On the intrinsic approaches in mechanics

This paper aims to illustrate the interest of so-called intrinsic or coordinate-free or geometric approaches in mechanics and to start a discussion about their positions with respect to the opposite aspects carried by computational mechanics. Due to recent developments of pure computational approaches using IA that could finally suggest that equations and formal developments are not necessarily so important in mechanics, it could obviously lead to philosophical and epistemological issues. Our main point of view can be summarized by the well-known sentence of René Thom: "To predict is not to explain". Even if we consider that stressing these questions in the community of mechanics should be fundamental and essential, it will not be however the theme of the present work. On the contrary, we will remain technic in order to defend the idea that intrinsic approaches are actually complementary to computational approaches in mechanics and that, even if these approaches may involve more abstract objects and less usual mathematical concepts, they can lead in fact to practically more efficient developments in applications. This thesis then defends the unity of mechanics and the non-sense to hermetically separate theoretical, computational and applied aspects in mechanics.