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

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Abstract

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.

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Authors and Affiliations

  1. Faculty of Aerospace Engineering, Delft University of Technology, P.O. Box 5058, 2600, GB, Delft, The Netherlands

    René de Borst & Julien Réthoré

  2. LTDS-ENISE - UMR CNRS 5513, 42043, Saint-Etienne, France

    Marie-Angèle Abellan

Authors
  1. René de Borst
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  2. Julien Réthoré
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  3. Marie-Angèle Abellan
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Correspondence to René de Borst.

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de Borst, R., Réthoré, J. & Abellan, MA. A Numerical Approach for Arbitrary Cracks in a Fluid-Saturated Medium. Arch Appl Mech 75, 595–606 (2006). https://doi.org/10.1007/s00419-006-0023-y

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  • DOI: https://doi.org/10.1007/s00419-006-0023-y

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