scholarly journals On reflected and transmitted stress waves at an elastic-plastic boundary

1980 ◽  
Vol 15 (1) ◽  
pp. 15-20 ◽  
Author(s):  
A S Khan
Keyword(s):  
Wave Theory ◽  
Finite Amplitude ◽  
Stress Waves ◽  
Constitutive Relationship ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Linear Elastic ◽  
Transmitted Waves ◽  
The One ◽  
Dynamic Plastic Deformation

A theoretical analysis for the reflected and transmitted waves at an elastic-plastic boundary is presented. The basis of this analysis is the linear elastic wave theory in a hard load-bar and the one-dimensional, strain-rate-independent theory of finite-amplitude plastic waves in a soft specimen. The constitutive relationship during dynamic plastic deformation is an experimentally determined dynamic response function in the soft material. The analysis predicts results that agree very closely with experimental results.

scholarly journals On sound waves of finite amplitude

1953 ◽  
Vol 216 (1127) ◽  
pp. 539-547 ◽  
Keyword(s):  
Integral Equation ◽  
Analytical Solution ◽  
Arbitrary Function ◽  
Initial Conditions ◽  
Finite Amplitude ◽  
Sound Waves ◽  
One Dimensional ◽  
The One ◽  
Complex Integral ◽  
Gas Cloud

An analytical solution of Riemann’s equations for the one-dimensional propagation of sound waves of finite amplitude in a gas obeying the adiabatic law p = k ρ γ is obtained for any value of the parameter γ. The solution is in the form of a complex integral involving an arbitrary function which is found from the initial conditions by solving a generalization of Abel’s integral equation. The results are applied to the problem of the expansion of a gas cloud into a vacuum.

scholarly journals Shock Initiation of a Satellite Tank under Debris Hypervelocity Impact

2019 ◽  
Vol 9 (19) ◽  
pp. 3957
Author(s):  
Zhao ◽  
Zhao ◽  
Cui ◽  
Wang
Keyword(s):  
Shock Wave ◽  
Power Density ◽  
Wave Theory ◽  
Hypervelocity Impact ◽  
Shock Initiation ◽  
One Dimensional ◽  
Minimum Power ◽  
Shock Wave Pressure ◽  
The One ◽  
Debris Impact

For the risk assessment of a satellite to determine whether the satellite tank explodes under the hypervelocity impact, the Walker–Wasley criterion is selected to predict the shock initiation of the satellite tank. Then, the minimum power density of liquid hydrazine is determined based on the tests, the expressions of shock wave pressure and pressure duration are constructed based on the one-dimensional wave theory, and the initiation criterion for the liquid hydrazine tank is established. Finally, numerical simulation and the initiation criterion are adopted to calculate the power density in the satellite tank under the debris impact at the velocity of 10 km/s. The calculated power density agrees well with the simulated power density, they are both larger than the minimum power density, demonstrating that the shock wave generated by the hypervelocity impact is sufficient to trigger an explosion in the satellite tank.

VERIFICATION OF THE SHB TEST RESULTS BASED ON THE ONE-DIMENSIONAL STRESS WAVE THEORY

2008 ◽  
Vol 22 (09n11) ◽  
pp. 1068-1073
Author(s):  
TOMOKAZU MASUDA ◽  
KENJI SAITO ◽  
IZUMI MORITA ◽  
SHUSHI IKEDA ◽  
KOICHI MAKII ◽  
...  
Keyword(s):  
Strain Rate ◽  
Stress Wave ◽  
High Speed ◽  
Wave Theory ◽  
High Speed Photography ◽  
Strain Rates ◽  
One Dimensional ◽  
Strain And Strain Rate ◽  
Deformation Behaviors ◽  
The One

In order to evaluate dynamic deformation behaviors under high strain rates, Kobe Steel has developed and applied a Split-Hopkinson Bar (SHB) apparatus. This paper discusses the validity of the strain measurements and strain rates measured by this SHB apparatus. The strain waves that propagated in the incident and transmitted bars and the specimen are captured using a high-resolution type high-speed photography in detail. The strain wave propagated many times in the incident and transmitted bars and the specimen when the specimen was not broken. The amount of the deformation of the specimen decreases with the propagation frequency of the incident wave. On the other hand, to improve accuracy at the strain and strain rate calculated by the one-dimensional stress wave theory, Young's modulus, the longitudinal wave speed, and the density were accurately determined. It was understood that the calculation value showed the strain and strain rate captured with the high-speed photography are a good agreement. As a result, the validity of the measurement accuracy of this SHB could be shown.

Modified spin-wave theory applied to one-dimensional Heisenberg ferromagnet with the nearest-neighbor and next-nearest-neighbor exchange anisotropies

2019 ◽  
Vol 33 (11) ◽  
pp. 1950106
Author(s):  
Yun Liao ◽  
Yuan Chen ◽  
Ji Pei Chen ◽  
Wen An Li
Keyword(s):  
Low Temperature ◽  
Specific Heat ◽  
Spin Wave ◽  
Nearest Neighbor ◽  
Wave Theory ◽  
Heisenberg Ferromagnet ◽  
Thermodynamic Quantities ◽  
One Dimensional ◽  
Spin Wave Theory ◽  
The One

The modified spin-wave theory is used to investigate the one-dimensional Heisenberg ferromagnet with the nearest-neighbor (NN) and next-nearest-neighbor (NNN) exchange anisotropies. The ground-state and low-temperature properties of the system are studied within the self-consistent method. It is found that the effect of the NN anisotropy on the thermodynamic quantities is stronger than that of the NNN anisotropy in the low-temperature region. The anisotropy dependence behaviors (such as the power, exponential and linear laws) are obtained for the position and the height of the maximum of the specific heat and its coefficient, as well as the susceptibility coefficient. The specific heat and its coefficient both display the low-temperature double maxima which are induced by the anisotropies and the NNN interaction. In the very low temperatures the specific heat and the susceptibility behave severally as T[Formula: see text] and T[Formula: see text] at the critical point J2/J1 = −0.25, where J1 and J2 are the NN and NNN interactions, respectively.

Study of Stress Wave Propagation in SHPB with NHDMOC

2013 ◽  
Vol 444-445 ◽  
pp. 158-162
Author(s):  
Ming Li Xu ◽  
Guang Ying Zhang ◽  
Ruo Qi Zhang
Keyword(s):  
Wave Propagation ◽  
Stress Wave ◽  
Elastic Stress ◽  
Constitutive Relationship ◽  
Stress Wave Propagation ◽  
One Dimensional ◽  
Elastic Bar ◽  
The One ◽  
Dispersion And Attenuation ◽  
Elastic Stress Wave

In this paper the NHDMOC method which succeeded in studying stress wave propagation with one dimensional strain was applied to study the one-dimensional stress wave propagation. In this paper, the ZWT nonlinear visco-elastic constitutive relationship with 7 parameters to NHDMOC, and corresponding equations were deduced The equations was verified from the comparison of elastic stress wave propagation in SHPB with elastic bar and visco-elastic bar respectively. Finally the dispersion and attenuation of stress wave in SHPB with visco-elastic bar was studied.

Determination of the Unloading Boundary in Longitudinal Elastic-Plastic Stress Wave Propagation

1971 ◽  
Vol 38 (4) ◽  
pp. 888-894 ◽  
Author(s):  
P. A. Tuschak ◽  
A. B. Schultz
Keyword(s):  
Wave Propagation ◽  
Moving Boundary ◽  
Stress Waves ◽  
Stress Wave Propagation ◽  
Initial Portion ◽  
One Dimensional ◽  
Elastic Plastic ◽  
In Series ◽  
Plastic Stress

For several types of excitation of one-dimensional elastic-plastic stress waves in a rod, unloading waves propagate which interact with the loading waves. The moving boundary at which this interaction occurs is the unloading boundary. A knowledge of the location of this boundary and the behavior exhibited on it is necessary for the solution of wave-propagation problems of this kind. A technique is presented to obtain an arbitrary number of terms in series expressions describing the response in semi-infinite rods. Several examples, including finite mass impact of the rod, are given to illustrate the use of the technique. The technique will determine the initial portion of the boundary in a finite length rod.

An Analysis of Longitudinal Elastic-Plastic Pulse Propagation

1966 ◽  
Vol 33 (2) ◽  
pp. 248-255 ◽  
Author(s):  
R. J. Clifton ◽  
S. R. Bodner
Keyword(s):  
Pulse Propagation ◽  
Pure Aluminum ◽  
General Shape ◽  
Stress Strain ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Strain Behavior ◽  
Commercially Pure ◽  
Strain Axis ◽  
The One

The one-dimensional, rate-independent theory of elastic-plastic wave propagation for smooth stress-strain curves concave toward the strain axis is applied to the problem of a long uniform bar loaded at one end by a pressure pulse of short duration. The essential features of the solution are obtained for the case of a semi-infinite bar and for the case of a finite bar whose other end is stress-free by using the method of characteristics in the t-x plane. The general shape of boundaries in the t-x plane which separate regions governed by the dynamic elastic equations from regions governed by the dynamic plastic equations is presented. The nature of the discontinuities that occur at these boundaries is also discussed. For the finite-bar case the analysis is given for materials which exhibit isotropic work hardening and for materials for which the stress-strain behavior in tension is independent of any previous compression. The main features of the solution are in agreement with the behavior observed for annealed, commercially pure aluminum bars subjected to explosive loading at one end. These experiments will be reported subsequently.

Influence of next-nearest neighbor interaction on low temperature properties of the spin-1/2 one-dimensional ferromagnetic XY model

2015 ◽  
Vol 29 (31) ◽  
pp. 1550225 ◽  
Author(s):  
Songqiu Yin ◽  
Yuan Chen
Keyword(s):  
Low Temperature ◽  
Specific Heat ◽  
Spin Wave ◽  
Nearest Neighbor ◽  
Wave Theory ◽  
Xy Model ◽  
Neighbor Interaction ◽  
One Dimensional ◽  
Spin Wave Theory ◽  
The One

In this paper, we apply spin-wave theory to the one-dimensional spin-1/2 ferromagnetic XY model with the next-nearest neighbor interaction. The thermodynamic divergences which the conventional spin-wave theory encounters with, are solved by implementing Takahashi’s idea through introducing a Lagrange multiplier in the Hamiltonian to keep zero magnetization. It is shown that the next-nearest neighbor interaction has an influence on the ground-state and low temperature properties of the system. The exponential laws which are induced by the next-nearest neighbor interaction, are found for heights of maxima of the specific heat and its coefficient, as well as the maximum and minimum of the susceptibility coefficient. The maximum positions of the specific heat and its coefficient fit well to the linear and exponential laws under the next-nearest neighbor interaction, respectively.

Low-temperature thermodynamic properties of the Heisenberg antiferromagnetic chain with two easy-axis single-ion anisotropies

2021 ◽  
pp. 2150182
Author(s):  
Yuan Chen ◽  
Yun Liao ◽  
Wenan Li
Keyword(s):  
Low Temperature ◽  
Quantum Monte Carlo ◽  
Easy Axis ◽  
Wave Theory ◽  
Zero Temperature ◽  
Monte Carlo Data ◽  
One Dimensional ◽  
Disorder Phase Transition ◽  
The One ◽  
Small Anisotropy

In this paper, the spin wave theory is applied to the one-dimensional Heisenberg antiferromagnet in the coexistence of two different anisotropies [Formula: see text] and [Formula: see text], which are separately the easy-axis single-ion anisotropies for sublattice [Formula: see text] and sublattice [Formula: see text] of the system. Both the ground-state and low-temperature properties of the system are strongly affected by the competition between these two anisotropies. Two kinds of the competition in terms of the deviation parameter [Formula: see text] are discussed for the uniform anisotropy taking the values of [Formula: see text] and [Formula: see text], respectively. The [Formula: see text]-dependent behaviors (such as the power, exponential and linear laws) are obtained for the total magnetization, the staggered magnetizations, the internal energy, the specific heat and the susceptibility. It is found that at zero-temperature, the interplay between these two anisotropies induces the antiferromagnetic-disorder phase transition in the small anisotropy region with [Formula: see text]. For the selected cases of [Formula: see text], our results for are in agreement with the findings obtained by the existing theories and the quantum Monte Carlo data.

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