In finite elasticity, while developing representation for stress, it is customary to require the reference configuration to be stress free. This study relaxes this requirement and develops representations for stress from a stressed reference configuration. Using the fact that the value of Cauchy stress in the current configuration is independent of the choice of the reference configuration, even though the formula used to compute it depends on the choice of the reference configuration, the sought representation is obtained. It is then assumed that there exists a piecewise smooth mapping between a configuration with prestresses and a configuration that is stress free, and the representation obtained above is used to study the mechanical response of prestressed bodies. The prestress fields are obtained by directly integrating the balance of linear momentum along with the traction free boundary condition. Then, different classes of boundary value problems for the type of inhomogeneous and prestressed bodies of interest are formulated and studied. For the cases studied, it is found that even the global measures like axial-load required to engender a given stretch ratio for a prestressed body vary from the homogeneous stress free bodies, though not significantly. The local measures - stress and deformation - in a prestressed body differ considerably from their homogeneous stress free counterparts. The above gained knowledge is applied to understand the mechanics of circumflex arteries obtained from normotensive and hypertensive micro-mini pigs. It is found that the deformation of these arteries when subjected to inflation and axial extension is not of the form r = r(R), µ = £, z = Z. Comparison is also made between the response of an artery at various levels of smooth muscle activation and stretch ratio as well as normotensive and hypertensive specimens, using statistical methods.

Les anévrysmes de l'aorte ascendante sont un problème de santé publique qui peut menacer le pronostic vital par le risque de rupture ou de dissection. Actuellement, le seul critère permettant de décider d'une intervention est le diamètre maximal de l'anévrysme mesuré par le scanner. La recherche biomécanique a pour objectif de caractériser les propriétés élastiques de l'aorte et de proposer une approche patient-spécifique de l'évaluation du risque de complication. Le but de cette thèse était double. Dans une première partie, il était de déterminer les propriétés à rupture d'anévrysmes de l'aorte ascendante fraîchement excisés à partir d'un banc d'essai de tests en gonflement mis au point dans notre laboratoire. Les résultats ont permis de déterminer un index de risque de rupture basé sur l'extensibilité de l'aorte. Dans une deuxième partie, nous avons identifié les propriétés mécaniques des anévrysmes aortiques à l'aide d'un scanner dynamique préopératoire. Cette identification reposait sur la minimisation simultanée de deux fonctions coût, qui définissaient la différence entre les prédictions d"un modèle numérique et les mesures par le scanner du volume de l'anévrysme au milieu du cycle cardiaque et à la systole. Les résultats étaient corrélés à ceux des tests mécaniques en gonflement, montrant une application prometteuse du scanner dynamique pour l'identification du patient-scpécifique des propriétés mécaniques de l'aorte. Ce travail ouvre un peu plus la voie vers une évaluation patient-spécifique du risque de complication d'un anévrysme de l'aorte ascendante et vers une sélection plus affinée des patients pour la chirurgie. / Aneurysms of the ascending aorta are a life-threatening desease by the risk of rupture or dissection. Currently, the only criterion for deciding an intervention is the maximum diameter of the aneurysm mesured from CT-scan. Biomechanical research aims to characterize the elastic properties of the aorta and to provide a patient-specific approach too assessing the risk of complications. The aim of this thesiswas twofold. In the first part, it was tocharacterize the rupture properties of freshly excised acsending aortic tissue from an inflation bench-test developed in our laboratory. The results were derived to determine a rupture risk index based on the extensibility of the aorta. In the second part, we identified the mechanical properties of aortic aneurysms using preoperative dynamic CT-scan. This identification was based on the simultaneous minimization of two cost functions, which defined the difference between the predictionsof a numerical model and the volumes of the aneurysms measured from the CT-scan in the middle of the cardiac cycle and the sytole. The results were correlated with those of the inflation tests, showing promising application of the dynamic scan for the patient-specific identification of the mechanical properties of the aorta. This work opens a little more the way for the patient-specific assessment of the risk of complications of an aneurysm of the ascending aorta and for a more refined selection of patients for surgery.