An intrinsic Lagrangian statement of constitutive laws in large strain

A fundamental Lagrangian local strain variable for continuous media undergoing large strains, consistent with the classical Eulerian strain rate, is proposed, based on a rigorous definition of Eulerian tensors. This variable, named metric variable, is not a tensor and its domain of variation is a curved manifold. With these premises, we build an intrinsic Lagrangian framework for the statement of constitutive laws, which casts a new, unifying light on geometric aspects of large-strain theory. This approach is always completely consistent with the Eulerian approach. In the obtained new theoretical framework, the relation between this new theory and various classical approaches is studied. We examine the case of the new logarithmic rate.