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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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.
|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.|
|Subject Keywords:||Nonlinear elasticity; Geometric mechanics; Covariant elasticity|
|Classification Code:||Mathematics Subject Classification (2000): 51Pxx; 74Bxx|
|Usage Policy:||No commercial reproduction, distribution, display or performance rights in this work are provided.|
|Deposited By:||Tony Diaz|
|Deposited On:||20 Nov 2012 17:19|
|Last Modified:||20 Nov 2012 17:19|
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