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Covariantization of nonlinear elasticity

Yavari, Arash and Marsden, Jerrold E. (2012) Covariantization of nonlinear elasticity. Zeitschrift für Angewandte Mathematick und Physik, 63 (5). pp. 921-927. ISSN 0044-2275. http://resolver.caltech.edu/CaltechAUTHORS:20121115-155126102

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Abstract

In this paper we make a connection between covariant elasticity based on covariance of energy balance and Lagrangian field theory of elasticity with two background metrics. We use Kuchař’s idea of reparametrization of field theories and make elasticity generally covariant by introducing a "covariance field", which is a time-independent spatial diffeomorphism. We define a modified action for parameterized elasticity and show that the Doyle-Ericksen formula and spatial homogeneity of the Lagrangian density are among its Euler–Lagrange equations.


Item Type:Article
Related URLs:
URLURL TypeDescription
http://dx.doi.org/10.1007/s00033-011-0191-7DOIUNSPECIFIED
http://www.springerlink.com/content/dt3086kkl05n2365/PublisherUNSPECIFIED
Additional Information:© 2012 Springer Basel AG. Received: October 23, 2011. Published online January 7, 2012. AY benefited from discussions with M.J. Gotay and M.C. López. This work was partially supported by NSF—Grant No. CMMI 1042559.
Funders:
Funding AgencyGrant Number
NSFCMMI 1042559
Subject Keywords:Nonlinear elasticity; Geometric mechanics; Covariant elasticity
Classification Code:Mathematics Subject Classification (2000): 51Pxx; 74Bxx
Record Number:CaltechAUTHORS:20121115-155126102
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20121115-155126102
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:35498
Collection:CaltechAUTHORS
Deposited By: Tony Diaz
Deposited On:20 Nov 2012 17:19
Last Modified:20 Nov 2012 17:19

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