A two-scale approach for propagating cracks in a fluid-saturated porous material

An extension to a finite strain framework of a two-scale numerical model for propagating crack in porous material is proposed to model the fracture in intervertebral discs. In the model, a crack is described as a propagating cohesive zone by exploiting the partition-of-unity property of finite element shape functions. At the micro-scale, the flow in the cohesive crack is modelled as viscous fluid using Stokes' equations which are averaged over the cross section of the cavity. At the macro-scale, identities are derived to couple the local momentum and the mass balance to the governing equations for a saturated porous material. The resulting discrete equations are nonlinear due to the cohesive constitutive equations and the geometrically nonlinear kinematic relations. A Newton-Raphson iterative procedure is used to consistently linearise the derived system while a Crank-Nicholson scheme takes care of the time integration of the system. The derived model is used to analyse a quasi-static crack growth in confined compression under tensile loading.