Fluid–structure interaction within three-dimensional models of an idealized arterial wall A. El Baroudi a,⇑ , F. Razafimahery b , L. Rakotomanana b a Arts et Métiers ParisTech, 2 bd du Ronceray, 49035 Angers, France b IRMAR, Université de Rennes 1, Campus de Beaulieu, 35042 Rennes Cedex, France article info Article history: Received 27 May 2013 Received in revised form 4 June 2014 Accepted 30 June 2014 Available online 2 August 2014 Keywords: Fluid–structure interaction Modal analysis Arterial wall Finite element method Multilayer abstract The ascending branch of the aorta is one of the most stressed organ of the arterial system. We aim to design a biomechanical model for analysing the aorta dynamics under a shock. The model includes the aorta layers and the influence of the blood pressure. We undertake a three-dimensional modal analysis of the coupled aorta–blood system. We determine in the present work the coupled natural frequencies and the modes shapes of the system of the aorta and blood. Three models are presented in this study: three-layers model, two- layers model and one layer model. For the analytical solving a potential technique is used to obtain a general solution for an aorta domain. The finite element model is then validated by these original analytical solutions. The results from the proposed method are in good agreement with numerical solutions. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction Traumatic rupture of the thoracic aorta is commonly known as a fatal injury. The investigation and treatment of Blunt Traumatic Aortic Rupture (BTAR) or Blunt Traumatic Aortic Injury (BTAI) are nowadays well described. However, some uncertainty remains with regards of the pathogenic aetiology of BTAI. The injury and consequently the rupture are thought to be the result of both anatomic and mechanical factors. Initially, investigators proposed that BTAR was due to sudden increasing of arterial blood pressure. Later, recent theories suggest that injury or rupture result from a complex combination of mechanical stresses and is thus highly multi-parametric. Numerous factors are involved in the injury process but it remains uncertain to what extent, if any, each of them plays a part and under what circumstances. Of course, every mechan- ical force acting on the aorta may be important in the injury process (Zhao, Field, Diggers, & Richens, 2008). However, the relative importance of these forces still remains unclear and several different forces and hypotheses have been proposed over the years. It was thought that the injury was caused by a sudden stretching of the aorta. However, this mode of failure was probably not the only one since a cylindrical vessel under pressure would rupture axially rather than transversely. Then, some others attributed the occurrence of injury to a sudden increasing of blood pressure or also to the occurring of a water-hammer effect, which leads to high-pressure waves being reflected back along the vessel wall (Forman, Stacey, Evans, & Kent, 2008). Nevertheless, the water-hammer model is unable to consider the additional deformation of the aorta during an impact where increasing the curvature of the aorta could possibly lead to greater increases in the pressure wave in this region (Prosi, Perktold, Ding, & Friedman, 2004). More recent theories propose that aorta injury results from a http://dx.doi.org/10.1016/j.ijengsci.2014.06.015 0020-7225/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Corresponding author. E-mail address: adil.elbaroudi@ensam.eu (A. El Baroudi). International Journal of Engineering Science 84 (2014) 113–126 Contents lists available at ScienceDirect International Journal of Engineering Science journal homepage: www.elsevier.com/locate/ijengsci