Rate of Deformation, Area, Volume, Strain Rate Tensors, Spin Tensor and Convected Time Derivatives of Stress and Strain Tensors

2016 ◽  
pp. 205-238
Keyword(s):  
Strain Rate ◽  
Stress And Strain ◽  
Spin Tensor ◽  
Volume Strain ◽  
Strain Tensors ◽  
Deformation Area ◽  
Derivatives Of

scholarly journals Measurements and Characterization of Turbulence in the Tip Region of an Axial Compressor Rotor

2017 ◽  
Vol 139 (12) ◽  
Author(s):  
Yuanchao Li ◽  
Huang Chen ◽  
Joseph Katz
Keyword(s):  
Strain Rate ◽  
Shear Layer ◽  
Turbulent Flows ◽  
Reynolds Stress ◽  
Suction Side ◽  
Stress And Strain ◽  
Spatial And Temporal Variability ◽  
Mean Flow ◽  
The Mean ◽  
Stress And Strain Rate

Modeling of turbulent flows in axial turbomachines is challenging due to the high spatial and temporal variability in the distribution of the strain rate components, especially in the tip region of rotor blades. High-resolution stereo-particle image velocimetry (SPIV) measurements performed in a refractive index-matched facility in a series of closely spaced planes provide a comprehensive database for determining all the terms in the Reynolds stress and strain rate tensors. Results are also used for calculating the turbulent kinetic energy (TKE) production rate and transport terms by mean flow and turbulence. They elucidate some but not all of the observed phenomena, such as the high anisotropy, high turbulence levels in the vicinity of the tip leakage vortex (TLV) center, and in the shear layer connecting it to the blade suction side (SS) tip corner. The applicability of popular Reynolds stress models based on eddy viscosity is also evaluated by calculating it from the ratio between stress and strain rate components. Results vary substantially, depending on which components are involved, ranging from very large positive to negative values. In some areas, e.g., in the tip gap and around the TLV, the local stresses and strain rates do not appear to be correlated at all. In terms of effect on the mean flow, for most of the tip region, the mean advection terms are much higher than the Reynolds stress spatial gradients, i.e., the flow dynamics is dominated by pressure-driven transport. However, they are of similar magnitude in the shear layer, where modeling would be particularly challenging.

Linear elastic eigenstates of the compliance tensor for trigonal crystals

2000 ◽  
Vol 215 (1) ◽  
pp. 1-9 ◽  
Author(s):  
P.S. Theocaris ◽  
D.P. Sokolis
Keyword(s):  
Strain Energy ◽  
Elastic Strain Energy ◽  
Symmetric Tensor ◽  
Stress And Strain ◽  
Linear Elastic ◽  
Trigonal System ◽  
Compliance Tensor ◽  
Characteristic Values ◽  
Strain Tensors ◽  
Elastic Strain Energy Density

The spectral decomposition of the compliance fourth-rank tensor, representative of a trigonal crystalline or other anisotropic medium, is offered in this paper, and its characteristic values and idempotent fourth-rank tensors are established, with respect to the Cartesian tensor components. Consequently, it is proven that the idempotent tensors serve to analyse the second-rank symmetric tensor space into orthogonal subspaces, resolving the stress and strain tensors for the trigonal medium into their eigentensors, and, finally, decomposing the total elastic strain energy density into distinct, autonomous components. Finally, bounds on the values of the compliance tensor components for the trigonal system, dictated by the classical thermodynamical argument for the elastic potential to be positive definite, are estimated by imposing the characteristic values of the compliance tensor to be strictly positive.

Research on Numerical Algorithm of Constitutive Equation under High Speed Deformation in Hadfield Steel

2012 ◽  
Vol 562-564 ◽  
pp. 688-692 ◽  
Author(s):  
Deng Yue Sun ◽  
Jing Li ◽  
Fu Cheng Zhang ◽  
Feng Chao Liu ◽  
Ming Zhang
Keyword(s):  
High Strain Rate ◽  
Strain Rate ◽  
Deformation Behavior ◽  
High Speed ◽  
High Strain ◽  
Equivalent Stress ◽  
Hadfield Steel ◽  
Stress And Strain ◽  
Strain Rates ◽  
The Finite Element Method

The influence of the strain rate on the plastic deformation of the metals was significant during the high strain rate of loading. However, it was very difficult to obtain high strain rate data (≥ 104 s-1) by experimental techniques. Therefore, the finite element method and iterative method were employed in this study. Numerical simulation was used to characterise the deformation behavior of Hadfield steel during explosion treatment. Base on experimental data, a modified Johnson-Cook equation for Hadfield steel under various strain rate was fitted. The development of two field variables was quantified during explosion hardening: equivalent stress and strain rates.

Experimental uniaxial stress and strain derivatives of the Fermi surface of rhenium

1980 ◽  
Vol 58 (8) ◽  
pp. 1191-1199 ◽  
Author(s):  
E. Fawcett ◽  
F. W. Holroyd ◽  
J. M. Perz
Keyword(s):  
Fermi Surface ◽  
Uniaxial Stress ◽  
Stress And Strain ◽  
Strong Anisotropy ◽  
Quantum Oscillations ◽  
Band Structure Calculations ◽  
Landau Quantum ◽  
Derivatives Of ◽  
Structure Calculations ◽  
The Magnetic Field

The derivatives of the areas of extremal orbits on all the small sheets of the Fermi surface of rhenium, with respect to stress and strain along the hexad axis, have been determined from simultaneous measurements of Landau quantum oscillations in magnetostriction and torque, and also in sound velocity and torque. Strong anisotropy is observed in the stress derivatives of orbits in zones five and six as the direction of the magnetic field defining the normal to the orbit is varied; the anisotropy is most pronounced for orbits which come close to the line of degeneracy AL on the hexagonal Brillouin zone face. The derivatives of the small void in zone eight are found to be very large; this is consistent with the results of band structure calculations which show that this feature of the Fermi surface is very sensitive to small changes in the Fermi energy. Cyclotron effective masses for a number of orbits on the void have also been measured.

MATHEMATICAL MODEL OF MATERIALS OF STRUCTURES AND ELEMENTS OF RESTORED SOIL DAMS FOR NUMERICAL CALCULATIONS

2021 ◽  
pp. 46-51
Author(s):  
V. YA. ZHARNITSKIY ◽  
◽  
A. P. SMIRNOV
Keyword(s):  
Negative Impact ◽  
Emergency Situation ◽  
Numerical Calculations ◽  
Stress And Strain ◽  
Operational Parameters ◽  
Reliable Operation ◽  
Operational Factors ◽  
Materials Used ◽  
Technical Operation ◽  
Strain Tensors

Identified in the process of analyzing the operation of the structure, in the conditions of its operation, allow to assess the actual reserves of the bearing capacity of the structure and take effective measures to restore the operational parameters. The main criteria influencing the choice of mathematical models of materials for structures and elements of soil dams are more consistent with the model of the equation of state connecting the components of stress and strain tensors, as well as the rate of their change, which are obtained and tested for numerical calculations and have a full set of constants for materials used in the calculations of earth dams, the choice of their structures (concrete,reinforced concrete, soils, etc.). Reliable operation of soil dams is possible only if all proper conditions are met. The causes of dam accidents and their damage must be known not only to eliminate errors at the design and construction stages, but also during their operation. In order to exclude the negative impact of operational factors on the safety of soil HTS, it is necessary not only to strictly observe the rules of technical operation and take measures to exclude the possibility of an emergency situation during technological operations at facilities, but also to have methods for predictive justification of the restoration of strength and operational indicators of structures and elements of soil dams.

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