A phase-field approach to the fracture of anisotropic medium

Tez Türü: Yüksek Lisans

Tezin Yürütüldüğü Kurum: Almanya

Tez Danışmanı: Christian Miehe; Hüsnü Dal

Tezin Onay Tarihi: 2014

Tezin Dili: İngilizce

Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu

Özet:

Mortality rates due to cardiovascular diseases are still high in developed countries despite a lot of researches conducted so far. Fracture of arterial walls are of fundamental concern in this respect which can be induced by, e.g., excessive growth of atherosclerotic plaque. Though experimental investigations are of primary importance, the practical issues thereof render the numerical analysis an indispensable tool to better understand the fracture of arterial walls subject to alterations in their mechanical properties under supra–physiological loading conditions.

In view of the anisotropic mechanical response of the arterial tissue, the finite strain continuum mechanics together with the corresponding constitutive models is outlined in Section 2 and 3, respectively. Section 4 introduces a one–dimensional finite element implementation of a recently developed crack phase–field approach to model fracture, which is followed by a three–dimensional Galerkin–type weak formulation featuring multi–crack phase–fields attributed to ground matrix and each family of collagen fibers embedded in that matrix. Later, the corresponding numerical model is tested for a two–dimensional replica of an artery cross–section suffering due to a plaque formation involving lipid pool and calcified regions. The results indicate the need for a mathematical model that should account for the anisotropic elastic and fracture behavior of arterial tissues which are comparable to engineered composite materials.