations

We systematically analyse the mechanical deformation behaviour, in particular Poisson's ratio, of floppy bar-and-joint frameworks based on periodic tessellations of the plane. For frameworks with more than one deformation mode, crystallographic symmetry constraints or minimization of an angular vertex energy functional are used to lift this ambiguity. Our analysis allows for systematic searches for auxetic mechanisms in archives of tessellations; applied to the class of one- or two-uniform tessellations by regular or star polygons, we find two auxetic structures of hexagonal symmetry and demonstrate that several other tessellations become auxetic when retaining symmetries during the deformation, in some cases with large negative Poisson ratios ν <−1 for a specific lattice direction. We often find a transition to negative Poisson ratios at finite deformations for several tessellations, even if the undeformed tessellation is infinitesimally non-auxetic. Our numerical scheme is based on a solution of the quadratic equations enforcing constant edge lengths by a Newton method, with periodicity enforced by boundary conditions.

Spatial tuning of negative and positive Poisson's ratio in a multi-layer scaffold

While elastic modulus is tunable in tissue engineering scaffolds, it is substantially more challenging to tune the Poisson's ratio of scaffolds. In certain biological applications, scaffolds with a tunable Poisson's ratio may be more suitable for emulating the behavior of native tissue mechanics. Here, we design and fabricate a scaffold, which exhibits simultaneous negative and positive Poisson's ratio behavior. Custom-made digital micro-mirror device stereolithography was used to fabricate single- and multiple-layer scaffolds using polyethylene glycol-based biomaterial. These scaffolds are composed of pore structures having special geometries, and deformation mechanisms, which can be tuned to exhibit both negative Poisson's ratio (NPR) and positive Poisson's ratio (PPR) behavior in a side-to-side or top-to-bottom configuration. Strain measurement results demonstrate that analytical deformation models and simulations accurately predict the Poisson's ratios of both the NPR and PPR regions. This hybrid Poisson's ratio property can be imparted to any photocurable material, and potentially be applicable in a variety of biomedical applications.

Poisson's ratio and modern materials

In comparing a material's resistance to distort under mechanical load rather than to alter in volume, Poisson's ratio offers the fundamental metric by which to compare the performance of any material when strained elastically. The numerical limits are set by ½ and -1, between which all stable isotropic materials are found. With new experiments, computational methods and routes to materials synthesis, we assess what Poisson's ratio means in the contemporary understanding of the mechanical characteristics of modern materials. Central to these recent advances, we emphasize the significance of relationships outside the elastic limit between Poisson's ratio and densification, connectivity, ductility and the toughness of solids; and their association with the dynamic properties of the liquids from which they were condensed and into which they melt.

Three-Dimensional Polymer Constructs Exhibiting a Tunable Negative Poisson's Ratio

Young's modulus and Poisson's ratio of a porous polymeric construct (scaffold) quantitatively describe how it supports and transmits external stresses to its surroundings. While Young's modulus is always non-negative and highly tunable in magnitude, Poisson's ratio can, indeed, take on negative values despite the fact that it is non-negative for virtually every naturally occurring and artificial material. In some applications, a construct having a tunable negative Poisson's ratio (an auxetic construct) may be more suitable for supporting the external forces imposed upon it by its environment. Here, three-dimensional polyethylene glycol scaffolds with tunable negative Poisson's ratios are fabricated. Digital micromirror device projection printing (DMD-PP) is used to print single-layer constructs composed of cellular structures (pores) with special geometries, arrangements, and deformation mechanisms. The presence of the unit-cellular structures tunes the magnitude and polarity (positive or negative) of Poisson's ratio. Multilayer constructs are fabricated with DMD-PP by stacking the single-layer constructs with alternating layers of vertical connecting posts. The Poisson's ratios of the single- and multilayer constructs are determined from strain experiments, which show (1) that the Poisson's ratios of the constructs are accurately predicted by analytical deformation models and (2) that no slipping occurrs between layers in the multilayer constructs and the addition of new layers does not affect Poisson's ratio.

Finding auxetic frameworks in periodic tessellations

It appears that most models for micro-structured materials with auxetic deformations were found by clever intuition, possibly combined with optimization tools, rather than by systematic searches of existing structure archives. Here we review our recent approach of finding micro-structured materials with auxetic mechanisms within the vast repositories of planar tessellations. This approach has produced two previously unknown auxetic mechanisms, which have Poisson's ratio νss=-1 when realized as a skeletal structure of stiff incompressible struts pivoting freely at common vertices. One of these, baptized Triangle-Square Wheels, has been produced as a linear-elastic cellular structure from Ti-6Al-4V alloy by selective electron beam melting. Its linear-elastic properties were measured by tensile experiments and yield an effective Poisson's ratio νLE≈-0.75, also in agreement with finite element modeling. The similarity between the Poisson's ratios νSS of the skeletal structure and νLE of the linear-elastic cellular structure emphasizes the fundamental role of geometry for deformation behavior, regardless of the mechanical details of the system. The approach of exploiting structure archives as candidate geometries for auxetic materials also applies to spatial networks and tessellations and can aid the quest for inherently three-dimensional auxetic mechanisms.

MATERIALS SCIENCE: Deformations in Extreme Matter

Most materials become narrower in cross section when stretched, but some materials, such as foams, have the counterintuitive property of becoming fatter when stretched (they have a negative Poisson's ratio). In this Perspective, Lakes discusses how his unusual property may arise in isotropic and anisotropic materials. He highlights the study by Baughman et al., who show that anisotropic materials with a negative Poisson's ratio in one direction can be incompressible, i.e., without an overall change in volume upon stretching. This behavior is predicted for materials with very high density, such as neutron star crusts, or very low density, such as ion plasmas, and the validity of the prediction is demonstrated with experimental data for ion plasmas.

Negative Poisson Ratio of Crystalline Cellulose in Kraft Cooked Norway Spruce

The tensile properties of kraft cooked Norway spruce were studied by tensile testing with in situ X-ray diffraction (XRD). Samples were of earlywood, cooked for varying times. The total lignin content of the samples was between 21.7% and 9.3%. Tensile tests with XRD were performed on wet samples, without XRD on dry samples. The tensile strength, the modulus of elasticity (MOE), and the elongation at fracture/yield were determined. X-ray diffraction was used to determine the microfibril angle (MFA) and the deformation of crystalline cellulose by monitoring the reflections 200 and 004. The (X-ray) Poisson ratio of crystalline cellulose was calculated, both before and after the yield point. The tensile strength and the MOE of the wet samples were significantly lower than in the dry samples. The tensile properties of dry samples were similar to dry earlywood samples of untreated Norway spruce. The MFA only showed notable changes due to strain when it was initially large, when a diminishing effect was observed. The Poisson ratio of crystalline cellulose was negative. The average values ranged between -0.26 and -1.17 before the yield point and between -0.86 and -1.05 after the yield point.

Elastic properties of dense solid phases of hard cyclic pentamers and heptamers in two dimensions

Systems of model planar, nonconvex, hard-body "molecules" of fivefold and sevenfold symmetry axes are studied by constant pressure Monte Carlo simulations with variable shape of the periodic box. The molecules, referred to as pentamers (heptamers), are composed of five (seven) identical hard disks "atoms" with centers forming regular pentagons (heptagons) of sides equal to the disk diameter. The elastic compliances of defect-free solid phases are computed by analysis of strain fluctuations and the reference (equilibrium) state is determined within the same run in which the elastic properties are computed. Results obtained by using pseudorandom number generators based on the idea proposed by Holian and co-workers [Holian et al., Phys. Rev. E 50, 1607 (1994)] are in good agreement with the results generated by DRAND48. It is shown that singular behavior of the elastic constants near close packing is in agreement with the free volume approximation; the coefficients of the leading singularities are estimated. The simulations prove that the highest density structures of heptamers (in which the molecules cannot rotate) are auxetic, i.e., show negative Poisson ratios.

Molecular origin of auxetic behavior in tetrahedral framework silicates

Recent analytical models for the Poisson's ratios (nu(ij)) of tetrahedral frameworks are applied to alpha-cristobalite and alpha-quartz for the first time. Rotation and dilation of the SiO4 tetrahedral subunits are considered. Each mechanism leads to negative nu(31) values, whereas negative and positive values are possible when they act concurrently. The concurrent model is in excellent agreement with experiment and explains the dichotomy between negative and positive nu(31) values in alpha-cristobalite and alpha-quartz, respectively. The predicted strain-dependent trends confirm those from molecular modeling.

Mechanism of human accommodation as analyzed by nonlinear finite element analysis

Results of nonlinear finite element analysis support the Schachar theory of accommodation and demonstrate that the long-held Helmholtz theory of accommodation is impossible.