Plane Waves in an Elastic-Plastic Half-Space Due to Combined Surface Pressure and Shear

1966 ◽  
Vol 33 (1) ◽  
pp. 149-158 ◽  
Author(s):  
H. H. Bleich ◽  
Ivan Nelson
Keyword(s):  
Wave Propagation ◽  
Differential Equations ◽  
Half Space ◽  
Nonlinear Differential Equations ◽  
Plane Waves ◽  
Yield Condition ◽  
Shear Stresses ◽  
Von Mises ◽  
Plane Wave Propagation ◽  
Normal And Shear Stresses

The most general case of plane wave propagation, when normal and shear stresses occur simultaneously, is considered in a material obeying the von Mises yield condition. The resulting nonlinear differential equations have not been solved previously for any boundary-value problem, except for special situations where the differential equations degenerate into linear ones. In the present paper, the stresses in a half-space, due to a uniformly distributed step load of pressure and shear on the surface, are obtained in closed form.

Plane Waves Due to Combined Compressive and Shear Stresses in a Half Space

1969 ◽  
Vol 36 (2) ◽  
pp. 189-197 ◽  
Author(s):  
T. C. T. Ting ◽  
Ning Nan
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Half Space ◽  
Plastic Material ◽  
Plane Waves ◽  
Shear Stresses ◽  
Elastic Plastic ◽  
Elastic Plastic Material ◽  
Plane Wave Propagation

The plane wave propagation in a half space due to a uniformly distributed step load of pressure and shear on the surface was first studied by Bleich and Nelson. The material in the half space was assumed to be elastic-ideally plastic. In this paper, we study the same problem for a general elastic-plastic material. The half space can be initially prestressed. The results can be extended to the case in which the loads on the surface are not necessarily step loads, but with a restricting relation between the pressure and the shear stresses.

An Experimental Investigation of the Yield Loci of 1100-0 Aluminum, 70:30 Brass, and an Overaged 2024 Aluminum Alloy After Various Prestrains

1986 ◽  
Vol 108 (4) ◽  
pp. 313-320 ◽  
Author(s):  
D. E. Helling ◽  
A. K. Miller ◽  
M. G. Stout
Keyword(s):  
Aluminum Alloy ◽  
Small Strain ◽  
Yield Locus ◽  
Material Behavior ◽  
Shear Stresses ◽  
2024 Aluminum Alloy ◽  
Yield Loci ◽  
Aluminum Alloy 2024 ◽  
Von Mises ◽  
Normal And Shear Stresses

The multiaxial yield behaviors of 1100-0 aluminum, 70:30 brass, and an overaged 2024 aluminum alloy (2024-T7) have been investigated for a variety of prestress histories involving combinations of normal and shear stresses. Von Mises effective prestrains were in the range of 1.2–32%. Prestress paths were chosen in order to investigate the roles of prestress and prestrain direction on the nature of small-strain offset (ε = 5 × 10−6) yield loci. Particular attention was paid to the directionality, i.e., translation and distortion, of the yield locus. A key result, which was observed in all three materials, was that the final direction of the prestrain path strongly influences the distortions of the yield loci. Differences in the yield locus behavior of the three materials were also observed: brass and the 2024-T7 alloy showed more severe distortions of the yield locus and a longer memory of their entire prestrain history than the 1100-0 aluminum. In addition, more “kinematic” translation of the subsequent yield loci was observed in brass and 2024-T7 than in 1100-0 aluminum. The 2024-T7 differed from the other materials, showing a yield locus which decreased in size subsequent to plastic straining. Finally, the implications of these observations for the constitutive modeling of multiaxial material behavior are discussed.

scholarly journals Numerical Study of Lorentz Force Interaction with Micro Structure in Channel Flow

Energies ◽  
2021 ◽  
Vol 14 (14) ◽  
pp. 4286
Author(s):  
Shabbir Ahmad ◽  
Kashif Ali ◽  
Sohail Ahmad ◽  
Jianchao Cai
Keyword(s):  
Heat Transfer ◽  
Differential Equations ◽  
Viscous Dissipation ◽  
Numerical Study ◽  
Nonlinear Differential Equations ◽  
Thermal Control ◽  
Shear Stresses ◽  
Fluid Temperature ◽  
X Rays ◽  
Micro Particles

The heat transfer Magnetohydrodynamics flows have been potentially used to enhance the thermal characteristics of several systems such as heat exchangers, electromagnetic casting, adjusting blood flow, X-rays, magnetic drug treatment, cooling of nuclear reactors, and magnetic devices for cell separation. Our concern in this article is to numerically investigate the flow of an incompressible Magnetohydrodynamics micropolar fluid with heat transportation through a channel having porous walls. By employing the suitable dimensionless coordinates, the flow model equations are converted into a nonlinear system of dimensionless ordinary differential equations, which are then numerically treated for different preeminent parameters with the help of quasi-linearization. The system of complex nonlinear differential equations can efficiently be solved using this technique. Impact of the problem parameters for microrotation, temperature, and velocity are interpreted and discussed through tables and graphs. The present numerical results are compared with those presented in previous literature and examined to be in good contact with them. It has been noted that the imposed magnetic field acts as a frictional force which not only increases the shear stresses and heat transfer rates at the channel walls, but also tends to rotate the micro particles in the fluid more rapidly. Furthermore, viscous dissipation may raise fluid temperature to such a level that the possibility of thermal reversal exists, at the geometric boundaries of the domain. It is therefore recommended that external magnetic fields and viscous dissipation effects may be considered with caution in applications where thermal control is required.

Examination of the Stress Distribution in the Tip of a Pencil

2005 ◽  
Vol 73 (2) ◽  
pp. 335-337
Author(s):  
E. Pogozelski ◽  
D. Cole ◽  
M. Wesley
Keyword(s):  
Stress Distribution ◽  
Fracture Surface ◽  
Initial Position ◽  
Von Mises Stress ◽  
Shear Stresses ◽  
Worst Case ◽  
Position And Orientation ◽  
Von Mises ◽  
The Impact ◽  
Normal And Shear Stresses

The stresses within the tip of a pencil are examined theoretically, numerically, and experimentally to determine the position and orientation of the fracture surface. The von Mises stress is used to evaluate the impact of the normal and shear stresses due to compression, bending, torsion, and shear. The worst-case stress is shown to occur along the top edge of the inclined pencil point, where the normal stress is compressive. The resulting crack propagates diagonally downwards and towards the tip from this initial position, and is frequently observed to contain a cusp.

The Method of Generalized Ray-Revisited

2000 ◽  
Vol 16 (1) ◽  
pp. 37-44
Author(s):  
Franz Ziegler ◽  
Piotr Borejko
Keyword(s):  
Wave Propagation ◽  
Parallel Computing ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Plane Waves ◽  
Solution Technique ◽  
New Developments ◽  
Infinite Space ◽  
Layered Half Space

ABSTRACTBased on a landmark paper by Pao and Gajewski, some novel developments of the method of generalized ray integrals are discussed. The expansion of the dynamic Green's function of the infinite space into plane waves allows benchmark 3-D solutions in the layered half-space and even enters the background formulation of elastic-viscoplastic wave propagation. New developments of software of combined symbolic-numerical manipulation and parallel computing make the method a competitive solution technique.

scholarly journals Temporal Frequency Spread of Plane Wave Propagation through Moderate to Strong Turbulence

2019 ◽  
Vol 8 (2S8) ◽  
pp. 1944-1947
Keyword(s):  
Wave Propagation ◽  
Temporal Frequency ◽  
Plane Waves ◽  
Energy Regulation ◽  
Anisotropic Component ◽  
Frequency Spread ◽  
Strong Turbulence ◽  
Kolmogorov Turbulence ◽  
Simulation Results ◽  
Plane Wave Propagation

In this study, we derive new expressions for the atmospheric-brought on frequency unfold of plane waves propagating thru slight to strong turbulence in a horizontal direction based on the modified anisotropic non-Kolmogorov electricity spectrum as antagonistic to conventional Kolmogorov electricity spectrum. The energy regulation price varies from three to 4 instead of the traditional Kolmogorov power law price; the general amplitude price differs from the conventional Kolmogorov regular cost 0.033. these new expressions are based on slight to robust fluctuation vicinity and anisotropic non-Kolmogorov turbulence. The simulation results show that temporal frequency unfold will decrease even as the anisotropic component   2  is increasing

scholarly journals Plane wave propagation in a 3D anisotropic half-space under Green-Naghdi theory II

2016 ◽  
Vol 2 (2) ◽  
pp. 114-134 ◽  
Author(s):  
N. Sarkar ◽  
S. Chakraborty ◽  
S. C. Mandal ◽  
A. K. Das ◽  
A. Lahiri
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Half Space ◽  
Plane Wave Propagation

REFLECTION OF PLANE WAVES FROM A LINEAR TRANSITION LAYER IN LIQUID MEDIA

Geophysics ◽  
1965 ◽  
Vol 30 (1) ◽  
pp. 122-132 ◽  
Author(s):  
Ravindra N. Gupta
Keyword(s):  
Wave Propagation ◽  
Bulk Modulus ◽  
Transition Layer ◽  
Plane Waves ◽  
Reflection Coefficients ◽  
Liquid Media ◽  
Approximation Solution ◽  
High Frequencies ◽  
First Order ◽  
Plane Wave Propagation

It is shown that care should be taken in using the term “velocity” in connection with wave propagation in inhomogeneous media. An expression is derived for phase velocity which depends on frequency and depth. Exact solutions are found for normal and oblique incidence, for plane‐wave propagation in a liquid medium in which density, ρ, and bulk modulus, λ, vary as follows: [Formula: see text] and [Formula: see text] where [Formula: see text], [Formula: see text], b, and p are arbitrary constants. It is shown that the geometrical optics approximation solution, valid for high frequencies, is the first term in an asymptotic expansion of the exact solution. The reflection coefficients are obtained for a linear transition layer between two homogeneous half‐spaces. Both first‐order and second‐order discontinuities in density and bulk modulus are considered at the boundaries of the transition layer.

General theorems relating to wave propagation governed by self-adjoint and Hermitian self-adjoint differential operators of order 2r

1978 ◽  
Vol 360 (1701) ◽  
pp. 279-300 ◽  
Keyword(s):  
Wave Propagation ◽  
Differential Equations ◽  
Free Space ◽  
Differential Operators ◽  
Plane Waves ◽  
Symmetric Matrices ◽  
Canonical Forms ◽  
Orthogonal Matrices ◽  
Transmission Coefficients

When plane waves are partly reflected and transmitted from a medium differing from free space, various conditions ensure the existence of simple identities between the reflexion and transmission coefficients. When differential equations of order In govern wave propagation, conditions to be placed both upon the generalized medium and upon the generalized waves are investigated so as to ensure the existence of exact analogues to these elementary identities. The theory is developed in terms of selfadjoint and Hermitian self-adjoint differential operators of order 2 The results fallout from the canonical forms for various skew-Hermitian and skew-symmetric matrices J with complex elements, unitary and orthogonal matrices being found so that J should be unitarily and/or orthogonally similar to its appropriate canonical forms.

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