Advanced

Acceleration Waves in Elasto-Plasticity

Ottosen, Niels Saabye LU and Runesson, Kenneth (1991) In International Journal of Solids and Structures 28(2). p.135-159
Abstract
A spectral analysis of the acceleration wave problem in general elasto-plastic materials is carried out, whereby explicit expressions for the eigenvalues and eigenvectors are obtained. In case of nonassociated plasticity, all eigenvectors become nonorthogonal and one eigenvalue always remains unchanged and equal to the shear modulus. For a very broad class of nonassociated plasticity models, it is shown that the eigenvalues are always real, implying that so-called “divergence” instability can occur, while “flutter” instability can never occur. It is found that a certain value of the hardening modulus exists for which specific propagation directions will always imply that all wave speeds are identical and equal to the elastic distortion... (More)
A spectral analysis of the acceleration wave problem in general elasto-plastic materials is carried out, whereby explicit expressions for the eigenvalues and eigenvectors are obtained. In case of nonassociated plasticity, all eigenvectors become nonorthogonal and one eigenvalue always remains unchanged and equal to the shear modulus. For a very broad class of nonassociated plasticity models, it is shown that the eigenvalues are always real, implying that so-called “divergence” instability can occur, while “flutter” instability can never occur. It is found that a certain value of the hardening modulus exists for which specific propagation directions will always imply that all wave speeds are identical and equal to the elastic distortion wave speed. Moreover, in this situation the eigenvectors are arbitrary, corresponding to a state of diffuse wave modes. The criteria of von Mises and Rankine are used to illustrate some of the findings. (Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
in
International Journal of Solids and Structures
volume
28
issue
2
pages
135 - 159
publisher
Elsevier
external identifiers
  • Scopus:0006763084
ISSN
0020-7683
DOI
10.1016/0020-7683(91)90202-Q
language
English
LU publication?
yes
id
2ff21d14-3a38-4957-a2dc-a4fd3154dc6b (old id 1370097)
date added to LUP
2010-08-24 16:05:17
date last changed
2016-10-13 05:01:57
@misc{2ff21d14-3a38-4957-a2dc-a4fd3154dc6b,
  abstract     = {A spectral analysis of the acceleration wave problem in general elasto-plastic materials is carried out, whereby explicit expressions for the eigenvalues and eigenvectors are obtained. In case of nonassociated plasticity, all eigenvectors become nonorthogonal and one eigenvalue always remains unchanged and equal to the shear modulus. For a very broad class of nonassociated plasticity models, it is shown that the eigenvalues are always real, implying that so-called “divergence” instability can occur, while “flutter” instability can never occur. It is found that a certain value of the hardening modulus exists for which specific propagation directions will always imply that all wave speeds are identical and equal to the elastic distortion wave speed. Moreover, in this situation the eigenvectors are arbitrary, corresponding to a state of diffuse wave modes. The criteria of von Mises and Rankine are used to illustrate some of the findings.},
  author       = {Ottosen, Niels Saabye and Runesson, Kenneth},
  issn         = {0020-7683},
  language     = {eng},
  number       = {2},
  pages        = {135--159},
  publisher    = {ARRAY(0x99b1540)},
  series       = {International Journal of Solids and Structures},
  title        = {Acceleration Waves in Elasto-Plasticity},
  url          = {http://dx.doi.org/10.1016/0020-7683(91)90202-Q},
  volume       = {28},
  year         = {1991},
}