SUMMARY

A hierarchical method is proposed to link the macroscale constitutive response of heterogeneous materials with evolutionary mechanisms that occur at the mesoscale. The kinematic scale transition (or sequence of transitions) is facilitated by a second order Taylor series expansion of the deformation field at the fine scale. The principle of virtual velocities (PVV) is employed to assert equivalence of linear momentum balance across scales, giving rise to multiscale balance laws. An analogous principle is applied to equate dissipation across scales (PVD). An internal state variable (ISV) framework is adopted by postulating the Helmholtz free energy as a state function of the above mentioned kinematic terms and three types of internal state variables. The evolution of these ISV’s during the thermomechanical response of heterogeneous materials is addressed at the mesoscale through direct finite element simulation of statistical volume elements of material mesostructure and at the next higher scale by the aforementioned PVV-D. A key distinction of the proposed multiscale approach is the manner in which ISV’s are introduced and eliminated during the transition between each scale of representation. . Additionally, geometrical correlation functions of microstructure attributes are employed in some cases as ISV’s in order to explicitly incorporate the influence of evolving mesoscale heterogeneity. It is intended that the proposed hierarchical ISV PVV-D framework be generally applicable to scale-linking of the response of heterogeneous materials undergoing irreversible processes where each scale is amenable to a continuum representation. In order to demonstrate the utility of the framework, it will be applied to the development and implementation of a constitutive model for the inelastic and damaged behavior of porous metal oxide nuclear fuels.