Biomechanics and Modeling in Mechanobiology

, Volume 18, Issue 6, pp 1791–1807 | Cite as

Computational modeling reveals the relationship between intrinsic failure properties and uniaxial biomechanical behavior of arterial tissue

  • Ronald N. Fortunato
  • Anne M. Robertson
  • Chao Sang
  • Spandan MaitiEmail author
Original Paper


Biomechanical failure of the artery wall can lead to rupture, a catastrophic event with a high rate of mortality. Thus, there is a pressing need to understand failure behavior of the arterial wall. Uniaxial testing remains the most common experimental technique to assess tissue failure properties. However, the relationship between intrinsic failure parameters of the tissue and measured uniaxial failure properties is not fully established. Furthermore, the effect of the experimental variables, such as specimen shape and boundary conditions, on the measured failure properties is not well understood. We developed a finite element model capable of recapitulating pre-failure and post-failure uniaxial biomechanical response of the arterial tissue specimen. Intrinsic stiffness, strength and fracture toughness of the vessel wall tissue were used as the input material parameters to the model. Two uniaxial testing protocols were considered: a conventional setup with a rectangular specimen held at the grips by cardboard inserts, and the other used a dogbone specimen with soft foam inserts at the grips. Our computational study indicated negligible differences in the peak stress and post-peak mechanical behavior between these two testing protocols. It was also found that the tissue experienced only modest localized failure until higher levels of applied stretch beyond the peak stress. A robust cohesive model was capable of modeling the post-peak biomechanical response, which was primarily governed by tissue fracture toughness. Our results suggest that the post-peak region, in conjunction with the peak stress, must be considered to evaluate the complete biomechanical failure behavior of the soft tissue.


Uniaxial testing Arterial tissue failure properties Intrinsic strength Fracture toughness Post-peak behavior Cohesive-volumetric finite-element method 



Research reported in this work was supported by the National Institutes of Health under Award Number 1R01- NS097457-01 and 5T32HL076124-12. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. Human basilar arteries were provided from the Alzheimer Disease Research Center (ADRC) (Grant No. NIA P50 AG005133). The authors would also like to thank Chelsea Stowell and Dr. Y. Wang for providing the sheep carotid arteries used for this study.

Compliance with ethical standards

Conflict of interest

The authors declare they have no conflict of interest.

Supplementary material

10237_2019_1177_MOESM1_ESM.pdf (2.3 mb)
Supplementary material 1 (pdf 2333 KB)


  1. Alfano G (2006) On the influence of the shape of the interface law on the application of cohesive-zone models. Compos Sci Technol 66(6):723–730. Advances in statics and dynamics of delaminationCrossRefGoogle Scholar
  2. Anderson T, Boyajian D, Latanision R Jr, Dodds R, Vasudevan A, Daniewicz S, Ainsworth R, Gangloff R (2005) Fracture mechanics: fundamentals and applications, 3rd edn. CRC Press, Boca RatonCrossRefGoogle Scholar
  3. Barenblatt GI (1962) The mathematical theory of equilibrium cracks in brittle fracture. Adv Appl Mech 7:55–129. MathSciNetCrossRefGoogle Scholar
  4. Bonet J, Wood RD (2008) Nonlinear continuum mechanics for finite element analysis, 2nd edn. Cambridge University Press, Cambridge. CrossRefzbMATHGoogle Scholar
  5. Brunon A, Bruyere-Garnier K, Coret M (2010) Mechanical characterization of liver capsule through uniaxial quasi-static tensile tests until failure. J Biomech 43(11):2221–7. CrossRefGoogle Scholar
  6. Chen C, Wang Z, Suo Z (2017) Flaw sensitivity of highly stretchable materials. Extreme Mech Lett 10:50–57. CrossRefGoogle Scholar
  7. Cortes DH, Lake SP, Kadlowec JA, Soslowsky LJ, Elliott DM (2010) Characterizing the mechanical contribution of fiber angular distribution in connective tissue: comparison of two modeling approaches. Biomech Model Mechanobiol 9(5):651–658. CrossRefGoogle Scholar
  8. Costalat V, Sanchez M, Ambard D, Thines L, Lonjon N, Nicoud F, Brunel H, Lejeune JP, Dufour H, Bouillot P, Lhaldky JP, Kouri K, Segnarbieux F, Maurage CA, Lobotesis K, Villa-Uriol MC, Zhang C, Frangi AF, Mercier G, Bonafe A, Sarry L, Jourdan F (2011) Biomechanical wall properties of human intracranial aneurysms resected following surgical clipping (IRRAS Project). J Biomech 44(15):2685–91. CrossRefGoogle Scholar
  9. Di Martino ES, Bohra A, Vande Geest JP, Gupta N, Makaroun MS, Vorp DA (2006) Biomechanical properties of ruptured versus electively repaired abdominal aortic aneurysm wall tissue. J Vasc Surg 43(3):570–6. CrossRefGoogle Scholar
  10. Dugdale DS (1960) Yielding of steel sheets containing slits. J Mech Phys Solids 8(2):100–104. CrossRefGoogle Scholar
  11. Farshad M, Barbezat M, Flüeler P, Schmidlin F, Graber P, Niederer P (1999) Material characterization of the pig kidney in relation with the biomechanical analysis of renal trauma. J Biomech 32(4):417–425. CrossRefGoogle Scholar
  12. Ferrara A, Pandolfi A (2008) Numerical modelling of fracture in human arteries. Comput Methods Biomech Biomed Eng 11(5):553–567. ISBN 1025-5842CrossRefGoogle Scholar
  13. Ferrara A, Morganti S, Totaro P, Mazzola A, Auricchio F (2016) Human dilated ascending aorta: mechanical characterization via uniaxial tensile tests. J Mech Behav Biomed Mater 53:257–71. CrossRefGoogle Scholar
  14. Forsell C, Swedenborg J, Roy J, Christian Gasser T (2013) The quasi-static failure properties of the abdominal aortic aneurysm wall estimated by a mixed experimental–numerical approach. Ann Biomed Eng 41(7):1554–1566. ISBN 1573-9686 (Electronic)\(\backslash\)r0090-6964 (Linking)CrossRefGoogle Scholar
  15. Garcia-Herrera CM, Atienza JM, Rojo FJ, Claes E, Guinea GV, Celentano DJ, Garcia-Montero C, Burgos RL (2012) Mechanical behaviour and rupture of normal and pathological human ascending aortic wall. Med Biol Eng Comput 50(6):559–66. CrossRefGoogle Scholar
  16. Gasser TC, Holzapfel GA (2006) Modeling the propagation of arterial dissection. Eur J Mech A Solids 25(4):617–633. ISBN 0997-7538MathSciNetCrossRefzbMATHGoogle Scholar
  17. Gasser TC, Ogden RW, Holzapfel GA (2006) Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J R Soc Interface 3(6):15–35. ISBN 1742-5689 (Print)\(\backslash\)r1742-5662 (Linking)CrossRefGoogle Scholar
  18. Goods SH, Neuschwanger CL, Henderson C, Skala DM (1997) Mechanical properties and energy absorption characteristics of a polyurethane foam. Report, Sandia National Labs., Albuquerque, NM (United States).
  19. Holzapfel GA (2001) Biomechanics of soft tissue. Handb Mater Behav Models 3(1):1049–1063MathSciNetGoogle Scholar
  20. Holzapfel GA, Ogden RW (2015) On the tensioncompression switch in soft fibrous solids. Eur J Mech A Solids 49:561–569. MathSciNetCrossRefzbMATHGoogle Scholar
  21. 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(1–3):1–48. ISBN 0374-3535MathSciNetCrossRefzbMATHGoogle Scholar
  22. Holzapfel GA, Sommer G, Gasser CT, Regitnig P (2005) Determination of layer-specic mechanical properties of human coronary arteries with nonatherosclerotic intimal thickening and related constitutive modeling. Heart Circ Physiol 289(5):2048–2058. CrossRefGoogle Scholar
  23. Iliopoulos DC, Deveja RP, Kritharis EP, Perrea D, Sionis GD, Toutouzas K, Stefanadis C, Sokolis DP (2009) Regional and directional variations in the mechanical properties of ascending thoracic aortic aneurysms. Med Eng Phys 31(1):1–9CrossRefGoogle Scholar
  24. Kelly PJ, Stein J, Shafqat S, Eskey C, Doherty D, Chang Y, Kurina A, Furie KL (2001) Functional recovery after rehabilitation for cerebellar stroke. Stroke 32(2):530–534. CrossRefGoogle Scholar
  25. Leng X, Chen X, Deng X, Sutton MA, Lessner SM (2015) Modeling of experimental atherosclerotic plaque delamination. Ann Biomed Eng 43(12):2838–2851. CrossRefGoogle Scholar
  26. Maiti S, Geubelle PH (2005) A cohesive model for fatigue failure of polymers. Eng Fract Mech 72(5):691–708. ISBN 00137944CrossRefGoogle Scholar
  27. Maiti S, Rangaswamy K, Geubelle PH (2005) Mesoscale analysis of dynamic fragmentation of ceramics under tension. Acta Mater 53(3):823–834. CrossRefGoogle Scholar
  28. Mantič V, Távara L, Blázquez A, Graciani E, París F (2015) A linear elastic–brittle interface model: application for the onset and propagation of a fibre-matrix interface crack under biaxial transverse loads. Int J Fract 195(1–2):15–38. CrossRefGoogle Scholar
  29. Masouros SD, Parker KH, Hill AM, Amis AA, Bull AMJ (2009) Testing and modelling of soft connective tissues of joints: a review. J Strain Anal Eng Des 44(5):305–318. CrossRefGoogle Scholar
  30. Masuda Y, Yamada Z, Morooka N, Watanabe S, Inagaki Y (1991) Prognosis of patients with medically treated aortic dissections. Circulation 84(5 Suppl):7–13Google Scholar
  31. Mészáros I, Mórocz J, Szlávi J, Schmidt J, Tornóci L, Nagy L, Szép L (2000) Epidemiology and clinicopathology of aortic dissection. Chest 117(5):1271–1278. CrossRefGoogle Scholar
  32. Monson KL, Goldsmith W, Barbaro NM, Manley GT (2005) Significance of source and size in the mechanical response of human cerebral blood vessels. J Biomech 38(4):737–44. CrossRefGoogle Scholar
  33. Nittur PG, Maiti S, Geubelle PH (2008) Grain-level analysis of dynamic fragmentation of ceramics under multi-axial compression. J Mech Phys Solids 56(56):993–1017CrossRefGoogle Scholar
  34. Noble C, van der Sluis O, Voncken RMJ, Burke O, Franklin SE, Lewis R, Taylor ZA (2017) Simulation of arterial dissection by a penetrating external body using cohesive zone modelling. J Mech Behav Biomed Mater 71(February):95–105. CrossRefGoogle Scholar
  35. Ogden RW (2009) Anisotropy and nonlinear elasticity in arterial wall mechanics. In: Holzapfel GA, Ogden RW (eds) 179–258. Vienna: Springer. 978-3-211-95875-9Google Scholar
  36. Ortiz M, Pandolfi A (1999) Finite-deformation irreversible cohesive elements for three-dimensional crack-propagation analysis. Int J Numer Methods Eng 44(9):1267–1282CrossRefGoogle Scholar
  37. Patel PS, Shepherd DE, Hukins DW (2008) Compressive properties of commercially available polyurethane foams as mechanical models for osteoporotic human cancellous bone. BMC Musculoskelet Disord 9:137. CrossRefGoogle Scholar
  38. Peloquin JM, Santare MH, Elliott DM (2016) Advances in quantification of meniscus tensile mechanics including nonlinearity, yield, and failure. J Biomech Eng 138(2):021002. CrossRefGoogle Scholar
  39. Pichamuthu JE, Phillippi JA, Cleary DA, Chew DW, Hempel J, Vorp DA, Gleason TG (2013) Differential tensile strength and collagen composition in ascending aortic aneurysms by aortic valve phenotype. Ann Thorac Surg 96(6):2147–54. CrossRefGoogle Scholar
  40. Purslow PP (1983) Positional variations in fracture toughness, stiffness and strength of descending thoracic pig aorta. J Biomech 16(11):947–953. CrossRefGoogle Scholar
  41. Raghavan ML, Webster MW, Vorp DA (1996) Ex vivo biomechanical behavior of abdominal aortic aneurysm: assessment using a new mathematical model. Ann Biomed Eng 24(5):573–582. ISBN 0090-6964 (Print)\(\backslash\)r0090-6964 (Linking)CrossRefGoogle Scholar
  42. Raghavan ML, Hanaoka MM, Kratzberg JA, de Lourdes Higuchi M, da Silva ES (2011) Biomechanical failure properties and microstructural content of ruptured and unruptured abdominal aortic aneurysms. J Biomech 44(13):2501–7. CrossRefGoogle Scholar
  43. Robertson AM, Duan X, Aziz KM, Hill MR, Watkins SC, Cebral JR (2015) Diversity in the strength and structure of unruptured cerebral aneurysms. Ann Biomed Eng 43(7):1502–15. CrossRefGoogle Scholar
  44. Ropper AH, Zervas NT (1984) Outcome 1 year after sah from cerebral aneurysm. J Neurosurg 60(5):909–915. PMID: 6716158CrossRefGoogle Scholar
  45. Rubod C, Boukerrou M, Brieu M, Jean-Charles C, Dubois P, Cosson M (2008) Biomechanical properties of vaginal tissue: preliminary results. Int Urogynecol J Pelvic Floor Dysfunct 19(6):811–6. CrossRefGoogle Scholar
  46. Sang C, Maiti S, Fortunato RN, Kofler J, Robertson AM (2018) A uniaxial testing approach for consistent failure in vascular tissues. J Biomech Eng 140(6):6061010–106101010. CrossRefGoogle Scholar
  47. Sato J, Hutchings IM, Woodhouse J (2007) Measurement of the elastic modulus of paperboard from the low-frequency vibration modes of rectangular plates. Jpn Tappi J 61(7):837–851. CrossRefGoogle Scholar
  48. Shah SB, Witzenburg C, Hadi MF, Wagner HP, Goodrich JM, Alford PW, Barocas VH (2014) Prefailure and failure mechanics of the porcine ascending thoracic aorta: experiments and a multiscale model. J Biomech Eng 136(2):021028. CrossRefGoogle Scholar
  49. Sichting F, Steinke H, Wagner MF, Fritsch S, Hadrich C, Hammer N (2015) Quantification of material slippage in the iliotibial tract when applying the partial plastination clamping technique. J Mech Behav Biomed Mater 49:112–7. CrossRefGoogle Scholar
  50. Smoljkic M, Fehervary H, Van den Bergh P, Jorge-Penas A, Kluyskens L, Dymarkowski S, Verbrugghe P, Meuris B, Vander Sloten J, Famaey N (2017) Biomechanical characterization of ascending aortic aneurysms. Biomech Model Mechanobiol 16(2):705–720. CrossRefGoogle Scholar
  51. Steiger HJ, Aaslid R, Keller S, Reulen HJ (1989) Strength, elasticity and viscoelastic properties of cerebral aneurysms. Heart Vessels 5(1):41–46. ISBN 0910-8327 (Print)CrossRefGoogle Scholar
  52. Stoll RR (1979) Set theory and logic. Dover books on advanced mathematics. Dover Publications, MineolaGoogle Scholar
  53. Taylor D (2018) Measuring fracture toughness in biological materials. J Mech Behav Biomed Mater 77:776–782. CrossRefGoogle Scholar
  54. Taylor D, OMara N, Ryan E, Takaza M, Simms C (2012) The fracture toughness of soft tissues. J Mech Behav Biomed Mater 6:139–147. CrossRefGoogle Scholar
  55. Teng Z, Tang D, Zheng J, Woodard PK, Hoffman AH (2009) An experimental study on the ultimate strength of the adventitia and media of human atherosclerotic carotid arteries in circumferential and axial directions. J Biomech 42(15):2535–9. CrossRefGoogle Scholar
  56. Walsh MT, Cunnane EM, Mulvihill JJ, Akyildiz AC, Gijsen FJ, Holzapfel GA (2014) Uniaxial tensile testing approaches for characterisation of atherosclerotic plaques. J Biomech 47(4):793–804. CrossRefGoogle Scholar
  57. Wang L, Roper SM, Hill NA, Luo X (2017) Propagation of dissection in a residually-stressed artery model. Biomech Model Mechanobiol 16(1):139–149. CrossRefGoogle Scholar
  58. Wren TAL, Carter DR (1998) A microstructural model for the tensile constitutive and failure behavior of soft skeletal connective tissues. J Biomech Eng 120(1):55. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mechanical Engineering and Materials ScienceUniversity of PittsburghPittsburghUSA
  2. 2.Department of BioengineeringUniversity of PittsburghPittsburghUSA
  3. 3.Department of Chemical and Petroleum EngineeringUniversity of PittsburghPittsburghUSA

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