Elastic-Plastic Boundaries in Combined Longitudinal and Torsional Plastic Wave Propagation

1968 ◽  
Vol 35 (4) ◽  
pp. 782-786 ◽  
Author(s):  
R. J. Clifton
Keyword(s):  
Wave Propagation ◽  
Time Derivative ◽  
Plastic Wave ◽  
Wave Speeds ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Simple Waves ◽  
Thin Walled Tube ◽  
Loading And Unloading ◽  
All Speeds

Assuming a one-dimensional rate independent theory of combined longitudinal and torsional plastic wave propagation in a thin-walled tube, restrictions are obtained on the possible speeds of elastic-plastic boundaries. These restrictions are shown to depend on the type of discontinuity at the boundary and on whether loading or unloading is occurring. The range of unloading (loading) wave speeds for the case when the nth time derivative of the solution is the first derivative that is discontinuous across the boundary is the complement of the range of unloading (loading) wave speeds for the case when the first discontinuity is in the (n + 1)th time derivative. Thus all speeds are possible for elastic-plastic boundaries corresponding to either loading or unloading. The general features of the discontinuities associated with loading and unloading boundaries are established, and examples are presented of unloading boundaries overtaking simple waves.

Plastic Wave Propagation in Linearly Work-Hardening Materials

1973 ◽  
Vol 40 (4) ◽  
pp. 1045-1049 ◽  
Author(s):  
T. C. T. Ting
Keyword(s):  
Work Hardening ◽  
Wave Speed ◽  
Plane Waves ◽  
Plastic Wave ◽  
Combined Stress ◽  
Hardening Material ◽  
One Dimensional ◽  
Simple Waves ◽  
Torsional Waves ◽  
Thin Walled Tube

The combined longitudinal and torsional waves in a linearly work-hardening thin-walled tube are studied. Explicit solutions are obtained for the stress paths in the stress space for the simple waves. The stress paths are all “similar”, and hence a proportionality property in the solutions exists for simple waves as well as for a more general initial and boundary-value problem. The same results apply to any type of plane waves of combined stress. Thus the “linearity” in the solutions of one-dimensional plastic waves in a thin rod of a linearly work-hardening material is not completely lost in the solutions of combined stress waves. Depending on whether the plastic wave speed cp is larger, equal, or smaller than c2, the nature of the solutions to a given combined stress wave problem can be quite different. Examples are given to illustrate this point.

On the Initial Speed of Elastic-Plastic Boundaries in Longitudinal Wave Propagation in a Rod

1971 ◽  
Vol 38 (2) ◽  
pp. 441-447 ◽  
Author(s):  
T. C. T. Ting
Keyword(s):  
Wave Propagation ◽  
Numerical Solution ◽  
Longitudinal Wave ◽  
Time Derivative ◽  
Initial Speed ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Before And After ◽  
Longitudinal Wave Propagation ◽  
Dimensional Wave

A study is given of elastic-plastic boundaries which start at the end x = 0 of a rod in one-dimensional wave propagation. The initial speed of the elastic-plastic boundaries at x = 0 and at any time, say t = t0, is determined analytically for all possible combinations of the time derivative σt of the stress σ(0, t) before and after t = t0. If σt at x = 0 is continuous and vanishes at t = t0, all possible combinations of σtt before and after t = t0 are considered. The analysis also gives the number of regions involved, the derivatives in each region, and distinguishes elastic regions from plastic regions. These are useful guides for a numerical solution of general initial and boundary-value problems.

scholarly journals Extension of the Hodograph Method for the One-Dimensional Elastic-Plastic Wave Propagation

1973 ◽  
Vol 16 (93) ◽  
pp. 492-502
Author(s):  
Hiroya MURAKAMI ◽  
Tadao MURATA ◽  
Takashi JIMMA
Keyword(s):  
Wave Propagation ◽  
Plastic Wave ◽  
Hodograph Method ◽  
One Dimensional ◽  
Elastic Plastic ◽  
The One

Constitutive Models for Wave Propagation in Soils

2006 ◽  
Vol 59 (3) ◽  
pp. 146-175 ◽  
Author(s):  
Frederick Bloom
Keyword(s):  
Wave Propagation ◽  
Entire Range ◽  
Constitutive Models ◽  
Volume Distribution ◽  
Single Model ◽  
Function Model ◽  
Material Models ◽  
Elastic Plastic ◽  
Variable Modulus ◽  
Loading And Unloading

A survey is provided of the various constitutive models that have been used to study the phenomena of wave propagation in soils. While different material models have been proposed for the response of soils, it is now generally understood that no single model may be used over the entire range of pressures which are typically studied. The constitutive models reviewed in this paper include a number of effective stress and multiphase models, the volume distribution function model, and various versions of the P−α model. Also discussed are classical elastic-plastic models, models possessing different elastic constants in loading and unloading, variable modulus models, and capped elastic-plastic models.

scholarly journals Analysis of Longitudinal Elastic-Plastic Wave Propagation Using Hodograph

1972 ◽  
Vol 38 (311) ◽  
pp. 1721-1730
Author(s):  
Hiroya MURAKAMI ◽  
Tadao MUROTA ◽  
Takashi JIMMA
Keyword(s):  
Wave Propagation ◽  
Plastic Wave ◽  
Elastic Plastic

Mechanical behaviour of austenitic steel and aluminium with respect to elastic-plastic wave propagation

1987 ◽  
Vol 58 (1) ◽  
pp. 33-39 ◽  
Author(s):  
Essam El-Magd ◽  
Karl-Josef Hellwig ◽  
Hans-Günter Höck ◽  
Mohamad Homayun
Keyword(s):  
Wave Propagation ◽  
Austenitic Steel ◽  
Mechanical Behaviour ◽  
Plastic Wave ◽  
Elastic Plastic
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