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Numerical algorithms for strong discontinuities in elastic-plastic solids

Publication ,  Journal Article
Trangenstein, JA; Pember, RB
Published in: Journal of Computational Physics
January 1, 1992

In this paper the implementation of second-order Godunov methods for dynamic wave propagation in one-dimensional elastic-plastic solids is investigated. First, the Lagrangian form of the algorithm is reviewed, and then the algorithm is extended to the Eulerian frame of reference. This extension requires additional evolution equations to handle the history of the material along particle paths. Both the Lagrangian and Eulerian versions of the algorithm require appropriately accurate approximations to the solution of Riemann problems, in order to represent the interaction of waves at cell boundaries. Two inexpensive approximations to the solution of the Riemann problem are constructed, and the resulting algorithms are tested against the analytic solution of the Riemann problem for longitudinal motion in an elastic-plastic bar. These approximations to the Riemann problem are shown to work well, even for strong discontinuities. Finally, the numerical experience gained from the simple longitudinal bar problem is used to design an algorithm for strong shocks predicted by a realistic soil model. © 1992.

Duke Scholars

Published In

Journal of Computational Physics

DOI

EISSN

1090-2716

ISSN

0021-9991

Publication Date

January 1, 1992

Volume

103

Issue

1

Start / End Page

63 / 89

Related Subject Headings

  • Applied Mathematics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences
 

Citation

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Trangenstein, J. A., & Pember, R. B. (1992). Numerical algorithms for strong discontinuities in elastic-plastic solids. Journal of Computational Physics, 103(1), 63–89. https://doi.org/10.1016/0021-9991(92)90326-T
Trangenstein, J. A., and R. B. Pember. “Numerical algorithms for strong discontinuities in elastic-plastic solids.” Journal of Computational Physics 103, no. 1 (January 1, 1992): 63–89. https://doi.org/10.1016/0021-9991(92)90326-T.
Trangenstein JA, Pember RB. Numerical algorithms for strong discontinuities in elastic-plastic solids. Journal of Computational Physics. 1992 Jan 1;103(1):63–89.
Trangenstein, J. A., and R. B. Pember. “Numerical algorithms for strong discontinuities in elastic-plastic solids.” Journal of Computational Physics, vol. 103, no. 1, Jan. 1992, pp. 63–89. Scopus, doi:10.1016/0021-9991(92)90326-T.
Trangenstein JA, Pember RB. Numerical algorithms for strong discontinuities in elastic-plastic solids. Journal of Computational Physics. 1992 Jan 1;103(1):63–89.
Journal cover image

Published In

Journal of Computational Physics

DOI

EISSN

1090-2716

ISSN

0021-9991

Publication Date

January 1, 1992

Volume

103

Issue

1

Start / End Page

63 / 89

Related Subject Headings

  • Applied Mathematics
  • 51 Physical sciences
  • 49 Mathematical sciences
  • 40 Engineering
  • 09 Engineering
  • 02 Physical Sciences
  • 01 Mathematical Sciences