Exact and approximate solutions of Riemann problems in non-linear elasticity

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dc.contributor.author Barton, Philip Trevor
dc.contributor.author Drikakis, Dimitris
dc.contributor.author Romenski, E.
dc.contributor.author Titarev, Vladimir A.
dc.date.accessioned 2009-08-12T14:13:29Z
dc.date.available 2009-08-12T14:13:29Z
dc.date.issued 2009-10-01
dc.identifier.citation P.T. Barton, D. Drikakis, E. Romenski, V.A. Titarev, Exact and approximate solutions of Riemann problems in non-linear elasticity, Journal of Computational Physics, Volume 228, Issue 18, 1 October 2009, Pages 7046-7068 en_UK
dc.identifier.issn 0021-9991
dc.identifier.uri http://hdl.handle.net/1826/3572
dc.identifier.uri http://dx.doi.org/10.1016/j.jcp.2009.06.014
dc.description.abstract Eulerian shock-capturing schemes have advantages for modelling problems involving complex non-linear wave structures and large deformations in solid media. Various numerical methods now exist for solving hyperbolic conservation laws that have yet to be applied to non-linear elastic theory. In this paper one such class of solver is examined based upon characteristic tracing in conjunction with high-order monotonicity preserving weighted essentially non-oscillatory (MPWENO) reconstruction. Furthermore, a new iterative method for finding exact solutions of the Riemann problem in non-linear elasticity is presented. Access to exact solutions enables an assessment of the performance of the numerical techniques with focus on the resolution of the seven wave structure. The governing model represents a special case of a more general theory describing additional physics such as material plasticity. The numerical scheme therefore provides a firm basis for extension to simulate more complex physical phenomena. Comparison of exact and numerical solutions of one-dimensional initial values problems involving three-dimensional deformations is presented. en_UK
dc.language.iso en en_UK
dc.publisher Elsevier en_UK
dc.subject Riemann problem en_UK
dc.subject WENO en_UK
dc.subject Solid mechanics en_UK
dc.subject Non-linear elasticity en_UK
dc.title Exact and approximate solutions of Riemann problems in non-linear elasticity en_UK
dc.type Article en_UK

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