The University of Southampton
University of Southampton Institutional Repository

A conservation law formulation of nonlinear elasticity in general relativity

A conservation law formulation of nonlinear elasticity in general relativity
A conservation law formulation of nonlinear elasticity in general relativity
We present a practical framework for ideal hyperelasticity in numerical relativity. For this purpose, we recast the formalism of Carter and Quintana as a set of Eulerian conservation laws in an arbitrary 3+1 split of spacetime. The resulting equations are presented as an extension of the standard Valencia formalism for a perfect fluid, with additional terms in the stress–energy tensor, plus a set of kinematic conservation laws that evolve a configuration gradient ?Ai. We prove that the equations can be made symmetric hyperbolic by suitable constraint additions, at least in a neighbourhood of the unsheared state. We discuss the Newtonian limit of our formalism and its relation to a second formalism also used in Newtonian elasticity. We validate our framework by numerically solving a set of Riemann problems in Minkowski spacetime, as well as Newtonian ones from the literature.
0264-9381
015005-[53pp]
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Hawke, Ian
fc964672-c794-4260-a972-eaf818e7c9f4
Erickson, Stephanie E.
b0675078-ef6c-482a-a843-51dd820a4fa6
Gundlach, Carsten
586f1eb5-3185-4b2b-8656-c29c436040fc
Hawke, Ian
fc964672-c794-4260-a972-eaf818e7c9f4
Erickson, Stephanie E.
b0675078-ef6c-482a-a843-51dd820a4fa6

Gundlach, Carsten, Hawke, Ian and Erickson, Stephanie E. (2011) A conservation law formulation of nonlinear elasticity in general relativity. Classical and Quantum Gravity, 29 (1), 015005-[53pp]. (doi:10.1088/0264-9381/29/1/015005).

Record type: Article

Abstract

We present a practical framework for ideal hyperelasticity in numerical relativity. For this purpose, we recast the formalism of Carter and Quintana as a set of Eulerian conservation laws in an arbitrary 3+1 split of spacetime. The resulting equations are presented as an extension of the standard Valencia formalism for a perfect fluid, with additional terms in the stress–energy tensor, plus a set of kinematic conservation laws that evolve a configuration gradient ?Ai. We prove that the equations can be made symmetric hyperbolic by suitable constraint additions, at least in a neighbourhood of the unsheared state. We discuss the Newtonian limit of our formalism and its relation to a second formalism also used in Newtonian elasticity. We validate our framework by numerically solving a set of Riemann problems in Minkowski spacetime, as well as Newtonian ones from the literature.

This record has no associated files available for download.

More information

Published date: 12 December 2011
Organisations: Applied Mathematics

Identifiers

Local EPrints ID: 202587
URI: http://eprints.soton.ac.uk/id/eprint/202587
ISSN: 0264-9381
PURE UUID: 01b5f6f7-0655-409e-9cf3-92bdbf82b535
ORCID for Carsten Gundlach: ORCID iD orcid.org/0000-0001-9585-5375
ORCID for Ian Hawke: ORCID iD orcid.org/0000-0003-4805-0309

Catalogue record

Date deposited: 08 Nov 2011 14:11
Last modified: 15 Mar 2024 03:22

Export record

Altmetrics

Contributors

Author: Ian Hawke ORCID iD
Author: Stephanie E. Erickson

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×