 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
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| V. N. Kukudzhanov, "Wave propagation in elastic-viscoplastic materials with a general stress-strain diagram," Mech. Solids. 36 (5), 75-88 (2001) |
| Year |
2001 |
Volume |
36 |
Number |
5 |
Pages |
75-88 |
| Title |
Wave propagation in elastic-viscoplastic materials with a general stress-strain diagram |
| Author(s) |
V. N. Kukudzhanov (Moscow) |
| Abstract |
We investigate propagation of stress waves in bars of an elastic-viscoplastic
material whose stress-strain curve may drop on some segments.
In previous works of the author, an asymptotic method has been developed for
solving boundary value problems of wave propagation in elastic-plastic media.
This method takes into account additional terms with small parameters
and has been used for solving some problems of wave propagation in
semi-infinite bars [1,2].
In the present paper, this method of matching slowly and rapidly varying
solutions is extended to the general case of boundary conditions and
materials whose diagram contains segments corresponding to softening.
It is shown that for elastic-viscoplastic media with softening,
there is a new boundary effect, absent in the case of hardening materials.
We also describe numerical results obtained by difference schemes
developed specifically for stiff systems of hyperbolic equations [3, 4].
These results confirm the conclusions made on the basis of the asymptotic solution.
It is shown that the strain field in a thin bar near
its end subjected to impact is determined not by the strain rate influence [5]
but by the presence in the stress-strain diagram of a segment
that corresponds to softening
at the stage prior to fracture. It is only for impacts with velocities
v≥v0 sufficient for the strain at the end of the bar to exceed the
value εh corresponding to the ultimate strength of the static
diagram that a strain localization region appears at the end of the bar
instead of a plateau (the region of constant distribution characteristic
of hardening materials), with the distribution having a mushroom-cap
shape.
We also study how softening affects propagation of pulses of
large (t0»τ) and medium (t0~10τ) duration and how it
affects spallation produced by such pulses in colliding bars. |
| References |
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| 2. | V. N. Kukudzhanov, "Investigation of shock waves structure in
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| 3. | V. N. Kukudzhanov, Finite-Difference Methods in Problems of
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of Solids], No. 3, pp. 99-104, 1985. |
|
| Received |
25 May 2001 |
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