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An Analog of Einstein’s General Relativity Emerging from Classical Finite Elasticity Theory: Analytical and Computational Issues

Published online by Cambridge University Press:  03 June 2015

C. Cherubini and
S. Filippi
C. Cherubini*
Affiliation:
Nonlinear Physics and Mathematical Modeling Lab, University Campus Bio-Medico, I-00128, Via A. del Portillo 21, Rome, ItalyInternational Center for Relativistic Astrophysics - I.C.R.A., University of Rome “La Sapienza”, I-00185 Rome, Italy
S. Filippi*
Affiliation:
Nonlinear Physics and Mathematical Modeling Lab, University Campus Bio-Medico, I-00128, Via A. del Portillo 21, Rome, ItalyInternational Center for Relativistic Astrophysics - I.C.R.A., University of Rome “La Sapienza”, I-00185 Rome, Italy
*
Corresponding author.Email:c.cherubini@unicampus.it
Email:s.filippi@unicampus.it
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Abstract

The “analogue gravity formalism”, an interdisciplinary theoretical scheme developed in the past for studying several non relativistic classical and quantum systems through effective relativistic curved space-times, is here applied to largely de-formable elastic bodies described by the nonlinear theory of solid mechanics. Assuming the simplest nonlinear constitutive relation for the elastic material given by a Kirchhoff-St Venant strain-energy density function, it is possible to write for the perturbations an effective space-time metric if the deformation is purely longitudinal and depends on one spatial coordinate only. Theoretical and numerical studies of the corresponding dynamics are performed in selected cases and physical implications of the results obtained are finally discussed.

Keywords

74Jxx35Lxx35Qxx83Cxx04.20.-q46.25.-y46.35.+zFinite elasticitygeneral relativityanalogue gravityfinite elements method

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Type
Research Article
Information
Communications in Computational Physics , Volume 14 , Issue 3 , September 2013, pp. 801 - 818
Copyright
Copyright © Global Science Press Limited 2013

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