Covariance in Linearized Elasticity
In this paper we covariantly obtain the governing equations of linearized elasticity. Our motivation is to see if one can make a connection between (global) balance of energy in nonlinear elasticity and 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.