A biodegradable elastic stent model. (English) Zbl 07254371
Summary: In this paper we derive and analyse a one-dimensional model of biodegradable elastic stents. The model is given as a nonlinear system of ordinary differential equations on a graph defined by the geometry of stent struts. The unknowns in the problem are the displacement of the middle curve of the struts, the infinitesimal rotation of the cross-sections of the stent struts, the contact couples and contact forces at struts and a function describing the degradation of the stent. The model is based on the one-dimensional model of a biodegradable elastic curved rod model by J. Tambača and B. Žugec [Z. Angew. Math. Phys. 66, No. 5, 2759–2785 (2015; Zbl 1327.74091)] and the ideas from the one-dimensional elastic stent modelling by J. Tambača et al. [SIAM J. Appl. Math. 70, No. 6, 1922–1952 (2010; Zbl 1427.74099)] used to formulate contact conditions at vertices. We prove the existence and uniqueness results for the model.
MSC:
| 74-XX | Mechanics of deformable solids |
References:
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