On Relationships Between Micro–Macro Quantities

This paper is devoted to the description of the general relationships between microscopic and macroscopic mechanical quantities in non-linear mechanics. Many studies have been dedicated to the relations between mechanical average quantities as stresses or strains in small or finite transformation [1–4]. Our purpose is to reformulate these relations in the framework of a thermodynamical point of view as proposed by Germain et al [5]. This paper proposes some extensions of classical relations to non linear mechanics. To determine the overall behaviour of a body, whose local properties are known, we must solve a complicated boundary value problem. The thermodynamical point of view is used to determine the partition between reversibility and irreversibility of the global response.