Elastic-Plastic Plane Waves With Combined Compressive and Two Shear Stresses in a Half Space

1971 ◽  
Vol 38 (4) ◽  
pp. 895-898 ◽  
Author(s):  
R. P. Goel ◽  
L. E. Malvern
Keyword(s):  
Half Space ◽  
Plane Waves ◽  
Simple Wave ◽  
Isotropic Hardening ◽  
Shear Stresses ◽  
Fast Wave ◽  
Hardening Material ◽  
Shear Wave Speed ◽  
Wave Solutions ◽  
Radial Loading

The simple wave solutions with one compression and two shear impact loadings on the boundary of a half space of isotropic hardening material are obtained. Both the fast simple wave and slow simple wave solutions imply a radial loading projection in the τ2, τ3 plane; i.e., in the plane of shear stress components. But the radial loading τ3/τ2 ratio for the fast wave may be different from the ratio for the slow wave. The transition is accompanied by jumps both in τ2 and τ3 traveling at the elastic shear wave speed c2.

Biaxial Plastic Simple Waves With Combined Kinematic and Isotropic Hardening

1970 ◽  
Vol 37 (4) ◽  
pp. 1100-1106 ◽  
Author(s):  
R. P. Goel ◽  
L. E. Malvern
Keyword(s):  
Wave Speed ◽  
Cylindrical Tube ◽  
Simple Wave ◽  
Isotropic Hardening ◽  
Hardening Material ◽  
One Dimensional ◽  
Shear Wave Speed ◽  
Simple Waves ◽  
Thin Walled ◽  
Elastic Shear

The study of one-dimensional combined longitudinal and torsional plastic wave propagation in a thin-walled cylindrical tube of isotropic-hardening material was first carried out by Clifton. In this paper, the same problem is studied for a combined kinematic and isotropic hardening material. Simple wave solutions are obtained. In some cases, a discontinuity in shear stress occurs, propagating at the elastic shear-wave speed c2, followed by a slow plastic simple wave.

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.

One wave: plane or curved

Optics f2f ◽  
2018 ◽  
pp. 15-32
Author(s):  
Charles S. Adams ◽  
Ifan G. Hughes
Keyword(s):  
Wave Front ◽  
Plane Waves ◽  
Simple Wave ◽  
Spherical Waves ◽  
Wave Solutions ◽  
Front Curvature

This chapter reviews simple wave solutions, in particular plane waves and spherical waves. The behaviour of plane waves inside a medium and at an interface is considered. The chapter concludes with a discussion of how lenses change the wave-front curvature.

scholarly journals Weighted Residual Method for Diffraction of Plane P-Waves in a 2D Elastic Half-Space Revisited: On an Almost Circular Arbitrary-Shaped Canyon

2015 ◽  
Vol 2015 ◽  
pp. 1-21 ◽  
Author(s):  
Vincent W. Lee ◽  
Heather P. Brandow
Keyword(s):  
Half Space ◽  
Plane Waves ◽  
Classical Problem ◽  
Strong Motion ◽  
Elastic Half Space ◽  
Shear Stresses ◽  
Weighted Residual Method ◽  
P Waves ◽  
Closed Form Solutions ◽  
P And Sv Waves

Scattering and diffraction of elastic in-plane P- and SV-waves by a surface topography such as an elastic canyon at the surface of a half-space is a classical problem which has been studied by earthquake engineers and strong-motion seismologists for over forty years. The case of out-of-plane SH-waves on the same elastic canyon that is semicircular in shape on the half-space surface is the first such problem that was solved by analytic closed-form solutions over forty years ago by Trifunac. The corresponding case of in-plane P- and SV-waves on the same circular canyon is a much more complicated problem because the in-plane P- and SV-scattered-waves have different wave speeds and together they must have zero normal and shear stresses at the half-space surface. It is not until recently in 2014 that analytic solution for such problem is found by the author in the work of Lee and Liu. This paper uses the technique of Lee and Liu of defining these stress-free scattered waves to solve the problem of the scattering and diffraction of these in-plane waves on an on an almost-circular surface canyon that is arbitrary in shape.

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.

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