Advertisement

A Numerical Approach to Predict Fracture in Bio-inspired Composites Using Ultrasonic Waves

  • Jacob Loving
  • Marco Fielder
  • Arun K. Nair
Article

Abstract

Bone is a biomaterial that has high resistance to fracture, but due to osteoporosis bone structure and properties deteriorates, which can lead to high fracture risk. Bio-inspired composites are an effective way to replace bone loss. We study here two bio-inspired composites, one inspired from circumferential lamella and the second from the compact bone properties respectively. The defects in bio-inspired composite materials can be detected using ultrasonic waves. The ultrasonic wave interaction with a medium can lead to information about its microstructure and material properties. To gain a better understanding of wave propagation through bio-inspired composites, ultrasound waves are modeled using the finite element method along with the Newmark’s constant acceleration method to study these composites with and without defects. For the bio-inspired composite based on circumferential lamella, we observe two in-plane energy flux waves. The faster quasi-longitudinal and the slower quasi-shear will deviate from the normal direction depending on the fiber orientation in the composites. The wave interaction with defects in bio-inspired composites will split the ultrasound wave into two components with finite energy peaks. We observe that the distance between these energy peaks of the waves correspond with the size of the defect in the composite. The change in the porosity of the bio-inspired composites causes a decrease in the maximum energy flux and wave speed. We also examine the use of biologically inspired signals, which has a lower relative attenuation with a higher frequency when compared to a typical transducer to study wave propagation in composites. For the cases studied in this paper, the different input signals show no significant difference in the peak-to-peak distance in energy flux after encountering a defect when compared to a sinusoidal signal.

Keywords

Ultrasonic waves in bio-inspired composites Finite element modeling Bio-inspired signals in ultrasonics 

Notes

Acknowledgements

AKN, JL and MF would like to thank support from Department of Mechanical Engineering, University of Arkansas. Authors also acknowledge the support in part by the National Science Foundation under the Grants ARI#0963249, MRI#0959124 and EPS#0918970, and a Grant from Arkansas Science and Technology Authority, managed by Arkansas High Performance Computing Center. Authors also acknowledge discussions with Dr. Ronald Kriz regarding glyph generation for anisotropic materials.

Compliance with Ethical Standards

Conflict of interest

The authors declare that they have no conflict of interest

Supplementary material

10921_2018_497_MOESM1_ESM.docx (237 kb)
Supplementary material 1 (docx 236 KB)
10921_2018_497_MOESM2_ESM.docx (34 kb)
Supplementary material 2 (docx 34 KB)

References

  1. 1.
    Hadjidakis, D.J., Androulakis, I.I.: Bone remodeling. Ann. N. Y. Acad. Sci. 1092(1), 385–396 (2006)CrossRefGoogle Scholar
  2. 2.
    Johnell, O., Kanis, J.: An estimate of the worldwide prevalence and disability associated with osteoporotic fractures. Osteoporos. Int. 17(12), 1726–1733 (2006)CrossRefGoogle Scholar
  3. 3.
    Kanis, J., et al.: European guidance for the diagnosis and management of osteoporosis in postmenopausal women. Osteoporos. Int. 19(4), 399–428 (2008)CrossRefGoogle Scholar
  4. 4.
    Matsukawa, M.: Application of a micro-Brillouin light scattering technique to characterize bone in the GHz range. Ultrasonics 54(5), 6 (2014)CrossRefGoogle Scholar
  5. 5.
    Morin, C., Hellmich, C.: A multiscale poromicromechanical approach to wave propagation and attenuation in bone. Ultrasonics 54(5), 1251–1269 (2014)CrossRefGoogle Scholar
  6. 6.
    World Health Organization: Prevention and Management of Osteoporosis: Report of a WHO Scientific Group. Diamond Pocket Books (P) Ltd, New Delhi (2003)Google Scholar
  7. 7.
    Meziere, F., et al.: Measurements of ultrasound velocity and attenuation in numerical anisotropic porous media compared to Biot’s and multiple scattering models. Ultrasonics 54(5), 1146–1154 (2014)CrossRefGoogle Scholar
  8. 8.
    Tatarinov, A., et al.: Multi-frequency axial transmission bone ultrasonometer. Ultrasonics 54(5), 1162–1169 (2014)CrossRefGoogle Scholar
  9. 9.
    Egorov, V., et al.: Osteoporosis detection in postmenopausal women using axial transmission multi-frequency bone ultrasonometer: clinical findings. Ultrasonics 54(5), 1170–1177 (2014)CrossRefGoogle Scholar
  10. 10.
    Cassereau, D., et al.: A hybrid FDTD-Rayleigh integral computational method for the simulation of the ultrasound measurement of proximal femur. Ultrasonics 54(5), 1197–1202 (2014)CrossRefGoogle Scholar
  11. 11.
    Potsika, V.T., et al.: Application of an effective medium theory for modeling ultrasound wave propagation in healing long bones. Ultrasonics 54(5), 1219–1230 (2014)CrossRefGoogle Scholar
  12. 12.
    Calle, S., et al.: Ultrasound propagation in trabecular bone: a numerical study of the influence of microcracks. Ultrasonics 54(5), 1231–1236 (2014)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Nagatani, Y., Mizuno, K., Matsukawa, M.: Two-wave behavior under various conditions of transition area from cancellous bone to cortical bone. Ultrasonics 54(5), 1245–1250 (2014)CrossRefGoogle Scholar
  14. 14.
    Berteau, J.P., et al.: In vitro ultrasonic and mechanic characterization of the modulus of elasticity of children cortical bone. Ultrasonics 54(5), 1270–1276 (2014)CrossRefGoogle Scholar
  15. 15.
    Baroncelli, G.I.: Quantitative ultrasound methods to assess bone mineral status in children: technical characteristics, performance, and clinical application. Pediatr. Res. 63(3), 220–228 (2008)CrossRefGoogle Scholar
  16. 16.
    Nagatani, Y., et al.: Applicability of finite-difference time-domain method to simulation of wave propagation in cancellous bone. Jpn. J. Appl. Phys. 45(9R), 7186 (2006)CrossRefGoogle Scholar
  17. 17.
    Fellah, Z.E.A., et al.: Ultrasonic wave propagation in human cancellous bone: application of Biot theory. J. Acoust. Soc. Am. 116(1), 61–73 (2004)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Bossy, E., et al.: Three-dimensional simulation of ultrasound propagation through trabecular bone structures measured by synchrotron microtomography. Phys. Med. Biol. 50(23), 5545 (2005)CrossRefGoogle Scholar
  19. 19.
    Fratzl, P., et al.: Structure and mechanical quality of the collagen-mineral nano-composite in bone. J. Mater. Chem. 14(14), 2115–2123 (2004)CrossRefGoogle Scholar
  20. 20.
    Launey, M.E., Buehler, M.J., Ritchie, R.O.: On the mechanistic origins of toughness in bone. Annu. Rev. Mater. Res. 40, 25–53 (2010)CrossRefGoogle Scholar
  21. 21.
    Yoon, Y.J., Cowin, S.C.: The estimated elastic constants for a single bone osteonal lamella. Biomech. Model. Mechanobiol. 7(1), 1–11 (2008)CrossRefGoogle Scholar
  22. 22.
    Haïat, G., et al.: Influence of a gradient of material properties on ultrasonic wave propagation in cortical bone: application to axial transmission. J. Acoust. Soc. Am. 125(6), 4043–4052 (2009)CrossRefGoogle Scholar
  23. 23.
    Amini, A.R., Laurencin, C.T., Nukavarapu, S.P.: Bone tissue engineering: recent advances and challenges. Critical reviews\(^{{\rm TM}}\). Biomed. Eng. 40(5), 363–408 (2012)Google Scholar
  24. 24.
    Asa’ad, F., et al.: 3D-Printed scaffolds and biomaterials: review of alveolar bone augmentation and periodontal regeneration applications. Int. J. Dent. 2016, 1239842 (2016)CrossRefGoogle Scholar
  25. 25.
    Kang, H.W., et al.: A 3D bioprinting system to produce human-scale tissue constructs with structural integrity. Nat. Biotechnol. 34(3), 312 (2016)CrossRefGoogle Scholar
  26. 26.
    Cardoso, L., Cowin, S.C.: The role of microarchitecture on absorption and scattering of ultrasound waves in Trabecular bone. In: Poromechanics V@s Proceedings of the Fifth Biot Conference on Poromechanics. ASCE (2013)Google Scholar
  27. 27.
    Cardoso, L., Cowin, S.C.: Role of structural anisotropy of biological tissues in poroelastic wave propagation. Mech. Mater. 44, 174–188 (2012)CrossRefGoogle Scholar
  28. 28.
    Cowin, S.C., Cardoso, L.: Fabric dependence of wave propagation in anisotropic porous media. Biomech. Model. Mechanobiol. 10(1), 39–65 (2011)CrossRefGoogle Scholar
  29. 29.
    Nair, A.K., Kriz, R.D., Prosser, W.H.: Nonlinear elastic effects in graphite/epoxy: an analytical and numerical prediction of energy flux deviation. Wave Motion 51(7), 1138–1148 (2014)CrossRefGoogle Scholar
  30. 30.
    Nair, A.K., Heyliger, P.R.: Elastic waves in combinatorial material libraries. Wave Motion 43(7), 529–543 (2006)CrossRefGoogle Scholar
  31. 31.
    Reddy, J.N.: Energy Principles and Variational Methods in Applied Mechanics. Wiley, New York (1984)Google Scholar
  32. 32.
    Bathe, K.-J., Wilson, E.L.: Numerical methods in finite element analysis, p. 543. Prentice-Hall, Englewood Cliffs, NJ (1976)zbMATHGoogle Scholar
  33. 33.
    Kriz, R.: Three visual methods: envisioning tensors, creating eigenvalue-eigenvector glyphs. http://www.esm.rkriz.net/classes/ESM5344/ESM5344_NoteBook/ESM4714/methods/EEG.html (2006)
  34. 34.
    Kriz, R.: Cijkl Glyphs. http://esm.rkriz.net/classes/ESM5344/ESM5344_NoteBook/Projects/Cijkl (2016). (Accessed 2016; open source code)
  35. 35.
    Kriz, R., Heyliger, P.: Finite element model of stress wave topology in unidirectional graphite/Epoxy: wave velocities and flux deviations. In: Review of Progress in Quantitative Nondestructive Evaluation. Springer, New York, pp. 141–148 (1989)CrossRefGoogle Scholar
  36. 36.
    Hamed, E., Lee, Y., Jasiuk, I.: Multiscale modeling of elastic properties of cortical bone. Acta Mech. 213(1–2), 131–154 (2010)CrossRefGoogle Scholar
  37. 37.
    Kriz, R., Stinchcomb, W.: Elastic moduli of transversely isotropic graphite fibers and their composites. Exp. Mech. 19(2), 41–49 (1979)CrossRefGoogle Scholar
  38. 38.
    Kriz, R.D., Stinchcomb, W.: Mechanical properties for thick fiber reinforced composite materials having transversely isotropic fibers. No. VPI-E-77-13 (1977)Google Scholar
  39. 39.
    Hakim, I., et al.: The effect of manufacturing conditions on discontinuity population and fatigue fracture behavior in carbon/epoxy composites. In: AIP Conference Proceedings. AIP Publishing (2017)Google Scholar
  40. 40.
    Li, H., Zhou, Z.: Air-coupled ultrasonic signal processing method for detection of lamination defects in molded composites. J. Nondestruct. Eval. 36(3), 45 (2017)CrossRefGoogle Scholar
  41. 41.
    Fierro, G.-P.M., et al.: Monitoring of self-healing composites: a nonlinear ultrasound approach. Smart Mater. Struct. 26(11), 115015 (2017)CrossRefGoogle Scholar
  42. 42.
    Hamed, E., Jasiuk, I.: Multiscale damage and strength of lamellar bone modeled by cohesive finite elements. J. Mech. Behav. Biomed. Mater. 28, 94–110 (2013)CrossRefGoogle Scholar
  43. 43.
    Baron, C., Talmant, M., Laugier, P.: Effect of porosity on effective diagonal stiffness coefficients (CII) and elastic anisotropy of cortical bone at 1 MHz: a finite-difference time domain study. J. Acoust. Soc. Am. 122(3), 1810–1817 (2007)CrossRefGoogle Scholar
  44. 44.
    Lakshmanan, S., Bodi, A., Raum, K.: Assessment of anisotropic tissue elasticity of cortical bone from high-resolution, angular acoustic measurements. IEEE Trans. Ultrason. Ferroelectr. Freq. Control 54(8), 1560–1570 (2007)CrossRefGoogle Scholar
  45. 45.
    Taylor, D., Lee, T.: Microdamage and mechanical behaviour: predicting failure and remodelling in compact bone. J. Anat. 203(2), 203–211 (2003)CrossRefGoogle Scholar
  46. 46.
    Hopper, C., et al.: Bioinspired low-frequency material characterisation. Adv. Acoust. Vib. 2012, 9 (2012)Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Multiscale Materials Modeling Lab, Department of Mechanical EngineeringUniversity of ArkansasFayettevilleUSA
  2. 2.Institute for Nanoscience and EngineeringUniversity of ArkansasFayettevilleUSA

Personalised recommendations