New solid-shell and solid-beam finite elements with applications to medical technology

In this paper, new solid-shell and solid-beam finite element formulations for finite deformation problems are introduced. One application of interest, concerning these types of elements, can be found in the simulation of stent implementation in the treatment of stenosis. The beam-like structure of the stent and the shell-like structure of the blood vessel can be modelled easily by using these types of elements. Moreover, the modelling of the interaction of the different structural types between each other and with the surounding tissue becomes more simple. A high rate of convergence, by using only one element in thickness direction that is comparable to classical structural elements, can be named as a major requirement for the element formulations. In this regard, different locking effects are cured by a special combination of the assumed natural strain method (ANS) and the enhanced assumed strain method (EAS). In addition a variable number of quadrature points can be used in thickness direction in order to capture nonlinearites. This is combined with the concept of reduced integration for the sake of computational efficiency. An adaptive hourglass stabilization that also accounts for material nonlinearities is a crucial issue in this regard. (© 2011 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)