An Eulerian finite-volume scheme for large elastoplastic deformations in solids

P. T. Barton, D. Drikakis, E. I. Romenski

Research output: Contribution to journalArticlepeer-review


Conservative formulations of the governing laws of elastoplastic solid media have distinct advantages when solved using high-order shock capturing methods for simulating processes involving large deformations and shock waves. In this paper one such model is considered where inelastic deformations are accounted for via conservation laws for elastic strain with relaxation source terms. Plastic deformations are governed by the relaxation time of tangential stresses. Compared with alternative Eulerian conservative models, the governing system consists of fewer equations overall. A numerical scheme for the inhomogeneous system is proposed based upon the temporal splitting. In this way the reduced system of non-linear elasticity is solved explicitly, with convective fluxes evaluated using high-order approximations of Riemann problems locally throughout the computational mesh. Numerical stiffness of the relaxation terms at high strain rates is avoided by utilizing certain properties of the governing model and performing an implicit update. The methods are demonstrated using test cases involving large deformations and high strain rates in one-, two-, and three-dimensions.

Original languageEnglish
Pages (from-to)453-484
Number of pages32
JournalInternational Journal for Numerical Methods in Engineering
Issue number4
Publication statusPublished - 22 Jan 2010


  • Elastic-plastic solids
  • Finite-volume
  • High-resolution schemes
  • Riemann solver
  • WENO


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