| A constitutive model is the mathematical relationship between load and displacements within the context of solid mechanics. The objective of this study is to investigate, to develop and to implement to finite element method, constitutive models of the resilient response of granular solids. These models are mainly used in analysis and design of airport and highway pavements; they characterize the response of granular layers in pavements under repeated wheel loads.; Two well known nonlinear elastic models, based on the concept of resilient modulus are investigated in detail. Due to their success in organizing the response data from cyclic triaxial tests and their success relative to competing material models in predicting the behavior observed in the field, these two models, namely the K-theta and the Uzan-Witzcak models, have been implemented to many computer programs used by researchers and design engineers. However, all of these implementations have been made to axisymmetric finite element codes which preclude the study of the effects of multiple wheel loads. This study provides a careful analysis of these models and addresses the issue of effectively implementing them in a 3-dimensional finite element analysis framework.; Also in this study, a new coupled constitutive model based on hyperelasticity is proposed to capture the resilient behavior of granular materials. The coupling property of the proposed model accounts for the shear dilatancy and pressure-dependent behavior of the granular materials. This model is demonstrated to yield better fits to experimental data than the K-theta the Uzan-Witzcak models.; Tensile stresses do not develop in a particulate medium under applied loading. To this end, several modifications to the coupled hyperelastic model are proposed to limit the buildup of tensile hydrostatic pressure. Another model based on eigenprojection operators is developed. This model which yields a tension-free response, is formulated in terms of principal stresses. The difficulties in achieving a robust implementation of this model to the finite element method are resolved.; Finally, a few boundary value problems are analyzed with the finite element method to demonstrate the response predicted by the models described above. |
