Premium
An Eulerian finite‐volume scheme for large elastoplastic deformations in solids
Author(s) -
Barton P. T.,
Drikakis D.,
Romenski E. I.
Publication year - 2009
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.2695
Subject(s) - eulerian path , conservation law , finite volume method , mechanics , shock wave , mathematics , stiffness , shock (circulatory) , relaxation (psychology) , linear elasticity , elasticity (physics) , riemann problem , classical mechanics , riemann hypothesis , mathematical analysis , finite element method , physics , structural engineering , engineering , lagrangian , medicine , psychology , social psychology , thermodynamics
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. Copyright © 2009 John Wiley & Sons, Ltd.