Deformation induced coupling of the generalized external actions in third-gradient materials

In this study, diverse typologies of external actions are outlined, which turn out to be admissible for the thirdgradient modeling of elastic materials. It is shown how such loading, when prescribed over the boundary surface, along the border edges and at the wedges of a deformable body in the Eulerian configuration, can be transformed into the Lagrangian description generating multiple interactions, with a surprising deformation-induced coupling. Such a phenomenon becomes more and more important at increasing the order of the β-forces, specified by duality as covectors expending work on the βth normal derivative of the virtual displacements, being herein at most β = 2. Insights are provided into the true nature of such generalized forces, resting on the differential geometric features of the deformation process