A functional framework for applied continuum mechanics

We present an abstract formulation of the mechanics of continuous bodies in which the kinematic description is given as basic and the statics is derived by duality. A proper definition of the functional spaces based on finite decompositions of the reference domain allows to include in the theory all the powerful tools usually adopted in the analysis of engineering structures. In this respect general proofs are provided for the Virtual Work Theorem, the abstract CAUCHY's Theorem and the Theorem of Kinematic Compatibility. A decomposition formula of special relevance in homogenization theory is derived as a direct application of the previous results.