A Numerical Approach for Arbitrary Cracks in a Fluid-Saturated Medium

• DOI: 10.1007/s00419-006-0023-y
• Publication Date: 2006-04-24T08:09:29Z
• Authors: René de Borst; Julien Réthoré; Marie-Angèle Abellan
• Keywords: Discontinuity (linguistics); Classification of discontinuities; Partition of unity; Darcy's law

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.