From Instability and Time Dependence on the Microscale to Stability and Time Independence on the Macroscale

The quasistatic inelastic deformation of ductile structural metals observed on the macroscale reflects a diversity of dynamic inelastic effects on the microscale. The generation, motion, and immobilization of dislocations are primary among them, but a host of other activities such as the opening and growth of cracks and voids, also may contribute. Dynamic activity on the microscale is strongly time-dependent on the time scales of importance to the microscopic processes. Also, the atomic configurations of single dislocations and groups of dislocations are highly unstable over a significant portion of each path of rapid motion. Nevertheless, engineers continue to design structures and machines with a reasonable factor of safety against failure on the basis of conventional plasticity theory with its assumption of both time-independence and stability (normality and convexity). This discussion of the validity of these simplifying assumptions for macroscopic constitutive relations despite instability and time-dependence on the atomic- and micro-scale expands upon a recent paper with Ming Li.