Discontinuous Versus Continuous Chemical Potential Across a Crack in a Swelling Porous Medium - Computer Models in Biomechanics - page 303

Chapter 23
Discontinuous Versus Continuous Chemical
Potential Across a Crack in a Swelling Porous
Medium

Jacques M. Huyghe, Famke Kraaijeveld, Joris J.C. Remmers,
and René de Borst

Abstract Understanding and prediction of mechanisms of failure is needed to
develop methods for prevention and treatment of failure. To increase the accu-
racy for the prediction of failure, advanced computational models are developed.
Mesh-independent modeling of cracks in porous media is obtained by enriching the
displacement field with a discontinuous shape function describing the crack. In a
poroelastic finite element modeling, an enrichment of the pressure field is manda-
tory around the crack. Two options are available to account for the sharp pressure
gradient around the crack. One is to resolve the pressure gradient using a continuous
pressure enrichment, the other is not to resolve the steep gradients and use discon-
tinuous jumps across the crack surface. In the latter case, analytical solutions of
the pressure field at an interface is used to evaluate the real pressure gradient. This
paper formulates criteria to decide whether to use one or the other approach. The
techniques are applied to swelling media in which the pressure degree of freedom
takes the form of a chemical potential.

23.1 Introduction

The mechanical causes of intervertebral disc (IVD) degeneration and herniation are
poorly known (Urban and Roberts, 2003 ). The presence of fixed charges in the col-
lagen network of tissues causes differences in ion concentrations with the surround-
ing fluid and, therefore, Donnan-osmotic pressure. This gives the IVD its prestress
and its protective nature against crack growth. During degeneration a loss of fixed

J.M. Huyghe ( R. de Borst

Eindhoven University of Technology, Eindhoven, The Netherlands
e-mail: [e-mail]
F. Kraaijeveld
e-mail: [e-mail]
J.J.C. Remmers
e-mail: [e-mail]
R. de Borst
e-mail: [e-mail]

) · F. Kraaijeveld · J.J.C. Remmers ·