Functional concepts in continuum mechanics

This paper is an attempt to give a concise presentation of the main concepts of continuum mechanics and to show their articulation. Functional definitions have been favoured. The first section is devoted to a review of continuum mechanics. The second section deals with the mechanics of materials. Constitutive equations of the material are given first by equations of state and then by complementary equations written in order to fulfil the fundamental inequality concerning the production of entropy and the physical properties of the material (viscosity, plasticity, damage etc.). Section 3 gives the Lagrangian and the Hamiltonian formulations for a moving body. Section 4 is devoted to the motion of surfaces through which discontinuities appear, to show briefly two examples of application of the previous concepts. One can easily define the source of intrinsic inhomogeneity, of heat, of irreversible entropy on a surface of phase transition and also for a shockwave.