Advertisement

Journal of Engineering Mathematics

, Volume 95, Issue 1, pp 249–265 | Cite as

Modelling of tear propagation and arrest in fibre-reinforced soft tissue subject to internal pressure

  • Lei Wang
  • Steven M. Roper
  • X. Y. Luo
  • N. A. Hill
Article

Abstract

The prediction of soft-tissue failure may yield a better understanding of the pathogenesis of arterial dissection and help to advance diagnostic and therapeutic strategies for the treatment of this and other diseases and injuries involving the tearing of soft tissue, such as aortic dissection. In this paper, we present computational models of tear propagation in fibre-reinforced soft tissue undergoing finite deformation, modelled by a hyperelastic anisotropic constitutive law. We adopt the appropriate energy argument for anisotropic finite strain materials to determine whether a tear can propagate when subject to internal pressure loading. The energy release rate is evaluated with an efficient numerical scheme that makes use of adaptive tear lengths. As an illustration, we present the calculation of the energy release rate for a two-dimensional strip of tissue with a pre-existing tear of length \(a\) under internal pressure \(p\) and show the effect of fibre orientation. This calculation allows us to locate the potential bifurcation to tear propagation in the \((a,p)\) plane. The numerical predictions are verified by analytical solutions for simpler cases. We have identified a scenario of tear arrest, which is observed clinically, when the surrounding connective tissues are accounted for. Finally, the limitations of the models and further directions for applications are discussed.

Keywords

Arterial dissection Energy release rate Finite-element analysis HGO model Soft tissue Tear propagation and arrest 

Notes

Acknowledgments

LW is supported by a China Scholarship Council Studentship and the Fee Waiver Programme at the University of Glasgow.

References

  1. 1.
    Khan IA, Nair CK (2002) Clinical, diagnostic, and management perspectives of aortic dissection. Chest J 122(1):311–328CrossRefGoogle Scholar
  2. 2.
    Foundation MHI (2013) Mortality for acute aortic dissection near one percent per hour during initial onset. ScienceDaily, 10 March 2013. www.sciencedaily.com/releases/2013/03/130310164230.htm. Accessed 6 January 2015
  3. 3.
    Rajagopal K, Bridges C, Rajagopal K (2007) Towards an understanding of the mechanics underlying aortic dissection. Biomech Model Mechanobiol 6:345–359CrossRefGoogle Scholar
  4. 4.
    de Figueiredo Borges L, Jaldin RG, Dias RR, Stolf NAG, Michel JB, Gutierrez PS (2008) Collagen is reduced and disrupted in human aneurysms and dissections of ascending aorta. Hum Pathol 39(3):437–443CrossRefGoogle Scholar
  5. 5.
    Tada H, Paris PC, Irwin GR, Tada H (2000) The stress analysis of cracks handbook. ASME Press, New YorkCrossRefGoogle Scholar
  6. 6.
    Krishnan VR, Hui CY, Long R (2008) Finite strain crack tip fields in soft incompressible elastic solids. Langmuir 24(24):14245–14253CrossRefGoogle Scholar
  7. 7.
    Stephenson RA (1982) The equilibrium field near the tip of a crack for finite plane strain of incompressible elastic materials. J Elast 12(1):65–99MATHMathSciNetCrossRefGoogle Scholar
  8. 8.
    Ionescu I, Guilkey JE, Berzins M, Kirby RM, Weiss JA (2006) Simulation of soft tissue failure using the material point method. J Biomech Eng 128(6):917CrossRefGoogle Scholar
  9. 9.
    Volokh KY (2004) Comparison between cohesive zone models. Commun Numer Methods Eng 20(11):845–856MATHCrossRefGoogle Scholar
  10. 10.
    Gasser TC, Holzapfel GA (2006) Modeling the propagation of arterial dissection. Eur J Mechs A 25(4):617–633MATHMathSciNetCrossRefGoogle Scholar
  11. 11.
    Elices M, Guinea G, Gomez J, Planas J (2002) The cohesive zone model: advantages, limitations and challenges. Eng Fract Mech 69(2):137–163CrossRefGoogle Scholar
  12. 12.
    Bhattacharjee T, Barlingay M, Tasneem H, Roan E, Vemaganti K (2013) Cohesive zone modeling of mode I tearing in thin soft materials. J Mech Behav Biomed Mater 28:37–46CrossRefGoogle Scholar
  13. 13.
    Ferrara A, Pandolfi A (2008) Numerical modelling of fracture in human arteries. Comput Methods Biomech Biomed Eng 11(5):553–567CrossRefGoogle Scholar
  14. 14.
    Ferrara A, Pandolfi A (2010) A numerical study of arterial media dissection processes. Int J Fract 166(1–2):21–33MATHCrossRefGoogle Scholar
  15. 15.
    Ortiz M, Pandolfi A (1999) Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int J Numer Methods Eng 44(9):1267–1282MATHCrossRefGoogle Scholar
  16. 16.
    Griffith AA (1921) The phenomena of rupture and flow in solids. Philos Transa R Soc Lond Ser A 221:163–198CrossRefADSGoogle Scholar
  17. 17.
    Irwin G, Wells A (1965) A continuum-mechanics view of crack propagation. Metallurg Rev 10(1):223–270Google Scholar
  18. 18.
    Willis J (1967) A comparison of the fracture criteria of Griffith and Barenblatt. J Mech Phys Solids 15(3):151–162MathSciNetCrossRefADSGoogle Scholar
  19. 19.
    Zehnder AT (2012) Fracture mechanics. Lecture notes in applied and computational mechanics, vol 62. SpringerGoogle Scholar
  20. 20.
    Knees D, Mielke A (2008) Energy release rate for cracks in finite-strain elasticity. Math Methods Appl Sci 31(5):501–528MATHMathSciNetCrossRefGoogle Scholar
  21. 21.
    Taylor RL (2011) FEAP— a finite element analysis program: Version 8.3 User manual. University of California at BerkeleyGoogle Scholar
  22. 22.
    Holzapfel GA, Gasser TC, Ogden RW (2000) A new constitutive framework for arterial wall mechanics and a comparative study of material models. J Elast 61(1):1–48MATHMathSciNetCrossRefGoogle Scholar
  23. 23.
    Flory P (1961) Thermodynamic relations for high elastic materials. Trans Faraday Soc 57:829–838MathSciNetCrossRefGoogle Scholar
  24. 24.
    Taylor RL (2011) FEAP—a finite element analysis program: Version 8.3 Programmer manual. University of California at BerkeleyGoogle Scholar
  25. 25.
    Holzapfel GA (2000) Nonlinear solid mechanics: a continuum approach for engineering. Wiley, New YorkGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  • Lei Wang
    • 1
  • Steven M. Roper
    • 1
  • X. Y. Luo
    • 1
  • N. A. Hill
    • 1
  1. 1.School of Mathematics and StatisticsUniversity of GlasgowGlasgowUK

Personalised recommendations