scholarly journals Poisson's ratio in cubic materials

Author(s):  
Andrew N Norris

Expressions are given for the maximum and minimum values of Poisson's ratio ν 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 occur in directions at which the Young 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.

Materials ◽  
2020 ◽  
Vol 13 (9) ◽  
pp. 2079 ◽  
Author(s):  
Jiao Cheng ◽  
Qidong Zhang

Based on first-principle calculations, the mechanical anisotropy and the electronic and optical properties of seven kinds of carbon materials are investigated in this work. These seven materials have similar structures: they all have X-type structures, with carbon atoms or carbon clusters at the center and stacking towards the space. A calculation of anisotropy shows that the order of elastic anisotropy in terms of the shear modulus, Young’s modulus and Poisson’s ratio of these seven carbon materials with similar structure is diamond < supercubane < T carbon < Y carbon < TY carbon < cubane-diyne < cubane-yne. As these seven carbon materials exhibit cubic symmetry, Young’s modulus has the same anisotropy in some major planes, so the order of elastic anisotropy in the Young’s modulus of these seven main planes is (111) plane < (001) plane = (010) plane = (100) plane < (011) plane = (110) plane = (101) plane. It is also due to the fact that their crystal structure has cubic symmetry that the elastic anisotropy in the shear modulus and the Poisson’s ratio of these seven carbon materials on the seven major planes are the same. Among the three propagation directions of [100], [110], and [111], the [110] propagation direction’s anisotropic ratio of the sound velocity of TY carbon is the largest, while the anisotropic ratio of the sound velocity of cubane-diyne on the [100] propagation direction is the smallest. In addition, not surprisingly, the diamond has the largest Debye temperature, while the TY carbon has the smallest Debye temperature. Finally, TY carbon, T carbon and cubane-diyne are also potential semiconductor materials for photoelectric applications owing to their higher or similar absorption coefficients to GaAs in the visible region.


1998 ◽  
Vol 65 (3) ◽  
pp. 786-787 ◽  
Author(s):  
M. Hayes ◽  
A. Shuvalov

For homogeneous cubic elastic materials with positive definite stored energy it is shown that the maximum and minimum values of Young’s modulus E are related to the maximum and minimum values of the shear modulus G through the simple connection 1/Gmin−1/Gmax=3(1/Emin−1/Emax). It is deduced that the ratio of compliances −s12/s44 is the maximum value of Poisson’s ratio v in the cubic materials with a positive parameter χ=2s11−2s12−s44, and the minimum value of ν in the cubic materials with negative χ.


BioResources ◽  
2021 ◽  
Vol 16 (2) ◽  
pp. 3200-3213
Author(s):  
Wei Wang ◽  
Yancai Cao ◽  
Liyue Sun ◽  
Mingshuai Wu

A formaldehyde-cellulose amorphous region model at the micro-level was established using the molecular dynamics software Materials Studio to simulate the change of cellulose and formaldehyde molecules in an external temperature field. The diffusion coefficients of formaldehyde molecules increased as the temperature increased. Moreover, the total number of hydrogen bonds decreased, and the interaction energy in the formaldehyde-cellulose model was reduced, which confirmed this conclusion and indicated that temperature increase could enhance the diffusion of formaldehyde in cellulose. The mechanical parameters of cellulose were analyzed in terms of Young’s modulus, shear modulus, bulk modulus, Poisson’s ratio, and the ratio of bulk modulus to shear modulus (K/G), which were affected by the temperature. The elastic modulus (E, G, and K) of cellulose decreased as the temperature increased, while the Poisson’s ratio V and K/G values increased. The results of the research explain how elevated temperature can promote the release of formaldehyde in furniture from a microscopic perspective, which supports each other with the results of previous experimental data and practical applications in production.


2010 ◽  
Vol 160-162 ◽  
pp. 1691-1698 ◽  
Author(s):  
Zhi Xin Huang ◽  
Cai Fu Qian ◽  
Peng Liu ◽  
Xu Liang Deng ◽  
Qing Cai ◽  
...  

This study aimed at investigating the effects of the post material properties on the maximum stress in the root and maximum deformation of the restorative system. Effects of material properties of fiber post on the maximum equivalent stress in the root and the maximum deformation of the restorative system were numerically investigated. Results show that the maximum equivalent stress in the root can be decreased by 8.3% and the maximum deformation of the restorative system decreased by 10% compared with corresponding maximum values if changing Young’s modulus, Shear modulus and Poisson’s ratio in the range studied here. The maximum equivalent stress in the root is more sensitive to Young’s modulus and Poisson’s ratio while the deformation of the restorative system is more seriously affected by the Shear modulus of the post material.


Author(s):  
Sayyad Zahid Qamar ◽  
Maaz Akhtar ◽  
Moosa S. M. Al-Kharusi

In the last ten years, a new type of advanced polymer known as swelling elastomer has been extensively used as sealing element in the oil and gas industry. These elastomers have been instrumental in various new applications such as water shutoff, zonal isolation, sidetracking, etc. Though swell packers can significantly reduce costs and increase productivity, their failure can lead to serious losses. Integrity and reliability of swelling-elastomer seals under different field conditions is therefore a major concern. Investigation of changes in material behavior over a specified swelling period is a necessary first step for performance evaluation of elastomer seals. Current study is based on experimental and numerical analysis of changes in compressive and bulk behavior of an elastomeric material due to swelling. Tests and simulations were carried out before and after various stages of swelling. Specimens were placed in saline water (0.6% and 12% concentration) at a temperature of 50°C, total swelling period being one month. Both compression and bulk tests were conducted using disc samples. A small test rig had to be designed and constructed for determination of bulk modulus. Young’s modulus (under compression) and bulk modulus were determined for specimens subjected to different swelling periods. Shear modulus and Poisson’s ratio were calculated using isotropic relations. Experiments were also simulated using the commercial finite element software ABAQUS. Different hyperelastic material models were examined. As Ogden model with second strain energy potential gave the closest results, it has been used for all simulations. The elastomer was a fast-swell type. There were drastic changes in material properties within one day of swelling, under both low and high salinity water. Values of elastic and shear modulus dropped by more than 90% in the first few days, and then remained almost constant during the rest of the one-month period. Poisson’s ratio, as expected, showed a mirror behavior of a sharp increase in the first few days. Bulk modulus exhibited a fluctuating pattern; rapid initial decrease, then a slightly slower increase, followed by a much slower decrease. Salinity shows some notable effect in the first 5 or 6 days, but has almost no influence in the later days. Very interestingly, Poisson’s ratio approaches the limiting value of 0.5 within the first 10 days of swelling, justifying the assumption of incompressibility used in most analytical and numerical models. In general, simulations results are in good agreement with experimental ones.


2016 ◽  
Vol 253 (7) ◽  
pp. 1288-1294 ◽  
Author(s):  
Duc Tam Ho ◽  
Soon-Dong Park ◽  
Soon-Yong Kwon ◽  
Tong-Seok Han ◽  
Sung Youb Kim

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