The focus of this dissertation is on constant displacment rate experiments on asphalt concrete and on developing continuum models in a general thermo-mechanical setting which will corroborate with the experimental results. Modeling asphalt concrete and predicting its response is of great importance to the pavement industry. More than 90 percent of the US Highways uses asphalt concrete as a pavement material. Asphalt concrete exhibits nonlinear response even at small strains and the response of asphalt concrete to different types of loading is quite different. The properties of asphalt concrete are highly influenced by the type and amount of the aggregates and the asphalt used. The internal structure of asphalt concrete keeps on evolving during the loading process. This is due to the influence of different kinds of activities at the microlevel and also due to the interaction with the environment. The properties of asphalt concrete depend on its internal structure. Hence we need to take the evolution of the internal structure in modeling the response of asphalt concrete. Experiments were carried out at different confinement pressures and displacement rates on cylindrical samples of asphalt concrete. Two different aggregates were used to make the sample -limestone and granite. The samples were tested at a constant displacement rate at a given confinement pressure. The force required to maintain this constant displacement rate is measured and recorded. The frame-work has been developed using the idea of multiple natural configurations that was introduced recently to study a variety of non-linear dissipative response of materials. By specifying the forms of the stored energy and rate of dissipation function of the material, specific models were developed using this frame work. In this work both a compressible and an incompressible model were developed by choosing appropriate forms of stored energy and rate of dissipation function. Finally the veracity of the models were tested by corroborating with the experimental results. It is anticipated that the present work will aid in the development of better constitutive equations which in turn will accurately model asphalt concrete in laboratory and in field.

In this work, a constitutive theory is developed, within the context of continuum mechanics, to describe the creep deformation of single crystal superalloys. The con- stitutive model that is developed here is based on the fact that as bodies deform the stress free state that corresponds to the current configuration (referred to as the "natural configuration", i.e., the configuration that the body would attain on the removal of the external stimuli) evolves. It is assumed that the material possesses an infinity of natural (or stress-free) configurations, the underlying natural configuration of the body changing during the deformation process, with the response of the body being elastic from these evolving natural configurations. It is also assumed that the evolution of the natural configurations is determined by the tendency of the body to undergo a process that maximizes the rate of dissipation. Central to the theory is the prescription of the forms for the stored energy and rate of dissipation functions. The stored energy reflects the fact that the elastic response exhibits cubic symmetry. Consistent with experiments, the elastic response from the natural configuration is assumed to be linearly elastic and the model also takes into account the fact that the symmetry of single crystals does not change with inelastic deformation. An ap- propriate form for the inelastic stored energy (the energy that is `trapped' within dislocation networks) is also utilized based on simple ideas of dislocation motion. In lieu of the absence of any experimental data to corroborate with, the form for the inelastic stored energy is assumed to be isotropic. The rate of dissipation function is chosen to be anisotropic, in that it reflects invariance to transformations that belong to the cubic symmetry group. The rate of dissipation is assumed to be proportional to the density of mobile dislocations and another term that takes into account the damage accumulation due to creep. The model developed herein is used to simulate uniaxial creep of <001>, <111> and <011> oriented single crystal nickel based su- peralloys for a range of temperatures. The predictions of the theory match well with the available experimental data for CMSX-4. The constitutive model is also imple- mented as a User Material (UMAT) in commercial finite element software ABAQUS to enable the analysis of more general problems. The UMAT is validated for simple problems and the numerical scheme based on an implicit backward difference formula works well in that the results match closely with those obtained using a semi-inverse approach.