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Zeitschrift für angewandte Mathematik und Physik

, Volume 66, Issue 5, pp 2759–2785

# One-dimensional quasistatic model of biodegradable elastic curved rods

• Josip Tambača
• Bojan Žugec
Article

## 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.

74K10 74E99

## Keywords

Elasticity Degradation Curved rods One-dimensional model

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## References

1. 1.
Andreucci, D.: Lecture Notes on Free Boundary Problems for Parabolic Equations. Doctoral School of Cisterna (2011)Google Scholar
2. 2.
Chen Y., Li Q.: Mathematical modeling of polymer biodegradation and erosion. Mater. Sci. Forum 654–656, 2071–2074 (2010)
3. 3.
Dautray R., Lions J.-L.: Mathematical Analysis and Numerical Methods for Science and Technology, vol. 5. Evolution Problems. I. Springer, Berlin (1992)
4. 4.
Evans L.C.: Partial Differential Equations, 2nd edn. American Mathematical Society, Providence (2010)
5. 5.
Göpferich A.: Mechanisms of polymer degradation and erosion. Biomaterials 17, 103–114 (1996)
6. 6.
Jamal R., Sanchez-Palencia É.: Théorie asymptotique des tiges courbes anisotropes. C. R. Acad. Sci. Paris Sér. I Math. 322, 1099–1106 (1996)
7. 7.
Jurak M., Tambača J.: Derivation and justification of a curved rod model. Math. Models Methods Appl. Sci. 9, 991–1014 (1999)
8. 8.
Jurak M., Tambača J.: Linear curved rod model: General curve. Math. Models Methods Appl. Sci. 11, 1237–1252 (2001)
9. 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)
10. 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)
11. 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)
12. 12.
Taylor M.: Partial Differential Equations I: Basic Theory. Springer, Berlin (2010)Google Scholar
13. 13.
Wu Z., Yin J., Wang C.: Elliptic & Parabolic Equations. World Scientific Publishing Co. Pte. Ltd., Hackensack (2006)
14. 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)Google Scholar

## Copyright information

© Springer Basel 2015

## Authors and Affiliations

1. 1.Department of MathematicsUniversity of ZagrebZagrebCroatia
2. 2.Faculty of Organization and InformaticsUniversity of ZagrebVaraždinCroatia