The mechanical behavior of asphalt binders is nonlinear. The binders exhibit shear thinning/thickening behavior in steady shear tests and non-proportational behavior in other standard viscoelastic tests such as creep-recovery or stress relaxation tests. Moreover, they develop normal stress differences even in simple shear flows - a characteristic feature of nonlinear viscoelastic behavior. Many researchers have asserted the importance of considering the nonlinearity of the mechanical behavior of asphalt binders for accurately estimating their performance under field conditions, and for comparing and ranking them accordingly. In order to do so, it is necessary to have a robust and reliable nonlinear viscoelastic model. However, most of the models available in the literature do not capture the various features of the nonlinear response of asphalt binders accurately. Those that could are too complicated and still possess other shortcomings. Considering these issues, a new nonlinear viscoelastic model is developed here using a new Gibbs-potential based thermodynamic framework. The model is then corraborated with data from experiments in which the shear-thinning behavior and the nonproportional creep-recovery behavior were observed together. Finally, the model is used to evaluate the various criteria available for predicting rutting susceptibility of asphalt binders. Results of the analysis of the rutting prediction criteria show that each criterion characterizes the resistance to permanent strain shown by asphalt binders over a different range of applied stress - the zero-shear viscosity at very low stress levels, the Superpave criterion at very high stress levels and the MSCR test in the intermediate range of stresses.

The aim of this work is to present a model for the superelastic response of Shape Memory Alloys (SMAs) by developing a Preisach Model with thermodynamics basis. The special features of SMA superelastic response is useful in a variety of applications (eg. seismic dampers and arterial stents). For example, under seismic loads the SMA dampers undergo rapid loading{unloading cycles, thus going through a number of internal hysteresis loops, which are responsible for dissipating the vibration energy. Therefore the design for such applications requires the ability to predict the response, particularly internal loops. It is thus intended to develop a model for the superelastic response which is simple, computationally fast and can predict internal loops. The key idea here is to separate the elastic response of SMAs from the dissipative response and apply a Preisach Model to the dissipative response as opposed to the popular notion of applying the Preisach Model to the stress{strain response directly. Such a separation allows for the better prediction of internal hysteresis, avoids issues due to at/negative slopes in the stress{strain plot, and shows good match with experimental data, even when minimal input is given to the model. The model is developed from a Gibbs Potential, which allows us to compute a driving force for the underlying phase transformation in the superelastic response. The hysteresis between the driving force for transformation and the extent of transformation (volume fraction of martensite) is then used with a Preisach model. The Preisach model parameters are identi ed using a least squares approach. ASTM Standards for the testing of NiTi wires (F2516-07^sigma 2), are used for the identi cation of the parameters in the Gibbs Potential. The simulations are run using MATLAB R . Results under di erent input conditions are discussed. It is shown that the predicted response shows good agreement with the experimental data. A couple of attempts at extending the model to bending and more complex response of SMAs is also discussed.