scholarly journals First-Principles Calculation of Third-Order Elastic Constants via Numerical Differentiation of the Second Piola-Kirchhoff Stress Tensor

2018 ◽  
Vol 121 (21) ◽  
Author(s):  
Tengfei Cao ◽  
David Cuffari ◽  
Angelo Bongiorno
Keyword(s):  
Stress Tensor ◽  
Elastic Constants ◽  
First Principles ◽  
Numerical Differentiation ◽  
First Principles Calculation ◽  
Third Order ◽  
Kirchhoff Stress ◽  
Third Order Elastic Constants ◽  
Kirchhoff Stress Tensor

scholarly journals First-Principles Calculations to Investigate the Third-Order Elastic Constants and Mechanical Properties of Mg, Be, Ti, Zn, Zr, and Cd

2021 ◽  
Vol 2021 ◽  
pp. 1-12 ◽  
Author(s):  
Xiaoqing Yang ◽  
Zhenya Meng ◽  
Hailin Cao
Keyword(s):  
High Pressure ◽  
Elastic Constants ◽  
First Principles ◽  
Deformation Gradient ◽  
Elastic Strain Energy ◽  
Pressure Effects ◽  
First Principles Calculation ◽  
Third Order ◽  
The Third ◽  
Third Order Elastic Constants

We present theoretical studies for the third-order elastic constants of Mg, Be, Ti, Zn, Zr, and Cd with a hexagonal-close-packed (HCP) structure. The method of homogeneous deformation combined with first-principles total-energy calculations is employed. The deformation gradient F i j is applied to the crystal lattice vectors r i , and the elastic strain energy can be obtained from the first-principles calculation. The second- and third-order elastic constants are extracted by a polynomial fit to the calculated energy-strain results. In order to assure the accuracy of our method, we calculated the complete set of the equilibrium lattice parameters and second-order elastic constants for Mg, Be, Ti, Zn, Zr, and Cd, and our results provide better agreement with the previous calculated and experimental values. Besides, we have calculated the pressure derivatives of SOECs related to third-order elastic constants, and high-pressure effects on elastic anisotropy, ductile-to-brittle criterion, and Vickers hardness are also investigated. The results show that the hardness model H v = 1.877 k 2 G 0.585 is more appropriate than H v = 2 k 2 G 0.585 − 3 for HCP metals under high pressure.

scholarly journals Nonlinear Elasticity of Borocarbide Superconductor YNi2B2C: A First-Principles Study

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Lili Liu ◽  
Cai Chen ◽  
Dingxing Liu ◽  
Zhengquan Hu ◽  
Gang Xu ◽  
...  
Keyword(s):  
High Pressure ◽  
Elastic Constants ◽  
Vickers Hardness ◽  
First Principles ◽  
Second Order ◽  
First Principles Calculations ◽  
Modulus Ratio ◽  
Third Order ◽  
Lattice Constants ◽  
Third Order Elastic Constants

First-principles calculations combined with homogeneous deformation methods are used to investigate the second- and third-order elastic constants of YNi2B2C with tetragonal structure. The predicted lattice constants and second-order elastic constants of YNi2B2C agree well with the available data. The effective second-order elastic constants are obtained from the second- and third-order elastic constants for YNi2B2C. Based on the effective second-order elastic constants, Pugh’s modulus ratio, Poisson’s ratio, and Vickers hardness of YNi2B2C under high pressure are further investigated. It is shown that the ductility of YNi2B2C increases with increasing pressure.

High-Pressure Third-Order Elastic Constants of MgO Single Crystal: First-Principles Investigation

2019 ◽  
Vol 74 (5) ◽  
pp. 447-456
Author(s):  
Jianbing Gu ◽  
Chenju Wang ◽  
Bin Sun ◽  
Weiwei Zhang ◽  
Dandan Liu
Keyword(s):  
High Pressure ◽  
Single Crystal ◽  
Total Energy ◽  
Elastic Constants ◽  
First Principles ◽  
Predictive Ability ◽  
Theoretical Method ◽  
Third Order ◽  
Third Order Elastic Constants ◽  
First Time

AbstractHigh-pressure third-order elastic constants of materials have rarely been investigated experimentally and theoretically to date, so the predictive ability of the method of the volume-conserving, homogeneous deformations based on the first-principles total-energy calculations is tested for the first time in this work. Using this approach, the high-pressure third-order elastic constants ${C_{111}}-3{C_{112}}+2{C_{123}}$, ${C_{111}}/2+3{C_{112}}+{C_{123}}$, ${C_{144}}-{C_{155}}$, and C456 of the MgO single crystal are obtained successfully. Meanwhile, the reliability of this method is also verified by comparing the calculated structural properties and high-pressure second-order elastic constants of the MgO single crystal with the available experimental results and other theoretical predications. Results not only indicate the accuracy of our calculations but also reveal the feasibility of the present theoretical method. It is hoped that the present theoretical method and predictions on the high-pressure third-order elastic constants of the MgO single crystal would serve as a valuable guidance or reference for further related investigations.

The Nonlinear Elasticity of Hexagonal Ti2C Monolayer from First-Principles Calculations

2015 ◽  
Vol 833 ◽  
pp. 150-153
Author(s):  
Shun Wang ◽  
Jing Xiao Li ◽  
Yuan Yuan Ou ◽  
Yu Lei Du
Keyword(s):  
Nonlinear Elasticity ◽  
Elastic Constants ◽  
First Principles ◽  
Breaking Strength ◽  
First Principles Calculations ◽  
Third Order ◽  
Breaking Strain ◽  
Third Order Elastic Constants ◽  
Nonlinear Stress ◽  
Strain Relationship

In this work, the nonlinear elasticity of hexagonal Ti2C monolayer is studied by first-principles calculations. The second-and third-order elastic constants were calculated using nonlinear elasticity theory. The nonlinear stress-strain relationship depending on higher order elastic constants was also revealed. The intrinsic breaking strength and corresponding breaking strain were deduced as 11.9 N/m at the maximum strain 16.6% for Ti2C monolayer.

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