Anisotropy Of Shear Modulus Research Articles

Maximum shear modulus anisotropy of rooted soils

The maximum shear modulus (G0(ij)) of rooted soils is crucial for assessing the deformation and liquefaction potential of vegetated infrastructures under seismic loading conditions. However, no data or theory is available to account for the anisotropy of G0(ij) of rooted soils. This study presents a new model that can predict G0(ij) anisotropy of rooted soils by incorporating the projection of the stress tensor on two independent tensors that describe soil fabric and root network. Bender element tests were conducted on bare and vegetated specimens under isotropic and anisotropic loading conditions. The presence of roots in the soil increased G0(VH) at all confining pressures (p′), as well as G0(HH) and G0(HV) at low p′. However, the trend was reversed at higher p′ because the roots reduced the effects of confinement on G0(ij) by replacing stronger soil–soil interfaces with weaker soil–root interfaces. Roots made the soil fabric and G0(ij) more anisotropic. The proposed model can effectively predict the observed anisotropy of G0(ij) under isotropic and anisotropic loading conditions. The new model also offers a new method for determining the fabric anisotropy of sand based on the anisotropy of shear modulus.

Design and investigated a novel BN polymorph in orthorhombic phase

In this work, a new BN polymorph with Pnma symmetry is proposed by RG2 and investigated by density functional theory. Pnma-II BN polymorph is shown to be dynamically and mechanically stable, and the relative enthalpy of Pnma-II BN is 0.187 eV per atom higher than that of c-BN, respectively. Mechanical properties calculations indicate that Pnma-II BN is also a potential superhard material with hardness of 49.7 GPa. The electronic band structures of Pnma-II BN show that the Pnma-II BN is a direct and ultrawide band gap semiconductor (band gap is 5.82 eV). The mechanical anisotropy of Young's modulus of Pnma-II BN and Pnma BN is greater than that of c-BN, while the mechanical anisotropy of shear modulus of Pnma-II BN in the (100), (001) plane is lower than that of c-BN. In addition, simulated X-ray diffraction patterns are provided for experimental confirmation of the predicted structures.

Structural, elastic, and electronic properties of BC12 carbon under pressure

The crystal structure, mechanical, elastic anisotropy in shear modulus, Young’s modulus and Poisson’s ratio, electronic band structures and X-ray diffraction (XRD) pattern of BC12 carbon are investigated by density functional theory. The elastic anisotropy calculations show that BC12 carbon has smaller anisotropy in Young's modulus, and shear modulus than that of Poisson's ratio. The elastic anisotropy in the shear modulus, Young's modulus, and Poisson's ratio is almost unchanged. The band structure calculations reveal that BC12 carbon is a direct band gap semiconductor material at ambient pressure, and it maintains the direct band gap semiconductor property up to 100 GPa. In addition, it is found that the diffraction angles of the same diffraction peak slightly increase with increasing pressure through the X-ray diffraction (XRD) pattern.

Two novel carbon allotropes with tetragonal symmetry: First-principles calculations

Two novel three-dimensional tetragonal symmetry carbon allotropes with space group P4/mmm are proposed based on density-functional theory in this work. The two carbon allotropes (denoted as tP24-II carbon and tP32 carbon) possess dynamic stability and mechanical stability, and tP24-II carbon and tP32 carbon are theoretically more favorable in energy compared to most other carbon allotropes. The Young's modulus E, shear modulus G and bulk modulus B of tP24-II carbon are greater than that of other P4/mmm phases (tP8, tP12, tP16, tP24 carbon, tP32 carbon), the E and G of tP32 carbon is the smallest among the P4/mmm phases in this work, while the B of tP32 carbon is greater than that of tP12 and tP24 carbon. For elastic anisotropy, the tP32 carbon has great elastic anisotropy in shear modulus and Young's modulus. Both tP24-II carbon and tP32 carbon are indirect band gap semiconductor materials, while the tP32 carbon is a wide band gap semiconductor material. Both tP24-II carbon and tP32 carbon may be potential materials for electronic devices.

A novel BN polymorph with ductile manner

A novel BN polymorph Pnc2 BN with sp2 hybridization is proposed and investigated in this work, which are mechanical stability and dynamical stability. The bulk modulus and shear modulus of Pnc2 BN are slightly greater than that of dz4 BN. The elastic anisotropy in shear modulus of Pnc2 BN is smaller than that of dz2 BN, dz4 BN, and lzlz2 BN, and the elastic anisotropy in Young's modulus of Pnc2 BN is smaller than that of dz4 BN and lzlz2 BN. The sound velocity of Pnc2 BN dz4 BN, and dz2 BN along [001], [010] and [100] propagation direction exhibit anisotropy. Compared with dz4 BN and dz2 BN, Pnc2 BN has the largest elastic anisotropy in sound velocity along [010] propagation direction. Among these four sp2 hybridization BN polymorphs, dz2 BN, dz4 BN, Pnc2 BN, and lzlz2 BN, only Pnc2 BN shows ductility. The Pnc2 BN is a semiconductor material with an indirect band gap of 3.543 ​eV calculated by using the Heyd–Scuseria–Ernzerhof (HSE06) functional. Finally, the x-ray diffraction (XRD) and Debye temperature of Pnc2 BN are also investigated. In future experimental studies, XRD characteristics may be very helpful in determining the crystal structure of Pnc2 BN.

A Novel BN Polymorph in P4/mbm Phase with a (4,4) Nanotube

Herein, based on density functional theory, a new boron nitride structure derived from diamond is designed, and its stability is also proved. The new boron nitride structure is denoted as P4/mbm BN. The elastic moduli (bulk modulus, shear modulus, and Young's modulus) of P4/mbm BN are slightly greater than those of C72 and T carbon, and the shear modulus and Young's modulus are larger than those of P‐4m2 B7N7, B11N11, and B15N15. The shear modulus and Young's modulus of P4/mbm BN exhibit a smaller mechanical anisotropy than that of P‐4m2 B7N7, B11N11, and B15N15, where P‐4m2 B15N15 exhibits the greatest mechanical anisotropy of shear modulus and Young's modulus. The anisotropy of shear modulus in the (100), (010) plane of P‐4m2 B15N15 is 26.5 times that of P4/mbm BN, and the mechanical anisotropy of Young's modulus in (110) plane of P‐4m2 B15N15 is 35.6 times that of P4/mbm BN. P4/mbm BN is a wide and indirect bandgap semiconductor material with bandgap of 4.8 eV. Compared with silicon carbide and gallium nitride, P4/mbm BN has a wider bandgap, it might be more suitable for making high temperature, high frequency, radiation resistance, and high‐power devices.

A porous nanotube network structure of metallic carbon

A porous nanotube network structure of carbon allotrope was designed, denoted as P4/mmm C96. Besides its structure similar to carbon nanotubes, the most interesting thing about P4/mmm C96 is that its band structure is metallic. The shear modulus G, Young’s modulus E, and bulk modulus B of P4/mmm C96 is 49.4 GPa, 128.6 GPa, and 107.8 GPa, respectively. Although the elastic modulus of P4/mmm C96 is low, it is still larger than other carbon allotropes, such as TY-II carbon, TY carbon, fcc-C10, Y carbon, Y-II carbon. The elastic anisotropy in shear modulus G, Poisson’s ratio v, and Young’s modulus E of P4/mmm C96 are larger than that of other C96 carbon allotropes, Finally, the elastic anisotropy of shear modulus of P4/mmm C96 in (100) plane is the greatest, the elastic anisotropy of E of P4/mmm C96 in (001) plane is the largest, while the elastic anisotropy in v in (001) plane is the greatest.

Impact of axisymmetric deformation on MR elastography of a nonlinear tissue-mimicking material and implications in peri-tumour stiffness quantification.

Solid tumour growth is often associated with the accumulation of mechanical stresses acting on the surrounding host tissue. Due to tissue nonlinearity, the shear modulus of the peri-tumoural region inherits a signature from the tumour expansion which depends on multiple factors, including the soft tissue constitutive behaviour and its stress/strain state. Shear waves used in MR-elastography (MRE) sense the apparent change in shear modulus along their propagation direction, thereby probing the anisotropic stiffness field around the tumour. We developed an analytical framework for a heterogeneous shear modulus distribution using a thick-shelled sphere approximation of the tumour and soft tissue ensemble. A hyperelastic material (plastisol) was identified to validate the proposed theory in a phantom setting. A balloon-catheter connected to a pressure sensor was used to replicate the stress generated from tumour pressure and growth while MRE data were acquired. The shear modulus anisotropy retrieved from the reconstructed elastography data confirmed the analytically predicted patterns at various levels of inflation. An alternative measure, combining the generated deformation and the local wave direction and independent of the reconstruction strategy, was also proposed to correlate the analytical findings with the stretch probed by the waves. Overall, this work demonstrates that MRE in combination with non-linear mechanics, is able to identify the apparent shear modulus variation arising from the strain generated by a growth within tissue, such as an idealised model of tumour. Investigation in real tissue represents the next step to further investigate the implications of endogenous forces in tissue characterisation through MRE.

Novel BCN2 and CN compounds in C2/m phase: First-principle calculations

A novel superhard CN (the stoichiometric ratio of carbon to nitrogen is 1:1) and BCN2 compound in C2/m phase are proposed and predicted according to density functional theory in this work. The physical properties, such as crystal structure, electronic properties, elastic properties, mechanical anisotropy properties and the stable of CN and BCN2 are investigated. The shear modulus G, Young's modulus E, and bulk modulus B of BCN2 and CN are 253 and 310 GPa; 448 and 719 GPa; and 186 and 323 GPa with GGA functional, respectively. Utilizing the Lyakhov-Oganov's model, CN and BCN2 are superhard materials, the hardness of CN and BCN2 is 60.99 GPa and 53.38 GPa, respectively. Compared with diamond and c-BN, although the hardness of CN and BCN2 is not as great as that of diamond, while they are both greater than that of c-BN. Using the Chen's model, CN also is a super-hard material with hardness is 58.63 GPa, while the hardness of BCN2 is only 26.67 GPa. C2/m CN is an indirect and wide band gap semiconductor material, while BCN2 is a metallic material. In addition, mechanical anisotropy of shear modulus G, Young's modulus E, and bulk modulus B of CN and BCN2 are also studied in detail.

First-principles calculations to investigate the anisotropic elasticity and thermodynamic properties of FeAl3 under pressure effect

We have employed the first-principles calculations and quasi-harmonic Debye model to investigate the effect of the pressure on anisotropic elasticity and thermodynamic properties of FeAl3. According to Christoffel’s equation, the wave velocity anisotropy of FeAl3 as a function of pressure was also studied. Based on 3D surfaces and 2D projection contours, the anisotropy of shear modulus for FeAl3 changes significantly with the increasing pressure, and increases more obviously on [001] direction than that on [100] direction under high pressure. The thermodynamic properties calculations show that the volume of FeAl3 decreases with the increasing temperature and pressure. The bulk modulus decreases with the increasing temperature, and increases with the increasing pressure. Onthecontrary, the thermal expansion coefficient, the heat capacities, and Grüneisen constant increase with the increasing temperature, and decrease as pressure increases. It is found that the bulk modulus and Grüneisen constant display strong pressure dependence, while the heat capacities are sensitive to the temperature. And the thermal expansion coefficient is affected simultaneously by the pressure and temperature.

Exploration of D022-Type Al3TM(TM = Sc, Ti, V, Zr, Nb, Hf, Ta): Elastic Anisotropy, Electronic Structures, Work Function and Experimental Design.

The structural properties, elastic anisotropy, electronic structures and work function of D022-type Al3TM (TM = Sc, Ti, V, Y, Zr, Nb, La, Hf, Ta) are studied using the first-principles calculations. The results indicate that the obtained formation enthalpy and cohesive energy of these compounds are in accordance with the other calculated values. It is found that the Al3Zr is the most thermodynamic stable compound. The mechanical property indexes, such as elastic constants, bulk modulus, shear modulus, Young’s modulus, Poisson’s ratio, and Vickers hardness are systematically explored. Moreover, the calculated universal anisotropic index, percent anisotropy and shear anisotropic factors of D022-type Al3TM are analyzed carefully. It demonstrates that the shear modulus anisotropy of Al3La is the strongest, while that of Al3Ta is the weakest. In particular, the density of states at Fermi level is not zero, suggesting that these phases have metal properties and electrical conductivity. More importantly, the mechanisms of correlation between hardness and Young’s modulus are further explained by the work function. Finally, the experimental design proves that D022-Al3Ta has an excellent strengthening effect.

Two novel superhard monoclinic phase of B–C–N compounds

Two novel superhard BCN compounds, namely m-B3CN3 and m-B2C3N2 are proposed in this work based on density functional theory. The physical properties, such as structural properties, mechanical properties, mechanical anisotropy properties and electronic properties, and the stability of m-B3CN3 and m-B2C3N2 are also predicted utilizing first-principles calculations. The bulk modulus, Young’s modulus and shear modulus of m-B3CN3 and m-B2C3N2 are 345/351, 778/816 and 346/367 ​GPa with GGA level/LDA level, respectively, they are slightly greater than those of o-BC6N, t-BC6N-1, t-BC6N-2. In addition, the hardness of m-B3CN3 and m-B2C3N2 are 58.36/63.68 ​GPa and 40.61/51.43 ​GPa with GGA level/LDA level, respectively, so both the m-B3CN3 and m-B2C3N2 are superhard materials. Furthermore, the mechanical anisotropy in shear modulus, Young’s modulus and Poisson’s ratio of m-B3CN3 and m-B2C3N2 are also investigated in this work.

Boundary element analysis of dynamic interaction of anisotropic elastic half-space and structure under impact load

In this paper, a direct boundary element formulation for numerical modelling of threedimensional dynamic soil-structure interaction is briefly described. Formulation is applicable to problems involving isotropic and anisotropic elastic materials. It is based on the Laplace domain regularized boundary integral equations for the displacements under assumption of vanishing initial conditions and zero body forces. Mixed boundary elements are employed for the spatial discretization of the boundary integral equations. Subdomain technique is used to tackle problems involving piecewise homogeneous material properties. The described formulation is employed for the boundary element analysis of dynamic soil-structure interaction problem involving a structure which contains a cavity with a complex geometrical form. Soil is represented by a transversely isotropic elastic half-space. Effect of material anisotropy of half-space on the transient response of the embedded structure is assessed. It is observed that the shear modulus anisotropy have substantial impact on the displacements response. Influence of the Young’s modulus in the plane of isotropy is lesser but still pronounced.

Accelerated relaxation in disordered solids under cyclic loading with alternating shear orientation

The effect of alternating shear orientation during cyclic loading on the relaxation dynamics in disordered solids is examined using molecular dynamics simulations. The model glass was initially prepared by rapid cooling from the liquid state and then subjected to cyclic shear along a single plane or periodically alternated in two or three dimensions. We showed that with increasing strain amplitude in the elastic range, the system is relocated to deeper energy minima. Remarkably, it was found that each additional alternation of the shear orientation in the deformation protocol brings the glass to lower energy states. The results of mechanical tests after more than a thousand shear cycles indicate that cyclic loading leads to the increase in strength and shear-modulus anisotropy.

Elastic anisotropy and thermal conductivity of silicon allotropes

Silicon is the most basic and commonly used semiconductor material in the modern microelectronics industry. Because diamond silicon is an indirect band gap semiconductor, its application in the optoelectronic industry is limited. Searching for new silicon allotropes with direct band gaps has been a hot topic in the fields of condensed matter and materials science. In this work, the elastic anisotropy and thermal conductivity of seven silicon allotropes with direct band gaps (D76, D63, D135, D243, D12, D239, and D979), a silicon allotrope with quasi-direct band gap (Q135) and a silicon allotrope with indirect band gap (I926) are investigated. The elastic anisotropy of shear modulus, Young’s modulus and Poisson’s ratio for Q135, D76, D63, D135, D243, D12, I926, D239, and D979 silicon allotropes are investigated by surface constructions of the 2D representation. The I926 phase has the greatest thermal conductivity among the nine silicon allotropes, and it is greater than that of the oC12 phase. In addition, the anisotropy of elastic moduli and the anisotropy of thermal conductivity in each main plane for Q135, D76, D63, D135, D243, D12, I926, D239, and D979 are studied for the first time.

Mechanical Anisotropic and Electronic Properties of Amm2-carbon under Pressure**Supported by the National Natural Science Foundation of China under Grant No. 61564005

Structural, electronic properties and mechanical anisotropy of Amm2-carbon are investigated utilizing frist-principles calculations by Cambridge Serial Total Energy Package (CASTEP) code. The work is performed with the generalized gradient approximation in the form of Perdew–Burke–Ernzerhof (PBE), PBEsol, Wu and Cohen (WC) and local density approximation in the form of Ceperley and Alder data as parameterized by Perdew and Zunger (CA-PZ). The mechanical anisotropy calculations show that Amm2-carbon exhibit large anisotropy in elastic moduli, such as Poisson’s ratio, shear modulus and Young’s modulus, and other anisotropy factors, such as the shear anisotropic factor and the universal anisotropic index AU. It is interestingly that the anisotropy in shear modulus and Young’s modulus, universal anisotropic index and the shear anisotropic factor all increases with increasing pressure, but the anisotropy in Poisson’s ratio decreases. The band structure calculations reveal that Amm2-carbon is a direct-band-gap semiconductor at ambient pressure, but with the pressure increasing, it becomes an indirect-band-gap semiconductor.

Phase stability, anisotropic elastic properties and electronic structures of C15-type Laves phases ZrM2 (M = Cr, Mo and W) from first-principles calculations

Systematic investigations of phase stability and mechanical properties of C15-type ZrM2 (M = Cr, Mo and W) Laves phases were performed using first-principles calculations. The formation enthalpies of ZrM2 are in good agreement with the theoretical and experimental values. The elastic properties, including elastic constants and moduli, Poisson’s ratio and B/G, were discussed. The elastic anisotropy was also investigated via the anisotropy indexes (AU, AZ, Ashear and Acomp), the anisotropy of shear modulus and the 3D construction of bulk and Young’s moduli. The elastic anisotropy of ZrM2 is in order of ZrCr2 < ZrMo2 < ZrW2. The variations in the shear modulus and hardness show similar trends with increasing values from ZrCr2 to ZrW2. The electronic structures for these C15-type Laves phases were analysed to obtain deeper understanding of chemical bonds and phase stabilities. Finally, the sound velocities and Debye temperatures were also investigated.

A theoretical study of elastic anisotropy and thermal conductivity for TATB under pressure

The elastic properties and thermodynamic properties of insensitive high explosive 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) are investigated by using molecular dynamics simulation. We first analyse the elastic anisotropy of TATB, which makes up for the shortage of research on the anisotropic mechanical properties of explosives. The three-dimensional contours and their planar projections of Young’s modulus and shear modulus are plotted to illustrate the anisotropy in elasticity. TATB shows high elastic anisotropy and strong dependence on direction. With pressure increasing from 0 to 50GPa, the anisotropy of Young’s modulus shows a decreasing trend, while the anisotropy of shear modulus exhibits an increasing trend. Based on Debye theory and phonon dispersion model, we use a method derived by our group to calculate the thermal conductivity of TATB in the temperature range 0–700K and pressure range 0–30GPa. The calculated thermal conductivity at 300K and 0GPa is 0.53W/mK, which is in agreement with the available experimental results. Using Cahill’s model, the minimum anisotropic thermal conductivity of TATB is discussed. The results indicate that the thermal conductivity of TATB has strong dependence on direction.

Phase stability, elastic anisotropy and electronic structure of cubic MAl2 (M = Mg, Ca, Sr and Ba) Laves phases from first-principles calculations

By performing first-principles calculations within the generalized gradient approximation, the phase stability, elastic constant and anisotropy, and density of states of cubic C15-type MAl2 (M = Mg, Ca, Sr and Ba) Laves phases have been investigated. Optimized equilibrium lattice parameters and formation enthalpies agree well with the available experimental data. Elastic constants Cij have been evaluated, and these C15-type MAl2 Laves phases are mechanically stable due to the meeting of Cij to the mechanical stability criteria. Polycrystalline elastic moduli have been deduced from elastic constants by Voigt–Reuss–Hill approximation. Plastic properties were characterized via values of B/G, Poisson’s ratio ν and Cauchy pressure (C12-C44). The elastic anisotropy has been considered by several anisotropy indexes (AU, AZ, Ashear and Acomp), anisotropy of shear modulus, and 3D surface constructions of bulk and Young’s moduli. Additionally, the sound velocity anisotropy and Debye temperature were predicted. Finally, electronic structures were carried out to reveal the underlying phase stability mechanism of these Laves phases.

First-Principles Calculations of the Mechanical and Elastic Properties of 2Hc- and 2Ha-WS2/CrS2 Under Pressure

Abstract By utilizing the first-principles method, the pressure-induced effects on phase transition, mechanical stability, and elastic properties of WS2/CrS2 are investigated in the pressure range from 0 to 80 GPa. Transitions from 2Hc to 2Ha for WS2 and CrS2 are found to occur at 17.5 and 25 GPa, respectively. It is found that both 2Ha and 2Hc phases of WS2 and CrS2 meet the mechanical stability criteria up to 80 GPa, suggesting that those structures are mechanically stable. The bulk and shear modulus anisotropy of the two phases of WS2 and CrS2 decrease rapidly under pressure and, finally, trend to isotropy. With increasing pressure, the elastic moduli (Y, B, and G), sound velocities (v s, v p, v m), and Debye temperatures (Θ) of 2Ha and 2Hc of WS2 and CrS2 increase monotonously. Moreover, the Debye temperature (Θ) of 2Hc phase is higher than that of 2Ha phase for both WS2 and CrS2. The bulk, shear, and Young’s modulus, Poisson coefficient, and brittle/ductile behaviour are estimated. The percentages of anisotropy in compressibility and shear and the ratio of bulk to shear modulus (B/G) are also studied.