A hierarchical framework for the multiscale modeling of microstructure evolution in heterogeneous materials.

All materials are heterogeneous at various scales of observation. The influence of material heterogeneity on nonuniform response and microstructure evolution can have profound impact on continuum thermomechanical response at macroscopic “engineering” scales. In many cases, it is necessary to treat this behavior as a multiscale process thus integrating the physical understanding of material behavior at various physical (length and time) scales in order to more accurately predict the thermomechanical response of materials as their microstructure evolves. The intent of the dissertation is to provide a formal framework for multiscale hierarchical homogenization to be used in developing constitutive models.