A two-scale approach for fluid flow in fracturing porous media

A derivation is given of two-scale models that are able to describe deformation and fluid flow in a 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 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 and the nonlinearity of the coupling terms and the possible use of a cohesive crack model. Examples are given to show the versatility of the approach.