Complex force-constant dependence of elastic constants

1990 ◽  
Vol 68 (1) ◽  
pp. 14-22 ◽  
Author(s):  
H. A. Rafizadeh
Keyword(s):  
Elastic Constant ◽  
Force Constant ◽  
Elastic Constants ◽  
Theoretical Calculations ◽  
Linear Chain ◽  
Chain Model ◽  
Crystalline Solids ◽  
Young’S Moduli ◽  
Complex Functions ◽  
Two Parameter

Expressions for the inner and bare components of the elastic constants of crystalline solids are derived. The inner elastic constants are complex functions of the force constants and vanish only for centrosymmetric solids. Using a linear-chain model, the force-constant dependence of inner, bare, and total elastic constants is studied. The linear-chain model is also utilized in derivation of composition-dependent elastic constant equations. Single-parameter and two-parameter theoretical calculations are compared with the experimental composition-dependent Young's moduli of a number of metal–metalloid glasses.

Interface Effects on the Raman Spectra of Si/3C-SiC Superlattices

2000 ◽  
Vol 640 ◽  
Author(s):  
E. F. Bezerra ◽  
A. G. Souza Filho ◽  
J. Mendes Filho ◽  
V. Lemos ◽  
V. N. Freire ◽  
...  
Keyword(s):  
Raman Spectra ◽  
Theoretical Calculations ◽  
Linear Chain ◽  
Dispersion Relations ◽  
Chain Model ◽  
Virtual Crystal Approximation ◽  
Smooth Interface ◽  
Bond Polarizability ◽  
Interface Effects

ABSTRACTTheoretical calculations are performed on the role of smooth interfaces in the Raman spectra of Si/3C-SiC superlattices. The dispersion relations were obtained using a linear chain model with the alloyed interface δ-(3C-SiC)0.5(Si)0.5 described in the virtual crystal approximation. A modified bond-polarizability model was used to calculate the Raman spectra. The main results are the enhancement of the Raman spectra and the appearance of new peaks in between those related to the Si quasi confined and the 3C-SiC-confined modes with increasing number δ?of interfacial monolayers (3C-SiC)0.5(Si)0.5. Some of the smooth interface related Raman peaks have intensity comparable with those of an abrupt Si/3C-SiC superlattice.

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.

scholarly journals Pressure Effect on Elastic Constants and Related Properties of Ti3Al Intermetallic Compound: A First-Principles Study

Materials ◽  
2018 ◽  
Vol 11 (10) ◽  
pp. 2015 ◽  
Author(s):  
Xianshi Zeng ◽  
Rufang Peng ◽  
Yanlin Yu ◽  
Zuofu Hu ◽  
Yufeng Wen ◽  
...  
Keyword(s):  
Intermetallic Compound ◽  
Debye Temperature ◽  
Elastic Constants ◽  
First Principles ◽  
Density Functional ◽  
Mechanical Stability ◽  
Theoretical Data ◽  
Young’S Moduli ◽  
Anisotropic Factor ◽  
Isotropic Pressure

Using first-principles calculations based on density functional theory, the elastic constants and some of the related physical quantities, such as the bulk, shear, and Young’s moduli, Poisson’s ratio, anisotropic factor, acoustic velocity, minimum thermal conductivity, and Debye temperature, are reported in this paper for the hexagonal intermetallic compound Ti 3 Al. The obtained results are well consistent with the available experimental and theoretical data. The effect of pressure on all studied parameters was investigated. By the mechanical stability criteria under isotropic pressure, it is predicted that the compound is mechanically unstable at pressures above 71.4 GPa. Its ductility, anisotropy, and Debye temperature are enhanced with pressure.

Calculation of the parameters of mechanical properties of the heart muscle

2020 ◽  
Vol 12 ◽  
pp. 42-52
Author(s):  
S. A. Muslov ◽  
◽  
A. I. Lotkov ◽  
S. D. Arutyunov ◽  
T. M. Albakova ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Young’S Modulus ◽  
Elastic Constants ◽  
Heart Muscle ◽  
Human Heart ◽  
Young's Modulus ◽  
Experimental Values ◽  
Two Parameter

A review of studies of the mechanical properties of human and animal heart tissues has been performed. Based on literature data, a form of approximating function is found for the dependence of the Young’s modulus of the ventricles of the human heart on the magnitude of the deformation. The average values of the Young’s modulus and other elastic constants were calculated and compared with the known experimental values. The coefficients C1 and C2 of the two-parameter hyperelastic myocardial Mooney-Rivlin model are calculated.

scholarly journals Extremely small twist elastic constants in lyotropic nematic liquid crystals

2020 ◽  
Vol 117 (44) ◽  
pp. 27238-27244 ◽  
Author(s):  
Clarissa F. Dietrich ◽  
Peter J. Collings ◽  
Thomas Sottmann ◽  
Per Rudquist ◽  
Frank Giesselmann
Keyword(s):  
Liquid Crystals ◽  
Elastic Constant ◽  
Elastic Constants ◽  
Nematic Phase ◽  
Elastic Moduli ◽  
Building Blocks ◽  
Lyotropic Liquid Crystals ◽  
Order Of Magnitude ◽  
Typical Range ◽  
Special Case

Recent measurements of the elastic constants in lyotropic chromonic liquid crystals (LCLCs) have revealed an anomalously small twist elastic constant compared to the splay and bend constants. Interestingly, measurements of the elastic constants in the micellar lyotropic liquid crystals (LLCs) that are formed by surfactants, by far the most ubiquitous and studied class of LLCs, are extremely rare and report only the ratios of elastic constants and do not include the twist elastic constant. By means of light scattering, this study presents absolute values of the elastic constants and their corresponding viscosities for the nematic phase of a standard LLC composed of disk-shaped micelles. Very different elastic moduli are found. While the splay elastic constant is in the typical range of 1.5 pN as is true in general for thermotropic nematics, the twist elastic constant is found to be one order of magnitude smaller (0.30 pN) and almost two orders of magnitude smaller than the bend elastic constant (21 pN). These results demonstrate that a small twist elastic constant is not restricted to the special case of LCLCs, but is true for LLCs in general. The reason for this extremely small twist elastic constant very likely originates with the flexibility of the assemblies that are the building blocks of both micellar and chromonic lyotropic liquid crystals.

scholarly journals Analysis of static forces generated in-track on a railway sleeper resting on an elastic foundation due to structural imperfections using the PONTOS system

2019 ◽  
Vol 262 ◽  
pp. 11001
Author(s):  
Włodzimierz Andrzej Bednarek
Keyword(s):  
Theoretical Calculations ◽  
Railway Track ◽  
Bernoulli Beam ◽  
Main Concept ◽  
Field Investigations ◽  
Railway Sleeper ◽  
Foundation Parameters ◽  
Euler Bernoulli Beam ◽  
Structural Imperfections ◽  
Two Parameter

In the paper a considered railway sleeper was analysed as an Euler-Bernoulli beam and a Timoshenko beam of finite length resting on a oneand two-parameter foundation. The foundation parameters were determined based on a modified and analogue Vlasov soil model and field investigations. The main concept for the executed investigations was to induce an intentional imperfection in an actual railway track, propose a way of appropriate measurement (e.g. the PONTOS system by GOM mbh), and utilize author’s field investigations results to calibrate necessary parameters for theoretical calculations. An experimental formula describing the value of the force transferred from the rail to the railway sleeper on the grounds of the survey site caused by a locomotive was given. Furthermore, the deflection of the chosen railway sleeper due to the generated imperfection was analysed. Finally the objective of the present analysis was to resolve the calculations into the beam element such that the results can be utilised in computational railway practice. In the presented paper also the computational examples, diagrams and tables reflecting influence of analyzed parameters on obtained a CWR track’s displacements are enclosed.

Linear-chain-model interpretation of resonant Raman scattering inGenSimmicrostructures

1996 ◽  
Vol 53 (23) ◽  
pp. 15871-15877 ◽  
Author(s):  
M. A. Araújo Silva ◽  
E. Ribeiro ◽  
P. A. Schulz ◽  
F. Cerdeira ◽  
J. C. Bean
Keyword(s):  
Raman Scattering ◽  
Linear Chain ◽  
Chain Model ◽  
Model Interpretation ◽  
Resonant Raman ◽  
Resonant Raman Scattering

Temperature Dependences of the Elastic Constants of Precipitation-Hardened Aluminum Alloys 2014 and 2219

1977 ◽  
Vol 99 (2) ◽  
pp. 181-184 ◽  
Author(s):  
D. T. Read ◽  
H. M. Ledbetter
Keyword(s):  
Aluminum Alloys ◽  
Shear Modulus ◽  
Bulk Modulus ◽  
Temperature Dependence ◽  
Elastic Properties ◽  
Elastic Constants ◽  
Ultrasonic Pulse ◽  
Young’S Moduli ◽  
Temperature Dependences ◽  
Sound Velocities

Elastic properties of precipitation-hardened aluminum alloys 2014 and 2219 were studied between 4 and 300 K using ultrasonic pulse techniques. Both the longitudinal and transverse sound velocities were measured. Also reported are the Young’s modulus, shear modulus, bulk modulus, and Poisson’s ratio. For both alloys, the Young’s moduli are about ten percent higher than for unalloyed aluminum, and they increase about ten percent on cooling from 300 to 4 K. All the elastic constants show normal temperature dependence.

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