Cinématiques des milieux généralisés et repères mobiles

This work presents a unified geometrical framework for modeling generalised continua in finite strains : in any dimension (rods, shells, 3D media), in any micromorphic theory of order one (micromorphic, Cosserat, micro-dilatation, etc) and in any second gradient theory (strain-gradient, couple-stresses, etc). Central to our approach is the use of moving frames defined at any point in the material, interpreted as generalised configurations. These frames provide an intuitive yet rigorous means of tracking deformations, encapsulating shifts in position, orientation, and scaling at each material point. In contrast to other approaches that rely on complex micro-mechanical structures, our framework relies on an intrinsic Lagrangian point of view aligning closely with the original insights of the Cosserat brothers. In this work, we focus on how this framework ease the understanding and the links between generalised theories of different types and different dimensions.