A numerical approach for arbitrary cracks in a fluid-saturated medium

René de Borst (1) , Julien Réthoré (2, 3) , Marie-Angèle Abellan (4)

1 University of Glasgow
2 LaMCoS - Laboratoire de Mécanique des Contacts et des Structures [Villeurbanne]
3 MIMESIS - Mécanique Multiéchelle pour les solides
4 LTDS - Laboratoire de Tribologie et Dynamique des Systèmes

A finite element method is proposed that can capture arbitrary discontinuities in a two-phase medium. The discontinuity is described in an exact manner by exploiting the partition-of-unity property of finite element shape functions. The fluid flow away from the discontinuity is modelled in a standard fashion using Darcy’s relation, while at the discontinuity a discrete analogon of Darcy’s relation is proposed. The results of this finite element model are independent of the original discretisation, as is demonstrated by an example of shear banding in a biaxial, plane-strain specimen.

Mots clés: shear bands; fracture; multi-phase medium; partition-of-unity method; finite elements

Domaines: Mécanique des solides [physics.class-ph]; Mécanique des solides [physics.class-ph]

René de Borst, Julien Réthoré, Marie-Angèle Abellan. A numerical approach for arbitrary cracks in a fluid-saturated medium. Archive of Applied Mechanics, 2006, 75, pp.595-606. ⟨10.1007/s00419-006-0023-y⟩. ⟨hal-00938532⟩