Elastic constants. II

1977 ◽  
Vol 357 (1690) ◽  
pp. 297-307
Keyword(s):  
Energy Density ◽  
Elastic Constant ◽  
Initial Stress ◽  
Elastic Constants ◽  
Interatomic Potential ◽  
Uniform Strain ◽  
Partial Derivatives ◽  
Constant Tensor ◽  
Derivatives Of

In the previous paper of this series we derived expressions for the initial stress and the elastic constant tensor for a crystal in terms of the partial derivatives of the energy density with uniform strain or sublattice displacement. In this paper we shall develop these equations further by considering the most general form of interatomic potential energies.

Elastic constants. I

1977 ◽  
Vol 357 (1690) ◽  
pp. 289-295 ◽  
Keyword(s):  
Energy Density ◽  
Initial Stress ◽  
Elastic Constants ◽  
Long Waves ◽  
Uniform Strain ◽  
Homogeneous Deformation ◽  
Piezoelectric Crystals

In these papers we shall derive expressions for the elastic constants of non-piezoelectric crystals under the most general form of initial stress, including body torques, by calculating the change in the energy density of a crystal when it is subjected to a further uniform strain. This method - the method of homogeneous deformation - gives results that are com­pletely general, whereas the method of long waves, developed by Huang, can give the complete results only in the case where the initial stress is zero.

scholarly journals Anısotropy Property of Dıfferent Types of Wood

2020 ◽  
pp. 1-3
Author(s):  
Faeq A.A Radwan ◽  
Keyword(s):  
Elastic Constant ◽  
Elastic Constants ◽  
The Other ◽  
Constant Tensor ◽  
Different Types ◽  
Anisotropy Degree

The norm of elastic constant tensor and the norms of the irreducible parts of the elastic constants of different types of wood. The relation of the scalar parts norms and the other parts norms and the anisotropy of these woods is presented. The norm ratios are used as a criterion to present the anisotropy degree of the properties of these woods

Elastic constants. Ill

1977 ◽  
Vol 357 (1690) ◽  
pp. 309-321 ◽  
Keyword(s):  
Energy Density ◽  
Elasticity Theory ◽  
Elastic Constants ◽  
Acoustic Waves ◽  
Uniform Strain ◽  
Piezoelectric Crystals ◽  
Phase Velocities ◽  
Limiting Case

In the previous papers we have derived expressions for the elastic constants of non-piezoelectric crystals by considering the change in the energy density when the crystal is subjected to a uniform strain. In this paper we shall show that, in the limiting case of long acoustic waves, the phase velocities are governed by the elastic constants in a way exactly equivalent to that derived from continuous elasticity theory. We also show in what conditions one can use the results of dynamical experiments to define the elastic constants.

Mechanicals Behaviors of Tungsten-Rhenium Alloy Single Crystals from 77K to 300K - Atomic Simulation Study

2020 ◽  
Vol 50 ◽  
pp. 177-181
Author(s):  
Abdellah Tahiri ◽  
Mohamed Idiri ◽  
Brahim Boubeker
Keyword(s):  
Elastic Constant ◽  
Single Crystals ◽  
Elastic Constants ◽  
Room Temperature ◽  
Interatomic Potential ◽  
Calculation Model ◽  
Atomic Simulation ◽  
Rhenium Alloy ◽  
Embedded Method ◽  
Good Agreement

The elastic constants of tungsten-rhenium alloy single crystals were calculated by simulation atomic method using embedded method atom of interatomic potential. The found results show that elastic constants are proportional to the rhenium concentration up to 25 at% Re at room temperature. By following, we observed the elastic constant C44 dependency of temperature and decreased of elastic constant C’=1/2(C11-C12) when the Re atom addition increases. We have found that a growing instability of the bcc crystal structure. Our parameter calculation model is in good agreement with experimental data.

scholarly journals Higher Order Elastic Constants, Gruneisen Parameters and Lattice Thermal Expansion of Lithium Niobate

2006 ◽  
Vol 3 (3) ◽  
pp. 122-133 ◽  
Author(s):  
Thresiamma Philip ◽  
C. S. Menon ◽  
K. Indulekha
Keyword(s):  
Energy Density ◽  
Lithium Niobate ◽  
Elastic Constants ◽  
Elastic Stiffness ◽  
Higher Order ◽  
Second Order ◽  
Third Order ◽  
Third Order Elastic Constants ◽  
Gruneisen Parameters ◽  
Derivatives Of

The second and third-order elastic constants and pressure derivatives of second- order elastic constants of trigonal LiNbO3(lithium niobate) have been obtained using the deformation theory. The strain energy density estimated using finite strain elasticity is compared with the strain dependent lattice energy density obtained from the elastic continuum model approximation. The second-order elastic constants and the non-vanishing third-order elastic constants along with the pressure derivatives of trigonal LiNbO3are obtained in the present work. The second and third-order elastic constants are compared with available experimental values. The second-order elastic constant C11which corresponds to the elastic stiffness along the basal plane of the crystal is less than C33which corresponds to the elastic stiffness tensor component along thec-axis of the crystal. The pressure derivatives, dC'ij/dp obtained in the present work, indicate that trigonal LiNbO3is compressible. The higher order elastic constants are used to find the generalized Gruneisen parameters of the elastic waves propagating in different directions in LiNbO3. The Brugger gammas are evaluated and the low temperature limit of the Gruneisen gamma is obtained. The results are compared with available reported values.

Effective Elastic Constants of Fiber-Eutectics and Transformation Particles Composite Ceramic

2010 ◽  
Vol 177 ◽  
pp. 182-185 ◽  
Author(s):  
Bao Feng Li ◽  
Jian Zheng ◽  
Xin Hua Ni ◽  
Ying Chen Ma ◽  
Jing Zhang
Keyword(s):  
Elastic Modulus ◽  
Elastic Constant ◽  
Effective Stress ◽  
Elastic Constants ◽  
Transverse Isotropy ◽  
Analytical Formula ◽  
Composite Ceramic ◽  
Phase Model ◽  
Composite Ceramics ◽  
Effective Elastic Constants

The composite ceramics is composed of fiber-eutectics, transformation particles and matrix particles. First, the recessive expression between the effective stress in fiber-eutectic and the flexibility increment tensor is obtained according to the four-phase model. Second, the analytical formula which contains elastic constant of the fiber-eutectic is obtained applying Taylor’s formula. The eutectic is transverse isotropy, so there are five elastic constants. Third, the effective elastic constants of composite ceramics are predicted. The result shows that the elastic modulus of composite ceramic is reduced with the increase of fibers fraction and fibers diameter.

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