A design method for metamaterials: 3D transversely isotropic lattice structures with tunable auxeticity

2021 ◽  
Author(s):  
Xiang-Long Peng ◽  
Swantje Bargmann
Keyword(s):  
Elastic Anisotropy ◽  
Design Method ◽  
Transversely Isotropic ◽  
Longitudinal Direction ◽  
Lattice Structures ◽  
Structural Geometry ◽  
Young’S Moduli ◽  
Auxetic Structures ◽  
Material Space ◽  
Effective Young's Moduli

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.

Microstructural Properties of Common Yew and Norway Spruce Determined with Silviscan

IAWA Journal ◽  
2009 ◽  
Vol 30 (2) ◽  
pp. 165-178 ◽  
Author(s):  
Daniel Keunecke ◽  
Robert Evans ◽  
Peter Niemz
Keyword(s):  
Mechanical Behaviour ◽  
Mechanical Response ◽  
Elastic Anisotropy ◽  
Longitudinal Direction ◽  
Structural Features ◽  
Structure Property ◽  
Tangential Plane ◽  
Cross Sectional ◽  
X Ray ◽  
The Difference

Yew wood holds a special position within the softwoods with regard to its exceptional elasto-mechanical behaviour. Despite a relatively high density, it is highly elastic in the longitudinal direction (the modulus of elasticity is low and the stretch to break high). In the radial-tangential plane, its elastic anisotropy is clearly less pronounced compared to other softwoods such as spruce. Knowledge of the anatomical organisation of yew wood is an indispensable precondition for the correct interpretation of this conspicuous mechanical behaviour. The aim of this study, therefore, was to interpret the difference in elasto-mechanical behaviour of yew and spruce (as a reference) through their relative microstructures as measured by SilviScan, a technology based on X-ray densitometry, X-ray diffractometry and optical microscopy. This system is able to measure a variety of structural features in a wood sample. The results reveal that the elasto-mechanical response of yew is primarily due to large microfibril angles and a more homogeneous cross-sectional tissue composition (regarding tracheid dimensions and density distribution) compared to spruce. With respect to structure-property relationships, it was concluded that yew wood combines properties of normal and compression wood and therefore takes an intermediate position between them.

Weak elastic anisotropy and the tube wave

Geophysics ◽  
1993 ◽  
Vol 58 (8) ◽  
pp. 1091-1098 ◽  
Author(s):  
Andrew N. Norris ◽  
Bikash K. Sinha
Keyword(s):  
Shear Modulus ◽  
Elastic Moduli ◽  
Wave Speed ◽  
Elastic Anisotropy ◽  
Transversely Isotropic ◽  
Anisotropic Formation ◽  
Inversion Procedure ◽  
Anisotropy Parameters ◽  
Tube Wave ◽  
Simple Inversion

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.

Long‐wave elastic anisotropy in transversely isotropic media

Geophysics ◽  
1979 ◽  
Vol 44 (5) ◽  
pp. 896-917 ◽  
Author(s):  
James G. Berryman
Keyword(s):  
Elastic Anisotropy ◽  
Transversely Isotropic ◽  
Layered Media ◽  
Seismic Signal ◽  
Perturbation Scheme ◽  
Low Velocity ◽  
Compressional Waves ◽  
Long Wave ◽  
Transversely Isotropic Media ◽  
Isotropic Media

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.

On: “Long‐wave elastic anisotropy in transversely isotropic media” by J. G. Berryman, and “Seismic velocities in transversely isotropic media” by F. K. Levin (GEOPHYSICS, v. 44, May 1979, p. 896–917 and p. 918–936, respectively).

Geophysics ◽  
1981 ◽  
Vol 46 (3) ◽  
pp. 336-338 ◽  
Author(s):  
Felix M. Lyakhovitskiy
Keyword(s):  
Poisson’S Ratio ◽  
Elastic Anisotropy ◽  
Transversely Isotropic ◽  
Layered Media ◽  
Thin Layers ◽  
Poisson's Ratio ◽  
Seismic Velocities ◽  
Long Wave ◽  
Transversely Isotropic Media ◽  
Isotropic Media

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).

Thermodynamic and Elastic Properties of the Phases Appearing in the Lightweight La-Mg Alloys

2011 ◽  
Vol 690 ◽  
pp. 15-18
Author(s):  
Jan S. Wróbel ◽  
Louis G. Hector ◽  
Walter Wolf ◽  
Krzysztof Jan Kurzydlowski
Keyword(s):  
Elastic Anisotropy ◽  
Linear Thermal Expansion ◽  
Elasticity Tensor ◽  
Enthalpies Of Formation ◽  
Young’S Moduli ◽  
Quasiharmonic Approximation ◽  
Thermal Expansion Tensor ◽  
Hill Criteria ◽  
Vibrational Energies ◽  
The Hill

Lattice parameters, electronic and vibrational energies, enthalpies of formation at 0 and 298 K, the elasticity tensor components,Cij, polycrystalline bulk, shear and Young’s moduli based on the Hill criteria were computed for LaMg, LaMg2, LaMg3, and La5Mg41, La2Mg17, and LaMg12. The quasiharmonic approximation was used to compute the linear thermal expansion tensor, aij(T), and the constant pressure heat capacity,Cp(T). Elastic anisotropy was analyzed in terms of the Young’s moduli dependence on crystallographic direction. Results were compared with available experimental data and discussed in terms of the applications of materials from the La-Mg system.

Application of Expansion Double Spherical Seismic Isolation Bearing in Seismic Design of Continuous Girder Bridges

2011 ◽  
Vol 243-249 ◽  
pp. 1928-1934 ◽  
Author(s):  
Tian Bo Peng ◽  
Zhen Nan Wang ◽  
Xun Tao Yu ◽  
Cheng Yu Yang
Keyword(s):  
Seismic Design ◽  
Seismic Isolation ◽  
Seismic Analysis ◽  
Design Method ◽  
Longitudinal Direction ◽  
Vertical Displacement ◽  
Girder Bridges ◽  
Earthquake Effect ◽  
Continuous Girder Bridge ◽  
Girder Bridge

The double spherical seismic isolation (DSSI for short) bearing has been adopted in seismic design of several important engineering projects since developed recently. It was used generally as fixed bearings in a continuous girder bridge in these projects, and only a few fixed piers, usually just one fixed pier would transmit the horizontal earthquake action to the foundation, which is uneconomical and results in the much larger seismic risk in the longitudinal direction of a continuous girder bridge than that in the transverse direction. In order to share the earthquake effect with all the piers and avoid relative vertical displacement among all the bearings under the normal traffic conditions, a new seismic design method of continuous girder bridges is introduced. The configuration and working mechanism of two kinds of DSSI bearings used to make the new seismic design possible are introduced. It’s shown that the method is preferable for the seismic design of continuous girder bridges by a numerical seismic analysis with a four-span continuous girder bridge.

Effective Young’s Modulus of Syntactic Foams with Hollow Glass Microspheres

2010 ◽  
Vol 29-32 ◽  
pp. 607-612 ◽  
Author(s):  
Chang Jun He ◽  
Hui Jian Li ◽  
Wei Yu ◽  
Xi Liang ◽  
Hai Yan Peng
Keyword(s):  
Young’S Modulus ◽  
Young's Modulus ◽  
Mechanical Analysis ◽  
Particulate Composites ◽  
Syntactic Foams ◽  
Glass Microspheres ◽  
Hollow Glass Microspheres ◽  
Hollow Glass ◽  
Young’S Moduli ◽  
Effective Young's Moduli

. The Young’s modulus of syntactic foams were studied both the experiment and the theory. The compressive test and dynamic mechanical analysis were progressed for a few of specimens, which were made of the syntactic foams with the epoxy resin and hollow glass microspheres (HGMs). the equations for Young’s modulus of concentrated particulate composites were derived using a differential scheme of an infinitely dilute system, and were employed to prediction the Young’s modulus of syntactic foams. The computed effective Young’s moduli were compared with the experimental results, the prediction values were between the lower and upper bounds of the experimental data, and the prediction model was acceptable and can estimate the Young’s modulus of syntactic foams.

RELATIONS OF ANISOTROPIC ELASTIC MODULI TO DENSITY AND CT NUMBER IN BOVINE CORTICAL BONE

2008 ◽  
Vol 20 (03) ◽  
pp. 139-143 ◽  
Author(s):  
Jui-Ting Hsu ◽  
Ming-Tzu Tsai ◽  
Heng-Li Huang
Keyword(s):  
Elastic Modulus ◽  
Bone Density ◽  
Cortical Bone ◽  
Elastic Moduli ◽  
Transversely Isotropic ◽  
Longitudinal Direction ◽  
Coefficient Of Determination ◽  
Ct Number ◽  
Noninvasive Technique ◽  
Anisotropic Elastic

It would be useful to be able to determine the mechanical properties of bone using a noninvasive technique such as computed tomography (CT). However, in contrast to cancellous bone tissue, quantifying the elastic modulus of cortical bone from bone density and CT number has not been investigated extensively. This study measured the elastic moduli of cortical bone from eight bovine femora in the longitudinal, circumferential, and radial directions using mechanical compressive testing. Before testing, the CT number and wet apparent bone density were obtained. The experimentally determined coefficient of determination between CT number and bone density was around 0.6. Bone density was a good predictor of the elastic modulus of cortical bone in the longitudinal direction (r2 > 0.79), but it could not be used to predict the elastic moduli in the circumferential (r2 < 0.4) and radial (r2 < 0.22) directions. The coefficient of determination between CT number and the elastic modulus in the longitudinal direction was higher than 0.41. However, the correlations between CT number and elastic moduli were weak in the circumferential (r2 < 0.21) and radial (r2 < 0.19) directions. Moreover, the elastic modulus was much higher in the longitudinal direction than the circumferential and radial directions, and hence cortical bone can be considered a transversely isotropic property.

First-principles study on the structural, elastic and electronic properties of the four Si3Sb4 compounds

2019 ◽  
Vol 33 (05) ◽  
pp. 1950047
Author(s):  
Ruike Yang ◽  
Bao Chai ◽  
Qun Wei ◽  
Minhua Xue ◽  
Ye Zhou
Keyword(s):  
Electronic Properties ◽  
First Principles ◽  
Density Functional ◽  
Phonon Dispersion ◽  
Elastic Anisotropy ◽  
Functional Theory ◽  
Shear Moduli ◽  
Young’S Moduli ◽  
Poisson's Ratios ◽  
Poisson’S Ratios

For novel [Formula: see text]-Si3Sb4, pseudocubic-Si3Sb4, cubic-Si3Sb4 and [Formula: see text]-Si3Sb4, the structural, elastic and electronic properties are investigated using first-principles density functional theory (DFT). The elastic constants and phonon dispersion spectra show that they are mechanically and dynamically stable. The bulk moduli, shear moduli, Young’s moduli, Poisson’s ratios and Pugh ratios for the four compounds have been calculated. The bulk moduli indicate that the bond strength of [Formula: see text]-Si3Sb4 is stronger than others. The values of the Poisson’s ratios and Pugh ratios show that pseudocubic-Si3Sb4 is the stiffest among the four Si3Sb4 compounds. Tetragonal Si3Sb4 are more brittle than cubic Si3Sb4. For the four Si3Sb4 compounds, the elastic anisotropies are analyzed via the anisotropic indexes and the 3D surface constructions. The [Formula: see text]-Si3Sb4 elastic anisotropy is stronger than others and the [Formula: see text]-Si3Sb4 is weaker than others. The calculated band structures show that they exhibit metallic features. The results of their TDOS show that there are many similarities. The peaks of TDOS are derived from the contributions of Si “s”, Si “p”, Sb “s” and Sb “p” states.

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