scholarly journals Elastic waves in the Hencky-Murnaghan material

2020 ◽  
pp. 108-120
Author(s):  
Марина Юрьевна Соколова ◽  
Юрий Владимирович Астапов
Keyword(s):  
Elastic Constants ◽  
Elastic Waves ◽  
Deformable Body ◽  
Polyamide 6 ◽  
Phase Velocities ◽  
Dynamic Methods ◽  
Nonlinear Elastic ◽  
The Given

Рассмотрены динамические методы идентификации модели нелинейно упругого деформируемого тела. По эффективным фазовым скоростям продольных и поперечных волн, распространяющихся вдоль и поперек оси сжимаемого стержня, возможно определить пять констант упругости второго и третьего порядков, входящих в соотношения модели. В статье получены расчетные формулы и приведен пример определения зависимости фазовых скоростей для полиамида 6. The dynamic methods for selecting models of a nonlinear elastic deformable body are considered. Depending on the model, five elastic constants of the second and third orders, which are available in the relations of the models, can be determined. The calculation formulas and the given example of determining the dependence of phase velocities for polyamide 6 are obtained in the article.

Identification of the Model of Nonlinear Elasticity in Dynamic Experiments

2021 ◽  
pp. 2150025
Author(s):  
Marina Sokolova ◽  
Yuri Astapov ◽  
Dmitrii Khristich
Keyword(s):  
Deformable Body ◽  
Polyamide 6 ◽  
Preliminary Deformation ◽  
Transverse Waves ◽  
Wave Velocities ◽  
Phase Velocities ◽  
Dynamic Methods ◽  
Dynamic Experiments ◽  
Effective Phase ◽  
Nonlinearly Elastic

Dynamic methods for identifying a model of a nonlinearly elastic deformable body are considered. By the effective phase velocities of longitudinal and transverse waves propagating along and across the axis of the compressed bar, it is possible to determine five elastic constants of the second and third orders included in the model relations. Calculation formulae are obtained and an example of determining the dependence of phase velocities on the preliminary deformation for polyamide 6 is given. The influence of preliminary deformations on polar diagrams of wave velocities is investigated.

Remarks on nonlinear elastic waves with null conditions

2020 ◽  
Vol 26 ◽  
pp. 121
Author(s):  
Dongbing Zha ◽  
Weimin Peng
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Elastic Waves ◽  
Wave Equations ◽  
Alternative Proof ◽  
Classical Solutions ◽  
Small Initial Data ◽  
Hyperelastic Materials ◽  
Variational Structure ◽  
Nonlinear Elastic

For the Cauchy problem of nonlinear elastic wave equations for 3D isotropic, homogeneous and hyperelastic materials with null conditions, global existence of classical solutions with small initial data was proved in R. Agemi (Invent. Math. 142 (2000) 225–250) and T. C. Sideris (Ann. Math. 151 (2000) 849–874) independently. In this paper, we will give some remarks and an alternative proof for it. First, we give the explicit variational structure of nonlinear elastic waves. Thus we can identify whether materials satisfy the null condition by checking the stored energy function directly. Furthermore, by some careful analyses on the nonlinear structure, we show that the Helmholtz projection, which is usually considered to be ill-suited for nonlinear analysis, can be in fact used to show the global existence result. We also improve the amount of Sobolev regularity of initial data, which seems optimal in the framework of classical solutions.

Pressure dependent ultrasonic properties of hcp hafnium metal

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Ramanshu P. Singh ◽  
Shakti Yadav ◽  
Giridhar Mishra ◽  
Devraj Singh
Keyword(s):  
Elastic Constants ◽  
Pressure Range ◽  
Room Temperature ◽  
Ultrasonic Attenuation ◽  
Coupling Constants ◽  
Ultrasonic Properties ◽  
Acoustic Coupling ◽  
Third Order Elastic Constants ◽  
The Stability ◽  
The Given

Abstract The elastic and ultrasonic properties have been evaluated at room temperature between the pressure 0.6 and 10.4 GPa for hexagonal closed packed (hcp) hafnium (Hf) metal. The Lennard-Jones potential model has been used to compute the second and third order elastic constants for Hf. The elastic constants have been utilized to calculate the mechanical constants such as Young’s modulus, bulk modulus, shear modulus, Poisson’s ratio, and Zener anisotropy factor for finding the stability and durability of hcp hafnium metal within the chosen pressure range. The second order elastic constants were also used to compute the ultrasonic velocities along unique axis at different angles for the given pressure range. Further thermophysical properties such as specific heat per unit volume and energy density have been estimated at different pressures. Additionally, ultrasonic Grüneisen parameters and acoustic coupling constants have been found out at room temperature. Finally, the ultrasonic attenuation due to phonon–phonon interaction and thermoelastic mechanisms has been investigated for the chosen hafnium metal. The obtained results have been discussed in correlation with available findings for similar types of hcp metals.

Acoustic Phase Velocity Measurements along General Directions in Non-Isotropic Crystals. I. Elastic Properties of Monoclinic K3Co(CN)6

1971 ◽  
Vol 49 (12) ◽  
pp. 1597-1605 ◽  
Author(s):  
T. H. Chou ◽  
S. L. McBride ◽  
N. Rumin
Keyword(s):  
Elastic Constants ◽  
Experimental Error ◽  
Acoustic Velocity ◽  
Acoustic Energy ◽  
Perturbation Calculation ◽  
Velocity Measurements ◽  
Phase Velocities ◽  
Low Symmetry ◽  
Acoustic Phase

The complete elastic constants tensor of monoclinic potassium cobalticyanide [K3Co(CN)6] has been determined from measured ultrasonic phase velocities. These were obtained as a function of direction in several crystal planes by measuring the acoustic energy reflection coefficient at a liquid–solid interface as a function of angle and plane of incidence. The measurements were made at 27.6 MHz in p-xylene at 21.5 °C. The elastic constants were determined using an existing perturbation method. Velocities calculated from the derived elastic constants are in agreement with the measured velocities to within experimental error and the approximations in the perturbation calculation. The usefulness of this method for the determination of the elastic constants of low symmetry crystals is thus established. The Debye temperature of K3Co(CN)6 is estimated from the results to be 290 ± 10 °K with a corresponding mean acoustic velocity of 2560 ± 80 m/s.

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