Jednodimenzionalni model biorazgradivog štapa

Racz, Gabriela Clara (2016) Jednodimenzionalni model biorazgradivog štapa. Diploma thesis, Faculty of Science > Department of Mathematics.

Language: Croatian

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In this thesis, we have studied modelling of elastic rod made from biodegradable polymers. Since rod has a shape of an elongated cylinder, that has one side much longer than the other two, we will consider it as one-dimensional structure placed in a three-dimensional space. In accordance with this assumption, we use one-dimensional elastic biodegradable rod model which includes mechanical and chemical degradation. This way, we have transformed a three-dimensional problem into one-dimensional problem, which requires less memory for numerical simulations. One of the main goals of this research was to study the effect of chemical and mechanical degradation on the behaviour of biodegradable rod. In order to accurately model chemical degradation, we have used an empirical model and determined the degradation rate coefficient from experimental studies found in literature. In numerical simulations, we have used the approximation in polynomial spaces for the middle line shift of the rod and infinitesimal rotation of the cross-section of the rod. Furthermore, we have used Finite Element Method for numerical approximation of degradation in case that diffusion has an effect on mechanical degradation. In other case, when diffusion doesn't have an effect on mechanical degradation, Euler method was used instead. In all simulations, we have considered a biodegradable elastic rod fixed on both ends. We have examined how the behavior of the rod depends on the ratio of the chemical degradation rate coefficient k, and the mechanical degradation coefficient τ. In nearly all simulations, maximal degradation at the ends of the rod was observed. This means that ends of the rod represent critical points where the fracture occurs. Since the biodegradable polymers are widely used as biomedical implants, we've tried to modify shape of the rod in order to expand its lifespan and achieve more uniform degradation along its length. For that purpose, we have designed and tested five different models and compared its simulation results with the results of a homogeneous rods made out of the same amount of material. The best performance was achieved by Model 4 which lasts 2:38 times longer than its homogenous pair. It would be interesting to mathematically formulate and study this shape optimization problem in order to find most durable rod design, but it will be left for future research.

Item Type: Thesis (Diploma thesis)
Supervisor: Tambača, Josip
Date: 2016
Number of Pages: 54
Subjects: NATURAL SCIENCES > Mathematics
Divisions: Faculty of Science > Department of Mathematics
Depositing User: Iva Prah
Date Deposited: 26 Aug 2016 08:16
Last Modified: 26 Aug 2016 08:16

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