A variational formulation for finite elasticity with independent rotation and Biot-axial fields

Abstract.

The fundamentals of the geometrically nonlinear mechanics of the three-dimensional elastic continuum are derived, starting from a general variational framework established for the polar model and passing through a constitutive definition of the non-polar medium itself. A constrained variational setting follows, having as unknown vector fields the displacement, the rotation vector and the axial of the Biot stress. It embraces both the rotational equilibrium and the characterization of the rotation as Euler-Lagrange equations. These conditions can then be satisfied in a weak sense within discrete approximations. It is also shown that the classical approach of the non-polar continuum can be accomodated as a particular case of the present formulation.

A consistent linearization is then proposed and a simple solid finite element developed to test the computational viability of the formulation. A few examples assess the capability of the element to represent large three-dimensional rotations.