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

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dc.contributor.authorBarton, Philip Trevor
dc.contributor.authorDrikakis, Dimitris
dc.contributor.authorRomenski, E.
dc.contributor.authorTitarev, Vladimir A.
dc.date.accessioned2009-08-12T14:13:29Z
dc.date.available2009-08-12T14:13:29Z
dc.date.issued2009-10-01
dc.description.abstractEulerian 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.identifier.citationP.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 7046-7068en_UK
dc.identifier.issn0021-9991
dc.identifier.urihttp://hdl.handle.net/1826/3572
dc.identifier.urihttp://dx.doi.org/10.1016/j.jcp.2009.06.014
dc.language.isoenen_UK
dc.publisherElsevieren_UK
dc.subjectRiemann problemen_UK
dc.subjectWENOen_UK
dc.subjectSolid mechanicsen_UK
dc.subjectNon-linear elasticityen_UK
dc.titleExact and approximate solutions of Riemann problems in non-linear elasticityen_UK
dc.typeArticleen_UK

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