On the Microstructural Origin of Certain Inelastic Models

A unifying program modeling the evolution of microstructures and their effects on the macroscopic response of materials is outlined. The new physical assumption introduced is the distinction among “normal” states associated with the parent lattice and “excited” states associated with the occurring microstructures. Both states are described by the usual balance laws of continuum mechanics properly modified to account for their mechanical interaction (mass and momentum exchange). Emphasis is put on the spatial evolution of the microstructures and its nonconvex character which is stabilized by considering gradient effects. The program can lead to predictive models for the localization of microstructures and its relation to the localization of macroscopic deformation. Moreover, it provides a rigorous microstructural justification of macroscopic theories of plasticity and viscoplasticity, including isotropic and kinematic hardening, as well as various current inelastic models. Finally, it suggests a proper frame for considering large deformation and rotation effects.