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.
elastic waves;elastoplasticity;numerical analysis;