Abstract
Variational formulations for classical nonlinear elasticity amenable to finite element discretization are presented in which the rotation field plays the role of an independent variable. The central idea the proposed approach is to regard the classical theory as a generalized model with an added independent rotation field which is constrained to coincide with the rotation of the medium. For three-dimensional solids, the independent rotation field is the rotation tensor from the polar decomposition of the deformation gradient. The variational formulation is then constructed merely by enforcing the constraint on the independent rotation field via a Lagrange multiplier term which is shown to vanish at equilibrium.
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