Elastic constants of solids and fluids with initial pressure via a unified approach based on equations-of-state

Ultrasonics ◽  
2014 ◽  
Vol 54 (5) ◽  
pp. 1323-1331 ◽  
Author(s):  
John H. Cantrell
Keyword(s):  
Elastic Constants ◽  
Equations Of State ◽  
Initial Pressure ◽  
Unified Approach

FIRST-PRINCIPLES HIGH-PRESSURE ELASTIC AND THERMODYNAMIC PROPERTIES OF TANTALUM

2011 ◽  
Vol 25 (10) ◽  
pp. 1393-1407 ◽  
Author(s):  
JING-HE WU ◽  
XIAN-LIN ZHAO ◽  
YOU-LIN SONG ◽  
GUO-DONG WU
Keyword(s):  
Thermodynamic Properties ◽  
Elastic Constants ◽  
First Principles ◽  
Equations Of State ◽  
Debye Model ◽  
Thermal Expansivity ◽  
Orbital Method ◽  
Full Potential ◽  
Body Centered Cubic ◽  
Theoretical Results

The all-electron full-potential linearized muffin-tin orbital method, by means of quasi-harmonic Debye model, is applied to investigate the elastic constant and thermodynamic properties of body-centered-cubic tantalum (bcc Ta). The calculated elastic constants of bcc Ta at 0 K is consistent with the previous experimental and theoretical results. Our calculations give the correct trends for the pressure dependence of elastic constants. By using the convenient quasi-harmonic Debye model, we refined the thermal equations of state. The thermal expansivity and some other thermal properties agree well with the previous experimental and theoretical results.

scholarly journals Optimization of composite revolution shell by methods of theory of the optimal process

2020 ◽  
Vol 26 (5) ◽  
pp. 28-37
Author(s):  
A.P. Dzyuba ◽  
◽  
V.N. Sirenko ◽  
D.V. Klymenko ◽  
L.D. Levytina ◽  
...  
Keyword(s):  
Composite Material ◽  
Elastic Constants ◽  
Equations Of State ◽  
Experimental Testing ◽  
Necessary Optimality Conditions ◽  
Middle Surface ◽  
Variable Coefficients ◽  
Space Technology ◽  
Fiber Winding ◽  
Revolution Shell

We considered the problem of weight optimization of parameters of multi-layer composite shell produced by the method of continuous cross-winding under axisymmetric loading. Shell layers are placed symmetrically relative to the middle surface. The angles of the reinforcing material winding variable along the meridian and the thickness of layers are taken as the variation parameters. We propose an algorithm of the automated determination of the elastic constants of a composite material variable along the shell meridian anisotropy. The connection of the composite structure with the technological process of shell manufacturing by winding with a reinforcing tape under different angles to the axis of rotation is taken into account. The values of four elastic constants obtained as a result of experimental testing of witness specimens of the composite material along and orthogonal to the reinforcement are used as output. The equations of state of the moment theory of shells of the variable along the meridian orthotropy and wall thickness are obtained as a boundary value problem for a system of ordinary differential equations with variable coefficients. The use of the necessary optimality conditions in the form of the principle maximum of Pontryagin in the presence of arbitrary phrasal restraints made it possible to reduce the emerging multiparameter problem to a sequence of extreme problems of a significantly smaller dimension. This approach greatly simplifies taking into account the conditions of strength reliability, and technological and structural requirements of real design, and the process of finding an optimal project as a whole. The results of the optimization of a two-layer fiberglass shell of rotation are presented in the form of a change in the distribution of layers’ thickness and the glass fiber winding angle. Materials of research can be used to reduce the material consumption of structural elements in rocket and space technology and other branches.

scholarly journals First Principles Computations of Second-Order Elastic Constants (SOEC) and Equations of State of Rutile TiO2

2011 ◽  
Vol 2011 ◽  
pp. 1-7 ◽  
Author(s):  
Ghous Narejo ◽  
Warren F. Perger
Keyword(s):  
Equation Of State ◽  
Elastic Constants ◽  
First Principles ◽  
Equations Of State ◽  
Second Order ◽  
Lattice Parameters ◽  
Experimental Results ◽  
Basis Sets ◽  
Computational Results ◽  
Rutile Tio2

First principles computations of second-order elastic constants (SOECs) and bulk moduli (B) are carried out by ELASTCON and equation of state (EOS) programs. Computational results of lattice parameters, elastic constants, and bulk moduli are obtained with a wide variety of potentials and a limited combination of basis sets and are compared with computational and experimental results by other researchers in the field. DFT hybrid potentials provided the best comparison with the experiment.

Tight-Binding Hamiltonians for Carbon and Silicon

1997 ◽  
Vol 491 ◽  
Author(s):  
D. A. Papaconstantopoulos ◽  
M. J. Mehl ◽  
S. C. Erwin ◽  
M. R. Pederson
Keyword(s):  
Band Structure ◽  
Total Energy ◽  
Elastic Constants ◽  
First Principles ◽  
Equations Of State ◽  
Tight Binding ◽  
First Principles Calculations ◽  
Energy Bands ◽  
Tight Binding Method ◽  
Correct Energy

ABSTRACTWe demonstrate that our tight-binding method - which is based on fitting the energy bands and the total energy of first-principles calculations as a function of volume - can be easily extended to accurately describe carbon and silicon. We present equations of state that give the correct energy ordering between structures. We also show that quantities that were not fitted, such as elastic constants and the band structure of C60, can be reliably obtained from our scheme.

scholarly journals Radial Curvilinear Motion in a Free Flow of Compressible Viscoplastic Oil in a Homogeneous Formation

2019 ◽  
pp. 54-61
Author(s):  
Dzh.N. Aslanov ◽  
S.D. Mustafaev ◽  
V.A. Ibragimov ◽  
R.T. Aliyeva
Keyword(s):  
Pressure Gradient ◽  
Flow Rate ◽  
Equations Of State ◽  
Initial Pressure ◽  
Radius Vector ◽  
External Boundary ◽  
Oil Well ◽  
Depth Range ◽  
Oil Flow ◽  
Homogeneous Formation

The paper presents a solution to a steady-state hydrodynamic problem dealing with one-dimensional free-surface radial flow of compressible viscoplastic oil in a horizontal homogeneous circular formation. A vertical producing oil well is located in the centre of the formation, penetrating the pay zone fully, with no well casing or perforation present. We used generalised Darcy's law and equations of state for a compressible fluid to determine mass flow rate of the compressible viscoelastic oil and derive equations for current density, oil flow rate, current pressure distribution in the drainage area, and current pressure gradient. The equations take into account oil compressibility and initial pressure gradient. We also determined the time it takes an oil particle to reach the well starting from the current radius vector and from the external boundary. This is the case when the oil deposit lies close to the earth surface. This depth range features no shale beds or interbedded formations. Since subsurface mining is possible with shallow oil deposits, both wells and tunnels may be used for production.

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