Densification of a viscous porous layer with consideration for elastic effects

Georgiy M. Sevastyanov

Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 10 (2017) no. 3, pp. 345-352

Résumé

A viscous flow of a horizontal compressible layer under the gravity and constant external pressure is considered in this paper. It is assumed that medium motion is quasi-static and uniaxial, and the reversible and irreversible strains are finite. It is also assumed that the material is subject to the Green flow condition with coefficients depending on the material density and the plastic strain rate. The irreversible strains occur in the material at arbitrary non-zero load. The initial boundary value problem is reduced to the first-order differential equation with separable variables. This equation contains the time variable as a parameter. Evolution of the density distribution over the layer height is determined in the particular cases. An approximate analytical solution for the density in the initial phase of densification is obtained when reversible strains are negligible. The numerical solution for the density is obtained in the case of small elastic strains. These solutions are valid until a fully densified region on the underlying surface occurs. Further evolution of such region is not considered.

Détail

Keywords: compressible medium, finite strains, Almansi strain tensor, viscous flow, porosity, Green yield surface, gravity load
Mots-clés : uniaxial deformation, densification, von Mises transformation.