An intrinsic geometric formulation of Hyper-elasticity, pressure potential and non-holonomic constraints

Abstract

Isotropic hyper-elasticity, altogether with the equilibrium equation and the usual boundary conditions, are formulated directly on the body B, a three-dimensional compact and orientable manifold with boundary equipped with a mass measure. Pearson-Sewell-Beatty pressure potential is formulated in an intrinsic geometric manner. It is shown that Poincar{\'e}'s formula extended to infinite dimension, provides, in a straightforward manner, the optimal (non-holonomic) constraints for such a pressure potential to exist.