Young's and shear moduli and Poisson's ratio for elastic media of high and middle symmetry

Using bases of fourth rank tensorial bases of complete Voigt's symmetry elaborated by Walpole we obtained expressions for inverse of Young's modulus E, inverse of shear modulus G and Poisson's ratio, which depend on components of the stiffness tensor S, on direction cosines of vectors n of uniaxial load and the vector m of lateral strain with crystalline symmetry axes. Crystalline media of high and medium symmetries are considered. Such representation yields decomposition of the above elastic characteristics to isotropic and anisotropic parts. Expressions for Poisson's coefficient are well suited for studying the property of auxeticity.Comment: 14 pages, no figures, 2nd Workshop on Auxetics and Related Systems Bedlewo (near Poznan), August 19-23, 200

Poisson's ratio in cubic materials

Expressions are given for the maximum and minimum values of Poisson's ratio $\nu$ for materials with cubic symmetry. Values less than -1 occur if and only if the maximum shear modulus is associated with the cube axis and is at least 25 times the value of the minimum shear modulus. Large values of $|\nu|$ occur in directions at which the Young's modulus is approximately equal to one half of its 111 value. Such directions, by their nature, are very close to 111. Application to data for cubic crystals indicates that certain Indium Thallium alloys simultaneously exhibit Poisson's ratio less than -1 and greater than +2.Comment: 20 pages, 6 figure

Laser induced Zero-Group Velocity resonances in Transversely Isotropic cylinder

The transient response of an elastic cylinder to a laser impact is studied. When the laser source is a line perpendicular to the cylinder axis, modes guided along the cylinder are generated. For a millimetric steel cylinder up to ten narrow resonances can be locally detected by laser interferometry below 8 MHz. Most of these resonances correspond to Zero-Group Velocity guided modes while a few others can be ascribed to thickness modes. We observe that the theory describing the propagation of elastic waves in an isotropic cylinder is not sufficient to precisely predict the resonance spectrum. In fact, the texture of such elongated structure manifest as elastic anisotropy. Thus, a transverse isotropic (TI) model is used to calculate the dispersion curves and compare them with the measured one, obtained by moving the source along the cylinder. The five elastic constants of a TI cylinder are adjusted leading to a good agreement between measured and theoretical dispersion curves. Then, all the resonance frequencies are satisfactorily identified.Comment: 23 pages, 7 figures, submitted to the JAS

The variation and visualisation of elastic anisotropy in rock forming minerals

Acknowledgements David Healy thanks John Wheeler (Liverpool) for discussions and Ross Angel (Padua) for discussions and a reprint. This paper is dedicated to the memory of John Frederick Nye (1923–2019), whose seminal text book, first published in 1957 (Physical Properties of Crystals: Their Representation by Tensors and Matrices; reprinted as Nye, 1985), has had a huge influence on the lead author. Financial support This research has been supported by the NERC (grant no. NE/N003063/1).Peer reviewedPublisher PD

Wave-graphene: a full-auxetic carbon semiconductor with high flexibility and optical UV absorption

The abundant bonding possibilities of Carbon stimulate the design of numerous carbon allotropes, promising the foundation for exploring structure-functionality relationships. Herein, utilizing the space bending strategy, we successfully engineered a two-dimensional carbon allotrope with pure sp2 hybridization, named "Wave-graphene" from the unique wave-like ripple structure. The novel Wave-graphene exhibits full-auxetic behavior due to anisotropic mechanical response, possessing both negative and zero Poisson's ratios. The fundamental mechanism can be attributed to the fact that highly buckled out-of-plane structures lead to anisotropic responses of in-plane nonlinear interactions, which further lead to anisotropy of lattice vibrations. In addition, Wave-graphene is found having quasi-direct wide bandgap of 2.01 eV, the excellent optical transparency and the high flexibility. The successful design of Wave-graphene with excellent outstanding multifunctional properties shows that the utilization of space bending strategies can provide more degrees of freedom for designing novel materials, further enriching the carbon material family and supplementing its versatility

From Geometric Transformations to Auxetic Metamaterials

The paper introduces a new alternative towards fabrication of auxetic metamaterials (materials with negative Poisson’s ratio) controlled by geometric transformations. These transformations are derived from the theory of small (infinitesimal) elastic deformation superimposed on finite elastic deformations. By using this theory, a cylindrical region filled with initial deformed foam is transformed through deformation into a cylindrical shell region filled with auxetic metamaterial. As an example, the realization of the seismic cloak device becomes a practical possibility