In this paper we formulate and analyze the mixed formulation of the one-dimensional equilibrium model of elastic stents. The model is based on the curved rod model for the inextensible and ushearable struts and is formulated in the weak form in [5]. It is given by a system of ordinary differential equations at the graph structure. In order to numerically treat the model using finite element method the mixed formulation is plead for. We obtain equivalence of the weak and the mixed formulation by proving the Babuska-Brezzi condition for the stent structure.

No abstract

No abstract

No abstract

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 Tambača and Žugec (‘One-dimensional quasistatic model of biodegradable elastic curved rods’, Zeitschrift für Angewandte Mathematik und Physik 2015; 66(5): 2759–2785) and the ideas from the one-dimensional elastic stent modelling by Tambača et al. (‘Mathematical modeling of vascular stents’, SIAM Journal on Applied Mathematics 2010; 70(6): 1922–1952) used to formulate contact conditions at vertices. We prove the existence and uniqueness results for the model.