Shell Models of the Artery Wall

In this paper we presented different shell models and discuss their applicability to model the mechanical behavior of arterial walls. Presented models are: stationary and evolutionary, linear and nonlinear, membrane dominated and bending dominated. Special focus is put on the physically nonlinear stationary models which were first presented by the author in [11]. We give the well posedness results for the physically nonlinear stationary problem and linear nonstationary problem. We also discuss the numerical methods for solving the presented equations for the three dimensional field of displacement of the middle surface of the wall. Finally we give some simple computational examples.