A Novel Quasi-Planar Two-dimensional Carbon Sulfide with Negative Poisson's Ratio and Dirac Fermions.

In the present study, a novel and unconventional two-dimensional (2D) material with Dirac electronic features has been designed using sulflower with the help of density functional theory methods and first principles calculations. This 2D material comprises of hetero atoms (C, S) and belongs to the tetragonal lattice with P4 /nmm space group. Scrutiny of the results show that the 2D nanosheet exhibits a nanoporous wave-like geometrical structure. Quantum molecular dynamics simulations and phonon mode analysis emphasize the dynamical and thermal stability. The novel 2D nanosheet is an auxetic material with an anisotropy in the in-plane mechanical properties. Both composition and geometrical features are completely different from the conditions necessary for the formation of Dirac cones in graphene. However, the presence of semi-metallic nature, linear band dispersion relation, massive fermions and massless Dirac fermions are observed in the novel 2D nanosheet. The massless Dirac fermions exhibit highly isotropic Fermi velocities (vf =0.68×106  m/s) along all crystallographic directions. The zero-band gap semi metallic features of the novel 2D nanosheet are perturbative to the electric field and external strain.

The rise of mechanical metamaterials: Auxetic constructs for skin wound healing.

Auxetic materials are known for their unique ability to expand/contract in multiple directions when stretched/compressed. In other words, they exhibit a negative Poisson's ratio, which is usually positive for most of materials. This behavior appears in some biological tissues such as human skin, where it promotes wound healing by providing an enhanced mechanical support and facilitating cell migration. Skin tissue engineering has been a growing research topic in recent years, largely thanks to the rapid development of 3D printing techniques and technologies. The combination of computational studies with rapid manufacturing and tailored designs presents a huge potential for the future of personalized medicine. Overall, this review article provides a comprehensive overview of the current state of research on auxetic constructs for skin healing applications, highlighting the potential of auxetics as a promising treatment option for skin wounds. The article also identifies gaps in the current knowledge and suggests areas for future research. In particular, we discuss the designs, materials, manufacturing techniques, and also the computational and experimental studies on this topic.

Lower hardness than strength: The auxetic composite microstructure of limpet tooth.

The limpet tooth is widely recognized as nature's strongest material, with reported strength values up to 6.5 GPa. Recently, microscale auxeticity has been discovered in the leading part of the tooth, providing a possible explanation for this extreme strength. Utilizing micromechanical experiments, we find hardness values in nanoindentation that are lower than the respective strength observed in micropillar compression tests. Using micromechanical modeling, we show that this unique behavior is a result of local tensile strains during indentation, originating from the microscale auxeticity. As the limpet tooth lacks ductility, these tensile strains lead to microdamage in the auxetic regions of the microstructure. Consequently, indentation with a sharp indenter always probes a damaged version of the material, explaining the lower hardness and modulus values gained from nanoindentation. Micropillar tests were found to be mostly insensitive to such microdamage due to the lower applied strain and are therefore the suggested method for characterizing auxetic nanocomposites. STATEMENT OF SIGNIFICANCE: This work explores the micromechanical properties of limpet teeth, nature's strongest biomaterial, using micropillar compression testing and nanoindentation. The limpet tooth microstructure consists of ceramic nanorods embedded in a matrix of amorphous SiO2 and arranged in a pattern that leads to local auxetic behavior. We report lower values for nanoindentation hardness than for compressive strength, a unique behavior usually not achievable in conventional materials. Utilizing micromechanical finite element simulations, we identify the reason for this behavior to be microdamage formation resultant of the auxetic behavior, sharp indenter tip and lack of ductility of the limpet tooth microstructure. This formation of microdamage is not expected in micropillar compression tests due to lower locally imposed strain.

The quest for a bidirectional auxetic, elastic, and enhanced fracture toughness material: Revisiting the mechanical properties of the BeH2 monolayers.

Herein we show a density functional theory-based study performed on two recently predicted polymorphs of the BeH2 monolayer, α-BeH2 and ß-BeH2 . The α-BeH2 phase possesses an in-plane negative Poisson's ratio (NPR), introducing it into the unique group of auxetic materials. Our assessment delves into the linear-elastic and finite-strain regimes to understand both polymorphs' structural and mechanical responses to deformation. We find that the in-plane NPR is shown to be only parallel to the bonds in α-BeH2 and remains along the uniaxial tensile path. Concomitantly, an out-of-plane transition toward auxetic is also revealed in regions exhibiting conventional Poisson's ratios, making α-BeH2 a bidirectionally auxetic material. While phase transitions in ß-BeH2 are triggered at very short strains, α-BeH2 displays excellent elasticity against tension, superior to that of most currently known 2D materials.

Engineering Auxetic Cylinders and Intestine to Improve Longitudinal Intestinal Lengthening and Tailoring Procedure.

Auxetic materials can be exploited for coupling different types of tissues. Herein, we designed a material where the microorganism metabolic activity yields the formation of buckled/collapsed bubbles within gelling silicone cylinders thus providing auxetic properties. The finite element model of such hollow auxetic cylinders demonstrated the tubular structure to promote worm-like peristalsis. In this scenario, the described hybrid auxetic structures may be applied to the longitudinal intestinal lengthening and tailoring procedure to promote enteral autonomy in short bowel syndrome. The presented material and analytical design synergistic approach offer a pioneering step for the clinical translation of hybrid auxetic materials.

Toughened Hydrogels for 3D Printing of Soft Auxetic Structures.

Materials with negative Poisson's ratio have attracted considerable attention and offered high potential applications as biomedical devices due to their ability to expand in every direction when stretched. Although negative Poisson's ratio has been obtained in various base materials such as metals and polymers, there are very limited works on hydrogels due to their intrinsic brittleness. Herein, we report the use of methacrylated cellulose nanocrystals (CNCMAs) as a macro-cross-linking agent in poly(2-hydroxyethyl methacrylate) (pHEMA) hydrogels for 3D printing of auxetic structures. Our developed CNCMA-pHEMA hydrogels exhibit significant improvements in mechanical properties, which is attributed to the coexistence of multiple chemical and physical interactions between the pHEMA and CNCMAs. Structures printed by using CNCMA-pHEMA hydrogels show auxetic behavior with greatly enhanced toughness and stretchability compared to the hydrogel with a traditional cross-linking agent. Such strong and tough auxetic hydrogels would contribute toward establishing advanced flexible implantable devices such as biodegradable oesophageal self-expandable stents.

An Experimental Study of Auxetic Tubular Structures.

Auxetic tubular structures are widely known structures, characterized by a negative Poisson's ratio upon stretching and deformation in the axial and transverse directions, which have numerous application possibilities. In this paper, tubular structures were realized by rolling up planar auxetic structures and using rigid square frames as unit cells. Planar and tubular structures were built from square frames that were 3D printed with plastic or laser-cut from metal. The changes in linear dimensions of the studied structures were based on a hinge mechanism, the functioning of which was experimentally verified on different solutions leading to square unit cells. To connect the square frames of the structure, an innovative solution was used in the form of rotation axes on their surface at a preset distance from the edge of the square frame. The geometric parameter thus introduced was used to determine the relative change in the size of the structure when stretched (i.e., when moving from the closed to the open position).

Additively Manufactured Hierarchical Auxetic Mechanical Metamaterials.

Due to the ability to create structures with complex geometry at micro- and nanoscales, modern additive technologies make it possible to produce artificial materials (metamaterials) with properties different from those of conventional materials found in nature. One of the classes with special properties is auxetic materials-materials with a negative Poisson's ratio. In the review, we collect research results on the properties of auxetics, based on analytical, experimental and numerical methods. Special attention of this review is paid to the consideration of the results obtained in studies of hierarchical auxetic materials. The wide interest in the hierarchical subclass of auxetics is explained by the additional advantages of structures, such as more flexible adjustment of the desired mechanical characteristics (the porosity, stiffness, specific energy absorption, degree of material release, etc.). Possibilities of biomedical applications of hierarchical auxetic materials, such as coronary stents, filtration and drug delivery systems, implants and many others, where the ability for high-precision tuning is required, are underlined.

Highly Negative Poisson's Ratio in Thermally Conductive Covalent Organic Frameworks.

The prospect of combining two-dimensional materials in vertical stacks has created a new paradigm for materials scientists and engineers. Herein, we show that stacks of two-dimensional covalent organic frameworks are endowed with a host of unique physical properties that combine low densities, high thermal conductivities, and highly negative Poisson's ratios. Our systematic atomistic simulations demonstrate that the tunable mechanical and thermal properties arise from their singular layered architecture comprising strongly bonded light atoms and periodic laminar pores. For example, the negative Poisson's ratio arises from the weak van der Waals interactions between the two-dimensional layers along with the strong covalent bonds that act as hinges along the layers, which facilitate the twisting and swiveling motion of the phenyl rings relative to the tensile plane. The mechanical and thermal properties of two-dimensional covalent organic frameworks can be tailored through structural modularities such as control over the pore size and/or interlayer separation. We reveal that these materials mark a regime of materials design that combines low densities with high thermal conductivities arising from their nanoporous yet covalently interconnected structure.

Half-Auxeticity and Anisotropic Transport in Pd Decorated Two-Dimensional Boron Sheets.

Upon strain, most materials shrink normal to the direction of applied strain. Similarly, if a material is compressed, it will expand in the direction orthogonal to the pressure. Few materials, those of negative Poisson ratio, show the opposite behavior. Here, we show an unprecedented feature, a material that expands normal to the direction of stress, regardless if it is strained or compressed. Such behavior, namely, half-auxeticity, is demonstrated for a borophene sheet stabilized by decorating Pd atoms. We explore Pd-decorated borophene, identify three stable phases of which one has this peculiar property of half auxeticity. After carefully analyzing stability and mechanical and electronic properties we explore the origin of this very uncommon behavior and identify it as a structural feature that may also be employed to design further 2D nanomaterials.

Novel Method for Preparing a High-Performance Auxetic Foam Directly from Polymer Resin by a One-Pot CO2 Foaming Process.

So far, negative Poisson's ratio foam (auxetic foam) is usually prepared by the transformation of conventional polymer foam, and it is a challenge to prepare auxetic foam directly from polymer resin. In this work, a novel method based on the synergism between the phase transition of water and the permeability rate difference of the CO2 blowing agent from air in the foaming process is put forward to prepare auxetic foam directly from the polymer resin. Using this method, herein, nylon elastomer (NE) foam with auxetic behavior is successfully prepared from NE resin by a one-pot CO2 foaming method inside an autoclave aided by water; the obtained auxetic foam has a Poisson's ratio value of -1.29 and has excellent tensile cycle stability and energy absorption performance. This method breaks through the bottleneck for preparing auxetic foams from the polymer resin directly, which is also green and environment-friendly. It is believed that the abovementioned method also applies to other thermoplastic polymers, which paves a way for designing and preparing multifunctional auxetic foam materials in the future via a one-pot CO2 foaming process. Furthermore, this work first demonstrates that the transformation between auxetic foam and positive Poisson's ratio foam is reversible due to the closed cell structure, which provides an opportunity to reversibly adjust the performance and the shape of polymer foam materials.

Geometric Non-Linear Analysis of Auxetic Hybrid Laminated Beams Containing CNT Reinforced Composite Materials.

In the current work, a novel hybrid laminate with negative Poisson's ratio (NPR) is developed by considering auxetic laminate which is composed of carbon nanotube-reinforced composite (CNTRC) and fiber-reinforced composite (FRC) materials. The maximum magnitude of out-of-plane NPR is identified in the case of (20 F/20 C/-20 C/20 C) S laminate as well. Meanwhile, a method for the geometric non-linear analysis of hybrid laminated beam with NPR including the non-linear bending, free, and forced vibrations is proposed. The beam deformation is modeled by combining higher-order shear-deformation theory (HSDT) and large deflection theory. Based on a two-step perturbation approach, the asymptotic solutions of the governing equations are obtained to capture the linear and non-linear frequencies and load-deflection curves. Moreover, a two-step perturbation methodology in conjunction with fourth-order Runge-Kutta method is employed to solve the forced-vibration problem. Several key factors, such as CNT distribution, variations in the elastic foundation, and thermal stress, are considered in the exhaustive analysis. Theoretical results for some particular cases are given to examine the geometric non-linearity behavior of hybrid beam with NPR as well as positive Poisson's ratio (PPR).

3D Printable Strain Sensors from Deep Eutectic Solvents and Cellulose Nanocrystals.

Stretchable and conductive hydrogels have been intensively studied as wearable electronics to monitor the physiological activities of human bodies. However, it remains a challenge to fabricate robust hydrogels as sensors with complex 3D structures. Here, we designed a 3D printable ink from cellulose nanocrystals (CNCs), deep eutectic solvents (DESs), and ionically cross-linked polyacrylic acid (PAA). DESs composed of choline chloride and ethylene glycol served as a nonvolatile medium with high ionic conductivity. The dispersion of CNCs in a mixture of DESs, acrylic acid, and Al3+ ions formed ionogels with a reversible physical network for 3D printing. After the printing process, the ionogel was solidified by the photopolymerization of acrylic acid in the presence of Al3+ ions to form a second ionically cross-linked network. The first physical network of CNCs provides an energy-dissipating mechanism to make a strong and highly stretchable nanocomposite ionogel. When compared to hydrogels, we found that the DES/CNC nanocomposite ionogel was more stable in the air because of the low volatility of DESs. We further used the DES/CNC ink to 3D print an auxetic sensor with negative Poisson's ratios so that the sensor provided a conformal contact with the skin during large deformation. In addition, the auxetic sensor could continuously monitor and identify different motions of the human body by the change in resistance. These results demonstrate a simple and rapid strategy to fabricate stable and sensitive strain sensors from cheap and renewable feedstock.

Auxetic B4N Monolayer: A Promising 2D Material with in-Plane Negative Poisson's Ratio and Large Anisotropic Mechanics.

Auxetic materials, known with negative Poisson's ratio, are highly desirable for many advanced applications, but the candidates are rather scarce, especially at low dimension. Motivated by the re-entrant structure that often exposes negative Poisson's ratio, we predict a two-dimensional (2D) planar B4N monolayer as a promising auxetic material with unusual in-plane negative Poisson's ratio within the framework of density functional theory calculations. B4N monolayer also exhibits a highly emerged mechanical anisotropy, characterized by Young's modulus and Poisson's ratio. In addition, this monolayer shows superior mechanical flexibility in ideal tensile strength and critical strain values. The phonon dispersion calculations and ab initio molecular dynamics simulations further demonstrate that this monolayer also owns excellent dynamical and thermal stabilities. The fantastic mechanical properties coupled with robust structural stability render the auxetic B4N monolayer promising for future nanomechanical devices.

3D Printing of Auxetic Metamaterials with Digitally Reprogrammable Shape.

Two-dimensional lattice structures with specific geometric features have been reported to have a negative Poisson's ratio, termed as auxetic metamaterials, that is, stretching-induced expansion in the transversal direction. In this paper, we designed a novel auxetic metamaterial; by utilizing the shape memory effect of the constituent materials, the in-plane moduli and Poisson's ratios can be continuously tailored. During deformation, the curved meshes ensure the rotation of the mesh joints to achieve auxetics. The rotations of these mesh joints are governed by the mesh curvature, which continuously changes during deformation. Because of the shape memory effect, the mesh curvature after printing can be programmed, which can be used to tune the rotation of the mesh joints and the mechanical properties of auxetic metamaterial structures, including Poisson's ratios, moduli, and fracture strains. Using the finite element method, the deformation of these auxetic meshes was analyzed. Finally, we designed and fabricated gradient/digital patterns and cylindrical shells and used the auxetics and shape memory effects to reshape the printed structures.

Auxetic Cardiac Patches with Tunable Mechanical and Conductive Properties toward Treating Myocardial Infarction.

An auxetic conductive cardiac patch (AuxCP) for the treatment of myocardial infarction (MI) is introduced. The auxetic design gives the patch a negative Poisson's ratio, providing it with the ability to conform to the demanding mechanics of the heart. The conductivity allows the patch to interface with electroresponsive tissues such as the heart. Excimer laser microablation is used to micropattern a re-entrant honeycomb (bow-tie) design into a chitosan-polyaniline composite. It is shown that the bow-tie design can produce patches with a wide range in mechanical strength and anisotropy, which can be tuned to match native heart tissue. Further, the auxetic patches are conductive and cytocompatible with murine neonatal cardiomyocytes in vitro. Ex vivo studies demonstrate that the auxetic patches have no detrimental effect on the electrophysiology of both healthy and MI rat hearts and conform better to native heart movements than unpatterned patches of the same material. Finally, the AuxCP applied in a rat MI model results in no detrimental effect on cardiac function and negligible fibrotic response after two weeks in vivo. This approach represents a versatile and robust platform for cardiac biomaterial design and could therefore lead to a promising treatment for MI.

Modulation of Abnormal Poisson's Ratios and Electronic Properties in Mixed-Valence Perovskite Manganite Films.

Epitaxy and misfit strain imposed by underlying substrates have been intensively used to tailor the microstructure and electronic properties of oxide films, but this approach is largely restricted by commercially limited substrates. In contrast to the conventional epitaxial misfit strains with a positive Poisson's constant, we show here a tunable Poisson's ratio with anomalous values from negative, zero, to positive. This permits effective control over the out-of-plane lattice parameters that strongly correlate the magnetic and transport properties in perovskite mixed-valence La1- xSr xMnO3 thin films. Our results provide an unconventional approach to better modulation and understanding of elastic-mediated microstructures and physical properties of oxide films by engineering the Poisson's ratios.

The Isotropic and Cubic Material Designs. Recovery of the Underlying Microstructures Appearing in the Least Compliant Continuum Bodies.

The paper discusses the problem of manufacturability of the minimum compliance designs of the structural elements made of two kinds of inhomogeneous materials: the isotropic and cubic. In both the cases the unit cost of the design is assumed as equal to the trace of the Hooke tensor. The Isotropic Material Design (IMD) delivers the optimal distribution of the bulk and shear moduli within the design domain. The Cubic Material Design (CMD) leads to the optimal material orientation and optimal distribution of the invariant moduli in the body made of the material of cubic symmetry. The present paper proves that the varying underlying microstructures (i.e., the representative volume elements (RVE) constructed of one or two isotropic materials) corresponding to the optimal designs constructed by IMD and CMD methods can be recovered by matching the values of the optimal moduli with the values of the effective moduli of the RVE computed by the theory of homogenization. The CMD method leads to a larger set of results, i.e., the set of pairs of optimal moduli. Moreover, special attention is focused on proper recovery of the microstructures in the auxetic sub-domains of the optimal designs.

Persistently Auxetic Materials: Engineering the Poisson Ratio of 2D Self-Avoiding Membranes under Conditions of Non-Zero Anisotropic Strain.

Entropic surfaces represented by fluctuating two-dimensional (2D) membranes are predicted to have desirable mechanical properties when unstressed, including a negative Poisson's ratio ("auxetic" behavior). Herein, we present calculations of the strain-dependent Poisson ratio of self-avoiding 2D membranes demonstrating desirable auxetic properties over a range of mechanical strain. Finite-size membranes with unclamped boundary conditions have positive Poisson's ratio due to spontaneous non-zero mean curvature, which can be suppressed with an explicit bending rigidity in agreement with prior findings. Applying longitudinal strain along a singular axis to this system suppresses this mean curvature and the entropic out-of-plane fluctuations, resulting in a molecular-scale mechanism for realizing a negative Poisson's ratio above a critical strain, with values significantly more negative than the previously observed zero-strain limit for infinite sheets. We find that auxetic behavior persists over surprisingly high strains of more than 20% for the smallest surfaces, with desirable finite-size scaling producing surfaces with negative Poisson's ratio over a wide range of strains. These results promise the design of surfaces and composite materials with tunable Poisson's ratio by prestressing platelet inclusions or controlling the surface rigidity of a matrix of 2D materials.

Stress-shielding, growth and remodeling of pulmonary artery reinforced with copolymer scaffold and transposed into aortic position.

Ross operation, i.e., the use of autologous pulmonary artery to replace diseased aortic valve, has been recently at the center of a vivid debate regarding its unjust underuse in the surgical practice. Keystone of the procedure regards the use of an autologous biologically available graft which would preserve the anticoagulative and tissue homeostatic functions normally exerted by the native leaflets and would harmoniously integrate in the vascular system, allowing for progressive somatic growth of aortic structures. With this respect, recently, some of the authors have successfully pioneered a large animal model of transposition of pulmonary artery in systemic pressure load in order to reproduce the clinical scenario in which this procedure might be applied and allow for the development and testing of different devices or techniques to improve the pulmonary autograft (PA) performance, by testing a bioresorbable mesh for PA reinforcement. In the present work, to support and supplement the in vivo animal experimentation, a mathematical model is developed in order to simulate the biomechanical changes in pulmonary artery subjected to systemic pressure load and reinforced with a combination of resorbable and auxetic synthetic materials. The positive biological effects on vessel wall remodeling, the regional somatic growth phenomena and prevention of dilatative degeneration have been analyzed. The theoretical outcomes show that a virtuous biomechanical cooperation between biological and synthetic materials takes place, stress-shielding guiding the physiological arterialization of vessel walls, consequently determining the overall success of the autograft system.