Covariance in linearized elasticity |
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Authors: | Arash Yavari Arkadas Ozakin |
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Institution: | (1) School of Civil and Environmental Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA;(2) Georgia Tech Research Institute, Atlanta, GA 30332, USA |
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Abstract: | In this paper we covariantly obtain all the governing equations of linearized elasticity. Our motivation is to see if one
can make a connection between invariance (covariance) properties of the (global) balance of energy in nonlinear elasticity
and those of its counterpart in linear elasticity. We start by proving a Green-Naghdi-Rivilin theorem for linearized elasticity.
We do this by first linearizing energy balance about a given reference motion and then by postulating its invariance under
isometries of the Euclidean ambient space. We also investigate the possibility of covariantly deriving a linearized elasticity
theory, without any reference to the local governing equations, e.g. local balance of linear momentum. In particular, we study
the consequences of linearizing covariant energy balance and covariance of linearized energy balance. We show that in both
cases, covariance gives all the field equations of linearized elasticity.
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Keywords: | Mathematics Subject Classification(2000)" target="_blank">Mathematics Subject Classification(2000) 74A99 53Z05 |
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