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One-dimensional quasistatic model of biodegradable elastic curved rods

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Abstract

In this paper, we derive and analyze a one-dimensional model of biodegradable elastic curved rods. The model is given for displacement and degradation as unknown functions and is nonlinear. It is obtained from the three-dimensional equations of the biodegradable elastic rod-like bodies using formal asymptotic expansion techniques with respect to the small thickness of the rod. Existence and uniqueness of the solution of the one-dimensional model are proved. Some qualitative properties of the model are also obtained from the numerical approximation of the model.

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References

  1. Andreucci, D.: Lecture Notes on Free Boundary Problems for Parabolic Equations. Doctoral School of Cisterna (2011)

  2. Chen Y., Li Q.: Mathematical modeling of polymer biodegradation and erosion. Mater. Sci. Forum 654–656, 2071–2074 (2010)

    Article  Google Scholar 

  3. Dautray R., Lions J.-L.: Mathematical Analysis and Numerical Methods for Science and Technology, vol. 5. Evolution Problems. I. Springer, Berlin (1992)

    MATH  Google Scholar 

  4. Evans L.C.: Partial Differential Equations, 2nd edn. American Mathematical Society, Providence (2010)

    MATH  Google Scholar 

  5. Göpferich A.: Mechanisms of polymer degradation and erosion. Biomaterials 17, 103–114 (1996)

    Article  Google Scholar 

  6. Jamal R., Sanchez-Palencia É.: Théorie asymptotique des tiges courbes anisotropes. C. R. Acad. Sci. Paris Sér. I Math. 322, 1099–1106 (1996)

    MathSciNet  MATH  Google Scholar 

  7. Jurak M., Tambača J.: Derivation and justification of a curved rod model. Math. Models Methods Appl. Sci. 9, 991–1014 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. Jurak M., Tambača J.: Linear curved rod model: General curve. Math. Models Methods Appl. Sci. 11, 1237–1252 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  9. Milliken G.A., Akdeniz F.: A theorem on the difference of the generalized inverses of two nonnegative matrices. Commun. Stat. Theory Methods 6, 73–79 (1977)

    Article  MathSciNet  Google Scholar 

  10. Moore J.E. Jr, Soares J.S., Rajagopal K.R.: Biodegradable stents: biomechanical modeling challenges and opportunities. Cardiovasc. Eng. Technol. 1, 52–65 (2010)

    Article  Google Scholar 

  11. Soares J.S., Zunino P.: A mixture model for water uptake, degradation, erosion and drug release from polydisperse polymeric networks. Biomaterials 31, 3032–3042 (2010)

    Article  Google Scholar 

  12. Taylor M.: Partial Differential Equations I: Basic Theory. Springer, Berlin (2010)

    Google Scholar 

  13. Wu Z., Yin J., Wang C.: Elliptic & Parabolic Equations. World Scientific Publishing Co. Pte. Ltd., Hackensack (2006)

    Book  MATH  Google Scholar 

  14. Zunino, P., Vesentini, S., Porpora, A., Soares, J.S., Gautieri A., Redaelli, A.: Multiscale computational analysis of degradable polymers. In: Modeling of Physiological Flows. Springer, Milan, pp. 333–361 (2012)

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Authors and Affiliations

  1. Department of Mathematics, University of Zagreb, Zagreb, Croatia

    Josip Tambača

  2. Faculty of Organization and Informatics, University of Zagreb, Varaždin, Croatia

    Bojan Žugec

Authors
  1. Josip Tambača
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  2. Bojan Žugec
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Correspondence to Josip Tambača.

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Tambača, J., Žugec, B. One-dimensional quasistatic model of biodegradable elastic curved rods. Z. Angew. Math. Phys. 66, 2759–2785 (2015). https://doi.org/10.1007/s00033-015-0512-3

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  • DOI: https://doi.org/10.1007/s00033-015-0512-3

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