On Values Characterizing the Degree of Elastic Anisotropy of Transversely Isotropic Rocks; Role of Shear Modulus

2019 ◽  
Vol 54 (6) ◽  
pp. 958-967
Author(s):  
A. B. Zhuravlev ◽  
K. B. Ustinov
Geophysics ◽  
1993 ◽  
Vol 58 (8) ◽  
pp. 1091-1098 ◽  
Author(s):  
Andrew N. Norris ◽  
Bikash K. Sinha

Tube‐wave speed in the presence of a weakly anisotropic formation can be expressed in terms of an effective shear modulus for an equivalent isotropic formation. When combined with expressions for the speeds of the SH‐ and quasi‐SV‐waves along the borehole axis, a simple inversion procedure can be obtained to determine three of the five elasticities of a transversely isotropic (TI) formation tilted at some known angle with respect to the borehole axis. Subsequently, a fourth combination of elastic moduli can be estimated from the expression for the qP‐wave speed along the borehole axis. The possibility of determining all five elasticities of a TI formation based on an assumed correlation between two anisotropy parameters is discussed.


Author(s):  
Xiang-Long Peng ◽  
Swantje Bargmann

Abstract A method for designing 3D transversely isotropic auxetic lattice structures is proposed. Based on it, two new auxetic structures have been designed. Systematically, their effective elastic properties are investigated computationally and analytically in all loading directions. The effective Young's moduli and Poisson's ratios within the transverse plane and those along the longitudinal direction are widely tunable by tailoring the structural geometry. Both structures exhibit transverse and longitudinal auxeticities concurrently as well as separately. The proposed auxetic structures expand the existing auxetic material space in terms of elastic anisotropy.


Materials ◽  
2020 ◽  
Vol 13 (17) ◽  
pp. 3743 ◽  
Author(s):  
Qingyang Fan ◽  
Xin Ai ◽  
Junni Zhou ◽  
Xinhai Yu ◽  
Wei Zhang ◽  
...  

In this work, the elastic anisotropy, mechanical stability, and electronic properties for P42/mnm XN (XN = BN, AlN, GaN, and InN) and Pbca XN are researched based on density functional theory. Here, the XN in the P42/mnm and Pbca phases have a mechanic stability and dynamic stability. Compared with the Pnma phase and Pm-3n phase, the P42/mnm and Pbca phases have greater values of bulk modulus and shear modulus. The ratio of the bulk modulus (B), shear modulus (G), and Poisson’s ratio (v) of XN in the P42/mnm and Pbca phases are smaller than those for Pnma XN and Pm-3n XN, and larger than those for c-XN, indicating that Pnma XN and Pm-3n XN are more ductile than P42/mnm XN and Pbca XN, and that c-XN is more brittle than P42/mnm XN and Pbca XN. In addition, in the Pbca phases, XN can be considered a semiconductor material, while in the P42/mnm phase, GaN and InN have direct band-gap, and BN and AlN are indirect wide band gap materials. The novel III-V nitride polymorphs in the P42/mnm and Pbca phases may have great potential for application in visible light detectors, ultraviolet detectors, infrared detectors, and light-emitting diodes.


2019 ◽  
Vol 218 (2) ◽  
pp. 932-932
Author(s):  
Tongcheng Han ◽  
Denghui Xu ◽  
Li-Yun Fu ◽  
Fulai Li

Materials ◽  
2019 ◽  
Vol 12 (21) ◽  
pp. 3589 ◽  
Author(s):  
Qingyang Fan ◽  
Zhongxing Duan ◽  
Yanxing Song ◽  
Wei Zhang ◽  
Qidong Zhang ◽  
...  

The three-dimensional (3D) diamond-like semiconductor materials Si-diamondyne and Ge-diamondyne (also called SiC4 and GeC4) are studied utilizing density functional theory in this work, where the structural, elastic, electronic and mechanical anisotropy properties along with the minimum thermal conductivity are considered. SiC4 and GeC4 are semiconductor materials with direct band gaps and wide band gaps of 5.02 and 5.60 eV, respectively. The Debye temperatures of diamondyne, Si- and Ge-diamondyne are 422, 385 and 242 K, respectively, utilizing the empirical formula of the elastic modulus. Among these, Si-diamondyne has the largest mechanical anisotropy in the shear modulus and Young’s modulus, and Diamond has the smallest mechanical anisotropy in the Young’s modulus and shear modulus. The mechanical anisotropy in the Young’s modulus and shear modulus of Si-diamondyne is more than three times that of diamond as determined by the characterization of the ratio of the maximum value to the minimum value. The minimum thermal conductivity values of Si- and Ge-diamondyne are 0.727 and 0.524 W cm−1 K−1, respectively, and thus, Si- and Ge-diamondyne may be used in the thermoelectric industry.


Geophysics ◽  
1979 ◽  
Vol 44 (5) ◽  
pp. 896-917 ◽  
Author(s):  
James G. Berryman

Compressional waves in horizontally layered media exhibit very weak long‐wave anisotropy for short offset seismic data within the physically relevant range of parameters. Shear waves have much stronger anisotropic behavior. Our results generalize the analogous results of Krey and Helbig (1956) in several respects: (1) The inequality [Formula: see text] derived by Postma (1955) for periodic isotropic, two‐layered media is shown to be valid for any homogeneous, transversely isotropic medium; (2) a general perturbation scheme for analyzing the angular dependence of the phase velocity is formulated and readily yields Krey and Helbig’s results in limiting cases; and (3) the effects of relaxing the assumption of constant Poisson’s ratio σ are considered. The phase and group velocities for all three modes of elastic wave propagation are illustrated for typical layered media with (1) one‐quarter limestone and three‐quarters sandstone, (2) half‐limestone and half‐sandstone, and (3) three‐quarters limestone and one‐quarter sandstone. It is concluded that anisotropic effects are greatest in areas where the layering is quite thin (10–50 ft), so that the wavelengths of the seismic signal are greater than the layer thickness and the layers are of alternately high‐ and low‐velocity materials.


Geophysics ◽  
1981 ◽  
Vol 46 (3) ◽  
pp. 336-338 ◽  
Author(s):  
Felix M. Lyakhovitskiy

Berryman and Levin made an assumption about constancy or limited variations of Poisson’s ratio in the thin layers, in their analyses of elastic anisotropy in thin‐layered media. Berryman states (p. 913): “Rare cases can occur with large variations in Poisson’s ratio.” However, on p. 911 Berryman does point out (with reference to Benzing) that range of variations of the parameter γ = VS/VP from 0.45 to 0.65 is typical of rocks. That corresponds to a range of variations of Poisson’s ratio of 0.373 to 0.134 (i.e., almost three times as much).


2009 ◽  
Vol 5 (8) ◽  
pp. 598-601 ◽  
Author(s):  
Joshua T. West ◽  
Oleksandr Syshchenko ◽  
John Beamish ◽  
Moses H. W. Chan
Keyword(s):  

2011 ◽  
Vol 2011 ◽  
pp. 1-10
Author(s):  
Vitaly Yu. Topolov ◽  
Sergei V. Glushanin ◽  
Alexander A. Panich

A novel 0.88Pb(Zn1/3Nb2/3)O3-0.12PbTiO3 crystal/polymer composite with 2-2 connectivity is studied at variable orientations of spontaneous polarisation vector of the crystal component. Orientation and volume-fraction dependences of the hydrostatic piezoelectric coefficients dh*, eh*, and gh* and hydrostatic electromechanical coupling factor kh* are related to the important role of the piezoelectric and elastic anisotropy of single-domain layers of the 2-2 composite. The record value of |eh∗|≈77 C/m2 near the absolute-minimum point and the correlation between the hydrostatic (eh*) and piezoelectric (e3j*) coefficients and between the hydrostatic (gh*) and piezoelectric (g3j*) coefficients are first established. This discovery is of value for hydrostatic and piezotechnical applications. The hydrostatic performance of the composite based on the single-domain 0.88Pb(Zn1/3Nb2/3)O3-0.12PbTiO3 crystal is compared to the performance of the 2–2 composites based on either the same polydomain crystal or the related single-domain crystal.


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