| This dissertation focuses on the theoretical treatment for the stochastic modeling of materials with random microstructures in the framework of nonlocal theories. In this work, the random microstructural interactions are represented by the integration of subscale variables and become a part of the constitutive equation for global state variables as in the classical nonlocal field theory. The integration reflects the contribution from the subscale to the global states. The Green's function associated with the integration should be calibrated as a constitutive property. The global behavior, being the overall contributions accumulated from all the scales, must satisfy the admissible condition and boundary conditions. In this manner the behavior of a multiscale system can be stated as a boundary value problem. |
