The systematic application of the definition of internal forces, by means of the virtual
power produced in a class of virtual motions, leads to a consistent mathematical
representation of stresses and strains in any given mechanical model. It is thus
possible to write the statical and dynamical equations and to state well
posed boundary value problems. The second-gradient theory, presented here
by way of example, can be developed without any ambiguity. An essential
distinction is drawn between intrinsic and classical stresses so as to avoid
certain issues of interpretation. It is shown that all the results of classical
linear elasticity can be immediately extended to the case of second-gradient
elastic media. The constitutive equations of nonlinear elasticity are also
formulated.
Translated by Marcelo Epstein and
Ronald E. Smelser
