As a basic mechanical parameter, Poisson's ratio (ν) measures the mechanical responses of solids against external loads In rare cases, materials have a negative Poisson's ratio (NPR), and present an interesting auxetic effect That is, when a material is stretched in one direction, it will expand in the perpendicular direction To design modern nanoscale electromechanical devices with special functions, two dimensional (2D) auxetic materials are highly desirable In this work, based on first principles calculations, we rediscover the previously proposed δ-phosphorene (δ-P) nanosheets [Jie Guan, et al, Phys Rev Lett, 2014, 113, 046804] which are good auxetic materials with a high NPR The results show that the Young's modulus and Poisson's ratio of δ-P are all anisotropic The NPR value along the grooved direction is up to -0267, which is much higher than the recently reported 2D auxetic materials The auxetic effect of δ-P originating from its puckered structure is robust and insensitive to the number of layers due to weak interlayer interactions Moreover, δ-P possesses good flexibility because of its relatively small Young's modulus and high critical crack strain If δ-P can be synthesized, these extraordinary properties would endow it with great potential in designing low dimensional electromechanical devices

δ-Phosphorene: a two dimensional material with a highly negative Poisson's ratio

Auxetic materials are endowed with a behavior that contradicts common sense, when subjected to an axial tensile load they increase their transverse dimension. In case of a compression load, they reduce their transverse dimension. Consequently, these materials have a negative Poisson’s ratio in such direction. This paper reviews research related to these materials. It presents the theories that explain their deformation behavior and reveals the important role represented by the internal structure. Their mechanical properties are explored and some potential applications for these materials are shown.

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Auxetic materials — A review

To analyze the IMC (Intermetallic Compound) properties and their effects on steel/aluminum welding, the equilibrium lattice constants, mechanical properties and electronic structures of the intermetallic compounds Fe3Al, FeAl, Fe2Al5, FeAl2, FeAl3 and Fe4Al13 were systematically calculated using the first-principle methods. The results show that the calculated elastic constants of the IMCs satisfy the mechanical stability conditions. Fe3Al and FeAl2 exhibit plastic characteristics; FeAl, Fe2Al5, FeAl3, and Fe4Al13 exhibit brittle characteristics; Fe-Al binary compounds have typical metallic properties; and the 3d bands of Fe contribute most significantly to the total density of states. In the vicinity of the Fermi level, the 3d bands of Fe contribute together with the bands of Al; the Fe-Al binary compounds have weak ionicity, relatively high hardness and high melting points; additionally, the effects of Fe-rich phases on the mechanical properties of the joints are superior compared to Al-rich phases. To verify the first principle calculations, T-joint laser welding experiments were conducted on 316L stainless steel and 6061 aluminum alloy sheets. The microstructure, reaction phases, fracture morphologies and mechanical properties of the welded joint were analyzed by optical microscopy, scanning electron microscopy (SEM), energy dispersive spectroscopy (EDS), X-ray diffraction (XRD) and nanoindentation. According to the XRD and EDS analysis, Fe3Al, FeAl, Fe2Al5, FeAl2, FeAl3 and Fe4Al13 were formed; their properties and effects on the joint of these phases are consistent with the calculated results.

First principle calculations and mechanical properties of the intermetallic compounds in a laser welded steel/aluminum joint

A partially-wetting liquid can deform the underlying elastic substrate upon which it rests. This situation requires the development of theoretical models to describe the wetting forces imparted by the drop onto the solid substrate, particularly those at the contact-line. We construct a general solution using a displacement potential function for the elastic deformations within a finite elastic substrate associated with these wetting forces, and compare the results for several different contact-line models. Our work incorporates internal contributions to the surface stress from both liquid/solid Σls and Σsg solid/gas solid surface tensions (surface stress), which results in a non-standard boundary-value problem that we solve using a dual integral equation. We compare our results to relevant experiments and conclude that the generalization of solid surface tension Σls ≠ Σsg is an essential feature in any model of partial-wetting. The comparisons also allow us to systematically eliminate some proposed contact-line models.

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Elastocapillary deformations on partially-wetting substrates: rival contact-line models.

Auxetic foams counter-intuitively expand (shrink) under stretching (compression). These foams can exhibit superior mechanical properties such as resistance to shear and indentation, improved toughness and energy absorption (EA) under several types of loadings. Their unique deformation mechanism and manufacturing process lead to special multiphysics properties such as variable permeability, synclastic curvature and shape memory. Except for traditional energy absorber stuff, the potential applications of auxetic foams have involved biomedicine, aerospace, smart sensing, etc. However, most of the potential applications are restrained in the theoretical stage due to complicated fabrication and a deficiency of stability. For removing the barrier for practical application, a series of issues remain to be resolved, though the explorations of the manufacture methodologies and potential applications are fruitful in the past decades. We present here a review article discussing the state-of-the-art for manufacturing, characterization and applications of auxetic foams. We also provide a view of the existing challenges and possible future research directions, aiming to state the perspective and inspire researchers to further develop the field of auxetic foams. 

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Manufacturing, characteristics and applications of auxetic foams: A state-of-the-art review

The lower bound customarily cited for Poisson's ratio ?, ?1, is derived from the relationship between ? and the bulk and shear moduli in the classical theory of linear elasticity. However, experimental verification of the theory has been limited to materials having ????0.2. From consideration of the longitudinal and biaxial moduli, we recently determined that the lower bound on ? for isotropic materials from this theory is actually . Herein we generalize this result, first by analyzing expressions for ? in terms of six common elastic constants, and then by considering arbitrary strains. The results corroborate that for classical linear elasticity to be applicable. Of course, a few materials exist for which ??<?0.2, thus deviating from this bound; accurate analysis of their mechanical behavior requires more sophisticated elasticity models.

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Limits to Poisson's ratio in isotropic materials—general result for arbitrary deformation

The lower bound usually cited for Poisson's ratio {\nu} is -1, derived from the relationship between {\nu} and the bulk and shear moduli. From consideration of the longitudinal and biaxial moduli, we recently determined that the lower bound on {\nu} for isotropic materials is actually 1/5, a value also consistent with experimental measurements on real materials. Herein we generalize this result, first by analyzing expressions for {\nu} in terms of six common elastic constants, and then by considering arbitrary strains. The results corroborate the prior finding that 1/5 <= {\nu} for linear elasticity to be applicable.

P. H. Mott

Papers

Limits to Poisson's ratio in isotropic materials—general result for arbitrary deformation

Limits to Poisson's ratio in isotropic materials - general result for arbitrary deformation