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

Licht, Christian

C. R. Acad. Sci., Paris, Sér. I 302, 51-53 (1986).

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

MSC:

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

Keywords:

periodically perforated medium; macroscopic behaviour; incompressible viscoplastic material; Norton-Hoff type; periodic structure; homogenization; asymptotic behaviour