One-dimensional quasistatic model of biodegradable elastic curved rods
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.
Mathematics Subject Classification74K10 74E99
KeywordsElasticity Degradation Curved rods One-dimensional model
Unable to display preview. Download preview PDF.
- 1.Andreucci, D.: Lecture Notes on Free Boundary Problems for Parabolic Equations. Doctoral School of Cisterna (2011)Google Scholar
- 12.Taylor M.: Partial Differential Equations I: Basic Theory. Springer, Berlin (2010)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)Google Scholar