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A numerical approach for arbitrary cracks in a fluid-saturated medium. (English) Zbl 1168.74447
Summary: 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.

MSC:
 74R99 Fracture and damage 74F10 Fluid-solid interactions (including aero- and hydro-elasticity, porosity, etc.) 74S05 Finite element methods applied to problems in solid mechanics
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