On variational aspects of a generalized continuum - J. SACZUK (Rendiconti di Matematica e delle Sue Applicazioni, 1996)
The intention of the paper is to sketch the background of the Finsler bundle approach to the continuum theory of solids using variational arguments. Within this approach the additive decomposition of the total deformation gradient is defined. For a given Lagrangian function and an assumed one-parameter family of transformations of dependent and independent variables, the fundamental variational formula identified with the virtual work principle of the generalized (microstructural) continuum is obtained. Stationarity conditions of the action integral lead to the balance equations and natural boundary conditions valid on both the base space and the fibre space of the body.