This project addresses characterization of the material properties of aortic tissue. Understanding of these properties is important for a variety of studies including tissue engineering, effects of aging and diseases, stents engineering, and traumatic aorta rupture. The goal of the presented research was to characterize the stress-strain relationship of aorta in dynamic oscillatory biaxial loading. A setup was developed that supplied pressure loading from the physiological to sub-failure levels (between 7 and 76 kPa) to porcine aorta at frequencies ranging from 0.50Hz to 5.00Hz. Samples tested were constrained at both ends while the deformation and the pressure were recorded. Volumetric strain versus pressure was used to characterize the structural behavior of the material which showed frequency dependency and hysteresis indicating viscoelastic response. An offset method was developed to account for drifting behavior exhibited by some of the samples. The structural behavior of aorta was modeled using a quasi-linear viscoelastic (QLV) creep theory. The QLV model included a logarithmic steady state elastic function v = 0.663 +/- 0.040 + 0.241 +/- 0.011 ln(P) for pressure in kPa, and a Prony series creep function ( J0 = 0.472 +/- 0.021, J2 = 0.109 +/- 0.060, J3 = 0.419 +/- 0.056). Modeling results were then used to determine the relationships between the circumferential and longitudinal stresses and strains of the material. The results exhibited that the stress in the transverse direction was about 1.5 times larger than in the axial direction. However, in the axial direction material was stiffer and the deformation was 30% less. The relaxation function of the material was determined by linearizing the non-linear component of the QLV model and applying to it the linear viscoelastic theory. Furthermore, literature comparison revealed that aorta's creep function, as well as its elastic modulus, is within the range of what has been reported in the literature. In conclusion, an experimental model was developed that can be used to predict the behavior of porcine aorta under physiological and sub-failure conditions at quasi-static and dynamic loading. / Mechanical Engineering

Several efforts have been made in the past half century to characterize the behavior of brain tissue under different modes of loading and deformation rates; however each developed model has been associated with limitations. This dissertation aims at addressing the non-linear and rate dependent behavior of brain tissue specially in high strain rates (above 100 s-1) that represents the loading conditions occurring in blast induced neurotrauma (BINT) and development of a universal constitutive model for brain tissue that describes the tissue mechanical behavior from medium to high loading rates.. In order to evaluate the nature of nonlinearity of brain tissue, bovine brain samples (n=30) were tested under shear stress-relaxation loading with medium strain rate of 10 s-1 at strain levels ranging from 2% to 40% and the isochronous stress strain curves at 0,1 s and 10 s after the peak force formed. This approach enabled verification of the applicability of the quasilinear viscoelastic (QLV) theory to brain tissue and derivation of its elastic function based on the physics of the material rather than relying solely on curve fitting. The results confirmed that the QLV theory is an acceptable approximation for engineering shear strain levels below 40% that is beyond the level of axonal injury and the shape of the instantaneous elastic response was determined to be a 5th order odd polynomial with instantaneous linear shear modulus of 3.48±0.18 kPa. To investigate the rate dependent behavior of brain tissue at high strain rates, a novel experimental setup was developed and bovine brain samples (n=25) were tested at strain rates of 90, 120, 500, 600 and 800 s-1 and the resulting deformation and shear force were recorded. The stress-strain relationships showed significant rate dependency at high rates and was characterized using a QLV model with a 739 s-1 decay rate and validated with finite element analysis. The results showed the brain instantaneous elastic response can be modeled with a 3rd order odd polynomial and the instantaneous linear shear modulus was 19.2±1.1 kPa. A universal constitutive model was developed by combining the models developed for medium and high rate deformations and based on the QLV theory, in which the relaxation function has 5 time constants for 5 orders of magnitude in time (from 1 ms to 10 s) and therefore, is capable of predicting the brain tissue behavior in a wide range of deformation rates. Although the universal model presented in this study was developed based on only shear tests and the material parameters could not be found uniquely, by comparing the results of this study with previously available data in the literature under tension unique material parameters were determined for a 5 parameter generalized Rivlin elastic function (C10=3.208±0.602 kPa, C01=4.191±1.074 kPa, C11=79.898±18.974 kPa, C20=-37.093±7.273 kPa, C02=-37.712±5.678 kPa). The universal constitutive model for brain tissue presented in this dissertation is capable of characterizing the brain tissue behavior under large deformation in a wide range of strain rates and can be used in computational modeling of Traumatic Brain Injury (TBI) to predict injuries that result from falls and sports to automotive accidents and BINT. / Mechanical Engineering