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

摘要

The fundamentals of the geometrically non- linear mechanics of the three-dimensional elastic con- tinuum are derived, starting from a general variationa; 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 ro- tation as Euler-Lagrange equations. These conditions can then be satisfied in a weak sense within discrete approx- imations. It is also shown that the classical approach of the non-polar continuum can be accomodated as a particular case of the present formulation.