Dünyadaki ekonomik, bilimsel ve tıp açısından oldukça önemli ve gözlemlenme oranı yüksek olan ateroskleroz ve disk dejenerasyonu gibi hastalıklar, temelde yumuşak doku hastalıkları olarak adlandırılabilirler. Bu bağlamda, disiplinler arası bir araştırma konusu olan yumuşak dokularda araştırma, sosyoekonomik olarak gittikçe büyüyen bir önem arz etmektedir. Donanım ve yazılım olanaklarındaki hızlı gelişmeler, yumuşak dokuların ve ilgili patalojilerin sayısal olarak detaylı şekilde modellenebilmesine olanak tanımaktadır. Bu çalışmada, viskoelastik özellikler gösteren damar dokusu üzerinde teorik bir modelin öncelikle matematiksel altyapısı oluşturulmuş ve fiziksel büyüklükler ile gerilme ve/veya şekil değiştirme büyüklükleri arasındaki ilişkiler elde edilmiştir. Yöntem olarak, öncelikle büyük deformasyonlar yapan katıların, Lagrangian esaslara göre deformasyon kinematikleri incelenmiş ve bünye denklemleri elde edilmiştir. Bu ifadeler, temel termodinamik kanunları ile ilişkilendirilerek, üç elemanlı viskoelastik bünye denklemi modeline uygulanmıştır. Plastisite teorisinde yaygın kullanım alanı bulan çarpımsal ayrıştırma prensibi kullanılarak, viskoelastik ve saf elastik davranışlar birbirinden ayrıştırılmıştır. Buradan elde edilen ifadelerle, damar yapısı için önemli büyüklükleri göz önüne alan bir kalın boru modeli için yüklenme ve deformasyon ilişkileri elde edilmiştir. Daha sonra, öngörülen modelin içinde bulunan malzeme parametrelerinin tahmini için kurulan deney düzeneği tanıtılmıştır. Bu esnada yapılan kabullerden bahsedilmiş ve kurulan ölçüm sisteminden elde edilen statik ve/veya dinamik yüklenmelere ait verilerin işlenebilmesi için gerekli detaylar sunulmuştur. Deneysel çalışmalarla, teorik sonuçların karşılaştırılması sonucunda elde edilen bulgular yorumlanmıştır.

The great majority of diseases in the (western) world, such as atherosclerosis and degeneration of intervertebral discs are diseases of soft tissues. Hence, the multidisciplinary field of soft tissue research is of crucial scientific, medical and socioeconomic importance. The fast progress in the developments of hardware and software facilities makes it possible to thoroughly investigate biological soft tissues and their pathologies on a computational basis. Since soft tissues are biological materials, which fulfill mechanical purposes and adapt to their mechanical environment (growth, remodeling and morphogenesis), it is of fundamental importance to identify the complex interactions of mechanical and biological responses. This work lays out a viscoelastic material model for the arterial tissue. In order to correctly describe the motion of a thick-walled tubular model of an arterial specimen under combined extension, inflation and torsion loads, large deformation kinematics theory is introduced. Lagrangian practice has been applied, which is a general notion in solid mechanics of hyperviscoelastic materials. The material model is introduced in parallel, which is a non-linear three element solid when regarded with a 1-D analog to standard viscoelastic practices. Principle of multiplicative decomposition, a common practice in large deformation plasticity, is successfully applied to get an insight to time-evolution characteristics of the tissue as well as pure elastic response in a decoupled manner. The material elastic stress law and thermodynamically consistent evolution law, namely the stress-strain relations are derived. The arterial tissue which has been modeled as a thick-walled mono-layered axisymmetric cylinder is, when explicitly stated, to be of a type that is called fiber reinforced composite. The governing equations of constitutive assumption are then represented for the fiber-reinforced model. The fiber constituents are mainly the collagen fibers that exist in bundles within a ground matrix material, known to exist mainly in the form of elastin and, within our model, passive existence of smooth muscles. The issues related to fiber-reinforced structure are the evolution of stretch of collagen fibers with ongoing deformation due to external applied loads, and the characteristics of dissipative behavior due to existence of fibers. To cope with experimental practices and realistic simulation of real life situations, the explicit relations between the stress (thus strain) values using the constitutive model and the applied loads, namely the internal pressure, the axial force and the torsional moment are successfully obtained. Due to the thick-walled tube assumption that has been the underlying base to model the arterial tissue, all the quantities had the form of a radial integration of some quantity through the wall thickness of the hollow cylinder at the deformed state, despite the constitutive assumptions have been laid in a Lagrangian manner. Details of the test setup, that has been facilitated at the Laboratory of Strength of Materials and Biomechanics, Faculty of Mechanical Engineering, Istanbul Technical University have been provided to let the readers have an insight of how the experimental system runs. The complexity involved in the loading protocols has required bringing up different sensors and techniques together. The use of high speed video imaging systems for optical strain measurement under dynamic extension, inflation and torsion have been successfully applied to obtain complete experimental data over specimens. Sample pictures and calculations from the optical strain measurement system synchronized to the loading frame control electronics have been provided to clarify the deformation data acquisition process. Parameter estimation has then been carried out with the collected data. Required post-processing of both strain and load data have been carried, preceding the estimation processes. Various scenarios have been applied over a fibrous arterial tissue. Data from these different tests have been analyzed and relevant graphical representations of fitting have been presented. Both quasi-static and dynamic loads up to 10 Hz and up to 100% Lagrangian strains in axial and tangential directions have been applied over the specimens. The observed discrepancies between the experimental and theoretical gatherings have been commented and finally the limitations of the model and the critics to its applicability over modeling the arterial tissue have been stated.