Discontinuous Versus Continuous Chemical Potential Across a Crack in a Swelling Porous Medium - Computer Models in Biomechanics - page 319

Fig. 23.11 13 . 71 mm (ahead of the

initial crack) on tangential flow in the crack, chemical potential in the crack and crack growth
against pull displacement at the top

Comparison of the effect of prestress for delamination d x =

adequate resolving of the chemical potential gradient, the time step should be larger
than 180 s, which is not suitable for crack propagation. The only option left is to
decrease x , in other words, increase the spatial resolution. x should decrease a
factor 40

= √ 180 / 0 . 1 in order to allow a time step of 0.1 s. If one does so through
a mesh refinement, the advantage of partition of unity is largely lost. Choosing for
high order polynomials for the enrichment function D is probably the only option
to handle fracture in saturated porous media by means of continuous enrichment for
the pressure. The lower the hydraulic permeability and the lower the Young's mod-
ulus of the porous medium, the higher the order of the polynomial has to be. The
computationally more effective approach is the discontinuous enrichment function
for the pressure.

Acknowledgements The authors acknowledge financial support from the Technology Founda-
tion STW, the technological branch of the Netherlands Organization of Scientific Research NWO
and the Ministry of Economic Affairs (DLR5790).

References

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Int J Numer Methods Eng 46:1673-1698
Babuska I, Melenk JM (1997) The partition of unity method. Int J Numer Methods Eng 40:727-
758
Belytschko T, Black T (1999) Elastic crack growth in finite elements with minimal remeshing. Int
J Numer Methods Eng 45:601-620