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Numerical simulation of elastic–plastic solid mechanics using an Eulerian stretch tensor approach and HLLD Riemann solver

López Ortega, A. and Lombardini, M. and Pullin, D. I. and Meiron, D. I. (2014) Numerical simulation of elastic–plastic solid mechanics using an Eulerian stretch tensor approach and HLLD Riemann solver. Journal of Computational Physics, 257 . pp. 414-441. ISSN 0021-9991.

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An Eulerian, multi-material numerical method is described for computing dynamic problems involving large deformations in elastic–plastic solids. This approach addresses algorithm failures associated with reconnection and change in topology observed in previously proposed formulations. Among the information contained in the deformation gradients commonly employed for defining constitutive laws suitable for solids, only the symmetric matrix tensor obtained from a polar decomposition of the elastic component of the deformation is required to determine the stress state. The numerical utilization of this symmetric tensor, associated with material stretch, eliminates undesirable, discontinuous deformation states produced by local rigid-body rotations at same-material reconnecting interfaces. Such states appear even where stress states in impacting regions are similar. The temporal evolution of the stretches neither modifies the eigenstructure of the system of equations nor changes its size. We also present a new multi-material approximate Riemann solver based on the HLLD approach, previously applied to other hyperbolic systems, in which waves of distinct velocity exist, for example, as in magnetohydrodynamics. This solver is employed in combination with the modified ghost fluid method (M-GFM) in the description of multi-material interfaces. These composite algorithms enable numerical simulations of the Richtmyer–Meshkov instability (i.e., the instability produced by the interaction of an interface separating materials of different density with a shock wave at an angle) in converging geometries for solid materials that would have previously led to the failure of the method.

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Meiron, D. I.0000-0003-0397-3775
Additional Information:© 2013 Elsevier Inc. Received 2 May 2013; Received in revised form 12 September 2013; Accepted 2 October 2013; Available online 10 October 2013. This work was supported by the Department of Energy National Nuclear Security Administration under Award No. DE-FC52-08NA28613.
Funding AgencyGrant Number
Department of Energy (DOE) National Nuclear Security AdministrationDE-FC52-08NA28613
Subject Keywords:Eulerian solid mechanics; Stretch tensor; Approximate multi-material Riemann solver; Richtmyer–Meshkov instability
Record Number:CaltechAUTHORS:20131223-152813111
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Official Citation:A. López Ortega, M. Lombardini, D.I. Pullin, D.I. Meiron, Numerical simulation of elastic–plastic solid mechanics using an Eulerian stretch tensor approach and HLLD Riemann solver, Journal of Computational Physics, Volume 257, Part A, 15 January 2014, Pages 414-441, ISSN 0021-9991, (
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:43153
Deposited By: Tony Diaz
Deposited On:23 Dec 2013 23:36
Last Modified:03 Oct 2019 06:05

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