A new variational principle for finite elastic displacements

After a discussion of existing variational principles, a new set of variational principles, of displacement, canonical or complementary energy types, is found to derive from the polar decomposition of the jacobian. It involves the engineering strain tensor and its conjugate stress tensor is to be regarded as a function of the Piola tensor and the material rotaion. The complementary energy formulation is discussed in terms of firs order stress functions. The presence of the rotational degrees of freedom opens the possibility of discretizing the rotational equilibrium equaions in approximate solutions.