Solid-beam finite element analysis of Nitinol stents

This paper discusses the finite element (FE) modelling of Nitinol stent structures by means of a recently introduced solid-beam finite element technology. FE stenting simulations based on standard 3D solid elements are computationally very expensive. An adequate FE discretization of the stent structure requires a large number of elements for two reasons: Several elements are needed in the thickness directions of the stent struts in order to resolve localized martensite transformations. Additionally, due to the slenderness of the struts, a dense discretization in longitudinal direction is required to retain reasonable element aspect ratios. In combination with non-linearities emerging from the non-linear material behaviour, large deformations, and contact, stenting simulations become very challenging and time consuming. The solid-beam finite element technology is considered to reduce computational costs by working with only one element in thickness direction and allowing larger aspect ratios while the results are still acceptable to be used in the iterative design process. The here suggested formulation based on an eight-node brick element geometry is suitable to efficiently model beam-like structures with prismatic cross-sections without the necessity of abstracting the beam axes from the three-dimensional (3D) geometry. All relevant locking phenomena are alleviated by a tailored combination of different techniques. The combination of the new finite element technology with a sophisticated material model that represents the pseudoelastic behaviour of Nitinol is an additional aspect to be investigated in this regard. Validations at the example of an isolated strut show that very accurate results are obtained for thick and thin strut geometries. Moreover, we successfully simulate the crimping–expanding process of an intracranial stent showing a very complex geometry. The results match those based on high density solid meshes very well. The computational benefit becomes clearly evident.