Two-scale approaches for fracture in fluid-saturated porous media

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 derivation is given of two-scale models that are able to describe deformation and flow in a fluid-saturated and progressively fracturing porous medium. From the micromechanics of the flow in the cavity, identities are derived that couple the local momentum and the mass balances to the governing equations for a fluid-saturated porous medium, which are assumed to hold on the macroscopic scale. By exploiting the partition-of-unity property of the finite element shape functions, the position and direction of the fractures are independent from the underlying discretization. The finite element equations are derived for this two-scale approach and integrated over time. The resulting discrete equations are nonlinear due to the cohesive crack model and the nonlinearity of the coupling terms. A consistent linearization is given for use within a Newton-Raphson iterative procedure. Finally, examples are given to show the versatility and the efficiency of the approach.

Mots clés: multiscale analysis; fracture; porous media; multiphase media; cohesive cracks

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

René de Borst, Julien Réthoré, Marie-Angèle Abellan. Two-scale approaches for fracture in fluid-saturated porous media. Interaction and Multiscale Mechanics, 2007, 1, pp.83-101. ⟨10.12989/imm.2007.1.1.083⟩. ⟨hal-00938554⟩