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.

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.

The Elastic-Plastic Boundary in One-Dimensional Wave Propagation

1968 ◽  
Vol 35 (4) ◽  
pp. 812-814 ◽  
Author(s):  
R. J. Clifton ◽  
T. C. T. Ting
Keyword(s):  
Wave Propagation ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Dimensional Wave

Error Bounds on Elastic-Plastic Strain Wave Measurements

1971 ◽  
Vol 93 (4) ◽  
pp. 478-480 ◽  
Author(s):  
J. G. Wagner
Keyword(s):  
Wave Propagation ◽  
Plastic Strain ◽  
Lower Bounds ◽  
Upper And Lower Bounds ◽  
Strain Wave ◽  
One Dimensional ◽  
Elastic Plastic ◽  
Strain Behavior ◽  
Wave Measurements ◽  
Dimensional Wave

Bounds are established on the errors associated with elastic-plastic strain wave measurements involving finite gage lengths. Attention is restricted to the case of one-dimensional wave propagation in a semi-infinite bar. A bi-linear model of the stress-strain behavior provides a means of calculating realistic upper and lower bounds on the relative error of amplitude measurements. Rise time errors are also discussed and illustrated.

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