Abstract
Understanding and prediction of mechanisms of failure is needed to develop methods for prevention and treatment of failure. To increase the accuracy 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 mandatory 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 discontinuous 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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Armero F, Callari C (1999) An analysis of strong discontinuities in a saturated poro-plastic solid. 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
Camacho GT, Ortiz M (1996) Computational modelling of impact damage in brittle materials. Int J Solids Struct 33:2899–2938
de Borst R, Réthoré J, Abellan MA (2006) A numerical approach for arbitrary cracks in a fluid-saturated medium. Arch Appl Mech 75:595–606
Gasser TC, Holzapfel GA (2006) Modeling the propagation of arterial dissection. Eur J Mech A, Solids 25:617–633
Gasser TC, Holzapfel GA (2007) A numerical framework to model 3-D fracture in bone tissue with application to failure of the proximal femur. In: Combescure A, de Borst R, Belytschko T (eds) Discretization methods for evolving discontinuities. Springer, Dordrecht, pp 199–211
Kim Y (2000) Prediction of peripheral tears in the anulus of the intervertebral disc. Spine 25:1771–1774
Kraaijeveld F, Huyghe JM, Baaijens FPT (2009) Singularity solution of Lanir’s osmoelasticity: verification of discontinuity simulations in soft tissues. J Biomech Eng 10:845–865
Lanir Y (1987) Biorheology and flux in swelling tissue. I. Biocomponent theory for small deformation including concentration effects. Biorheology 24:173–187
Larsson J, Larsson R (2000) Localization analysis of a fluid-saturated elastoplastic porous medium using regularized discontinuities. Mech Cohes-Frict Mater 5:565–582
Little JP, Adam CJ, Evans JH, Pettet GJ, Pearcy MJ (2007) Nonlinear finite element analysis of anular lesions in the 14/5 intervertebral disc. J Biomech 40:2744–2751
Natarajan RN, Williams JR, Lavender SA, Andersson GBJ (2007) Poro-elastic finite element model to predict the failure progression in a lumbar disc due to cyclic loading. Comput Struct 85:1142–1151
Remmers JJC (2006) Discontinuities in materials and structures. A unifying computational approach. PhD Thesis, Delft University of Technology, The Netherlands
Remmers JJC, de Borst R, Needleman A (2003) A cohesive segments method for the simulation of crack growth. Int J Numer Methods Eng 31:69–77
Remmers JJC, de Borst R, Needleman A (2008) The simulation of dynamic crack propagation using the cohesive segments method. J Mech Phys Solids 56:70–92
Réthoré J, de Borst R, Abellan, MA (2007) A discrete model for the dynamic propagation of shear bands in a fluid-saturated medium. Int J Numer Anal Methods Geomech 31:347–370
Steinmann P (1999) A finite element formulation for strong discontinuities in fluid-saturated porous media. Mech Cohes-Frict Mater 4:133–152
Urban JP, Roberts S (2003) Degeneration of the intervertebral disc. Arthritis Res Ther 5:120–130
Vermeer PA, Verruijt A (1981) An accuracy condition for consolidation by finite elements. Int J Numer Anal Methods Geomech 5:1–14
Wells GN, Sluys LJ (2001) Discontinuous analysis of softening solids under impact loading. Int J Numer Anal Methods 25:691–709
Xu XP, Needleman A (1993) Void nucleation by inclusion debonding in a crystal matrix. Model Simul Mater Sci Eng 1:111–132
Acknowledgements
The authors acknowledge financial support from the Technology Foundation STW, the technological branch of the Netherlands Organization of Scientific Research NWO and the Ministry of Economic Affairs (DLR5790).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer Science+Business Media Dordrecht
About this paper
Cite this paper
Huyghe, J.M., Kraaijeveld, F., Remmers, J.J.C., de Borst, R. (2013). Discontinuous Versus Continuous Chemical Potential Across a Crack in a Swelling Porous Medium. In: Holzapfel, G., Kuhl, E. (eds) Computer Models in Biomechanics. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-5464-5_23
Download citation
DOI: https://doi.org/10.1007/978-94-007-5464-5_23
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-007-5463-8
Online ISBN: 978-94-007-5464-5
eBook Packages: EngineeringEngineering (R0)