The anisotropic behavior of Poisson's ratio, Young's modulus, and shear modulus in hexagonal materials

Fused Deposition Modelling of Polymeric Auxetic Structures: A Review

Additive Manufacturing (AM) techniques have recently attracted the attention of scientists for the development of prototypes with complex or particular geometry in a fast and cheap way. Among the different AM processes, the Fused Deposition Modelling process (FDM) offers several advantages in terms of costs, implementation features and design freedom. Recently, it has been adopted to realise auxetic structures, which are characterised by negative Poisson ratio, enhanced mechanical properties, and a higher compression resistance than conventional structures. This review outlines the use of AM processes, in particular FDM, to design and obtain auxetic structures, with the final aim to exploit their applications in different fields. The first part of this work presents a brief classification of auxetic structures and materials. Subsequently, a summary of additive manufacturing processes is presented, focusing on the use of FDM and its limitations. Finally, the studies on the use of additive manufacturing to produce auxetic structures are shown, evidencing the potential of the concurrent combination of a fast prototyping technique such as FDM and the characteristics of polymer- and/or composite-based auxetic structures. Indeed, this new technological field opens the possibility of realising novel structures with integrated smart behaviour, multifunctional properties, compression resistance, and a tailored microstructure and shape.

Effects of geometrical and processing parameters on mechanical properties of auxetic polyurethane foams

This study aimed to investigate the influence of processing parameters on the mechanical properties of auxetic polyurethane foams including Poisson’s ratio and Young’s modulus. 12 different processing scenarios were considered using the method of Plackett–Burman in the design of experiments with three replicates for each one. Eventually, 36 foams were prepared with different densities and initial thicknesses, heating temperatures and times, applied compression ratios, and the rest times between two heating steps. The microstructures of the conventional and auxetic samples were observed by scanning electron microscopy (SEM). All samples were subjected to tensile loading in one direction with two different strain values. The strains of the foams in two other directions were recorded using a digital image correlation method. Also, the required force to create each strain value was recorded. The results showed that depending on the changing parameters, Poisson’s ratio of about 42% and 58% of the samples reduced at the strains of 10% and 20%, respectively. Heating temperature and time, the initial thickness of the foam, and the applied compression ratio were proved to have significant effects on the variations of both Poisson’s ratio and Young’s modulus of the foams. It was concluded that the Poisson’s ratio of foams was reduced at higher heating temperature, time, and applied compression ratio and also a lower foam initial thickness. On the other hand, these changes increased Young’s modulus of the polyurethane foams. The strain energy of the auxetic samples showed higher amounts of energy compared to the other foams.

Carbonate substitution significantly affects the structure and mechanics of carbonated apatites

Bone mineral comprises nanoparticles of carbonate-substituted bioapatite similar to hydroxylapatite. Yet mechanical values of macroscopic-sized geological hydroxylapatite are often used to model bone properties due to a lack of experimental data for bioapatite. Here, we investigated the effects of carbonate substitution and hydration on biomimetic apatite response to load using in situ hydrostatic pressure loading and synchrotron x-ray diffraction. We find that increasing carbonate levels reduced the bulk modulus and elastic strain ratio. Elastic constants, determined using computational optimization techniques, revealed that compliance values and elastic moduli decreased with increasing carbonate content, likely a result of decreased bond strength due to CO₃^2- substitution and Ca²⁺ loss. Hydration environment had no clear effects on the elastic properties likely due to dissolution and reprecipitation processes modifying the crystal structure organization. These results reinforce the need to consider carbonate composition when selecting mechanical properties and provide robust data for carbonate-substituted apatite stiffness.

Novel Bimorphological Anisotropic Bulk Nanocomposite Materials with High Energy Products

Nanostructuring of magnetically hard and soft materials is fascinating for exploring next-generation ultrastrong permanent magnets with less expensive rare-earth elements. However, the resulting hard/soft nanocomposites often exhibit random crystallographic orientations and monomorphological equiaxed grains, leading to inferior magnetic performances compared to corresponding pure rare-earth magnets. This study describes the first fabrication of a novel bimorphological anisotropic bulk nanocomposite using a multistep deformation approach, which consists of oriented hard-phase SmCo rod-shaped grains and soft-phase Fe(Co) equiaxed grains with a high fraction (≈28 wt%) and small size (≈10 nm). The nanocomposite exhibits a record-high energy product (28 MGOe) for this class of bulk materials with less rare-earth elements and outperforms, for the first time, the corresponding pure rare-earth magnet with 58% enhancement in energy product. These findings open up the door to moving from a pure permanent-magnet system to a stronger nanocomposite system at lower costs.

Auxetic Black Phosphorus: A 2D Material with Negative Poisson's Ratio

The Poisson's ratio of a material characterizes its response to uniaxial strain. Materials normally possess a positive Poisson's ratio - they contract laterally when stretched, and expand laterally when compressed. A negative Poisson's ratio is theoretically permissible but has not, with few exceptions of man-made bulk structures, been experimentally observed in any natural materials. Here, we show that the negative Poisson's ratio exists in the low-dimensional natural material black phosphorus and that our experimental observations are consistent with first-principles simulations. Through applying uniaxial strain along armchair direction, we have succeeded in demonstrating a cross-plane interlayer negative Poisson's ratio on black phosphorus for the first time. Meanwhile, our results support the existence of a cross-plane intralayer negative Poisson's ratio in the constituent phosphorene layers under uniaxial deformation along the zigzag axis, which is in line with a previous theoretical prediction. The phenomenon originates from the puckered structure of its in-plane lattice, together with coupled hinge-like bonding configurations.

Three decades of auxetic polymers: a review

Developments in design and technology in the engineering and medical fields necessitate the use of smart and high-performance materials to meet higher engineering specifications. The general requirements of such materials include a combination of high stiffness and strength with significant weight savings, resistance to corrosion, chemical resistance, low maintenance, and reduced costs. Over the last three decades, it has been demonstrated that auxetic materials offer a huge potential for the fields of engineering, natural sciences, and biomedical engineering, and for many other industries, including the aerospace and defense industries, through their unique deformation mechanism and measured enhancements in mechanical properties. To meet future engineering challenges, auxetic materials are increasingly being recognized as integral components of smart and advanced materials. Although materials with a negative Poisson’s ratio have been known since the early 1900s, they did not capture researchers’ attention until the late 1980s. Since 1991, these materials have been known as auxetic materials. Since then, their benefits and applications have been expanded to all major classes of materials such as metals, ceramics, polymers, and composites, and they are also now being used in engineering applications. The goal of this review was to present the development of auxetic polymers, which were first fabricated in the form of polyurethane foam approximately three decades ago and are now used in the fabrication of non-woven nano/micropolymeric structures. This review could provide useful information for the future development of auxetic polymers.

Auxetic two-dimensional lattices with Poisson's ratio arbitrarily close to −1

In this paper, we propose a class of lattice structures with macroscopic Poisson's ratio arbitrarily close to the stability limit −1. We tested experimentally the effective Poisson's ratio of the microstructured medium; the uniaxial test was performed on a thermoplastic lattice produced with a three-dimensional printing technology. A theoretical analysis of the effective properties was performed, and the expression of the macroscopic constitutive properties is given in full analytical form as a function of the constitutive properties of the elements of the lattice and on the geometry of the microstructure. The analysis was performed on three microgeometries leading to an isotropic behaviour for the cases of three- and sixfold symmetries and to a cubic behaviour for the case of fourfold symmetry.

Characterization of auxetic polyurethanes foam for biomedical implants

Aging, accidents and diseases are the leading causes of disability in today’s world. Therefore, implants and prostheses for hard and soft tissues are becoming increasingly common to restore daily activity and improve the quality of life of patients. Although implants have been extensively developed and are in the clinical use, deformation mechanism, inflexibility and mismatch of the elastic and mechanical behavior of the implants with native tissues are challenges for tissue engineering. The objective of this study was to characterize auxetic polyurethane foam as an auxetic soft tissue implant based on mathematical modeling using a nonlinear elasticity theory. The compressibility effects on auxetic soft tissue implants due to equibiaxial loading were studied. Numerical results were computed using experimentally obtained data and compared with the non-auxetic behavior of a soft tissue.

Metamaterials beyond electromagnetism

Metamaterials are rationally designed man-made structures composed of functional building blocks that are densely packed into an effective (crystalline) material. While metamaterials are mostly associated with negative refractive indices and invisibility cloaking in electromagnetism or optics, the deceptively simple metamaterial concept also applies to rather different areas such as thermodynamics, classical mechanics (including elastostatics, acoustics, fluid dynamics and elastodynamics), and, in principle, also to quantum mechanics. We review the basic concepts, analogies and differences to electromagnetism, and give an overview on the current state of the art regarding theory and experiment-all from the viewpoint of an experimentalist. This review includes homogeneous metamaterials as well as intentionally inhomogeneous metamaterial architectures designed by coordinate-transformation-based approaches analogous to transformation optics. Examples are laminates, transient thermal cloaks, thermal concentrators and inverters, 'space-coiling' metamaterials, anisotropic acoustic metamaterials, acoustic free-space and carpet cloaks, cloaks for gravitational surface waves, auxetic mechanical metamaterials, pentamode metamaterials ('meta-liquids'), mechanical metamaterials with negative dynamic mass density, negative dynamic bulk modulus, or negative phase velocity, seismic metamaterials, cloaks for flexural waves in thin plates and three-dimensional elastostatic cloaks.

Dislocation mobility in a quantum crystal: the case of solid 4He

We investigate the structure and mobility of dislocations in hcp 4He crystals. In addition to fully characterizing the five elastic constants of this system, we obtain direct insight into dislocation core structures on the basal plane, which demonstrates a tendency toward dissociation into partial dislocations. Moreover, our results suggest that intrinsic lattice resistance is an essential factor in the mobility of these dislocations. This insight sheds new light on the possible correlation between dislocation mobility and the observed macroscopic behavior of crystalline 4He.

Poisson's ratios of auxetic and other technological materials

Poisson's ratio, the relation between lateral contraction of a thin, linearly elastic rod when subjected to a longitudinal extension, has a long and interesting history. For isotropic bodies, it can theoretically range from +1/2 to -1; the experimental gamut for anisotropics is even larger. The ratio is positive for all combinations of directions in most crystals. But as far back as the 1800s, Voigt and others found that negative values were encountered for some materials, a property now called auxeticity. Here we examine this property from the point of view of crystal stability and compute extrema of the ratio for various interesting and technologically important materials. Potential applications of the auxetic property are mentioned.

Foam Structures with a Negative Poisson's Ratio

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.