Homogénéisation d’un milieu incompressible viscoplastique de type Norton-Hoff périodiquement perforé. (Homogenization of an incompressible viscoplastic, Norton-Hoff type, periodically perforated medium). (French) Zbl 0625.73018

In this paper the author studies the macroscopic behaviour of an incompressible viscoplastic material. The medium is supposed of Norton- Hoff type and of a periodic structure of period \(\epsilon\) Y with Y given by a rectangle of \(R^ n\), with some holes strongly enclosed in Y. In the framework of homogenization theory the asymptotic behaviour is studied as \(\epsilon\) goes to zero. In the limit, the law of a compressible viscoplastic material is obtained. The homogenized potential of dissipation is a convex and differentiable function; its differential satisfies the some kind of inequalities which are fulfilled by the differential of the microscopic potential.
Reviewer: M.Codegone


74E05 Inhomogeneity in solid mechanics
35B40 Asymptotic behavior of solutions to PDEs
74R20 Anelastic fracture and damage