15 - Flow-Evolutionary Law as a Working Hypothesis

Summary

The completion of the theory for MMMs (multiscale modeling of materials) is manifested itself partially as an identification of the right “flow-evolutionary” law explicitly, which describes generally the evolution of the inhomogeneous fields and the attendant local plastic flow accompanied by energy dissipation. The notion “duality” ought to be embodied by this law, although it still is a “working hypothesis,” deserving further investigations. Specifically, it represents the interrelationship between the locally stored strain energy and the local plastic flow as has been discussed in the context of polycrystalline plasticity in Chapter 12 for Scale C. In this final chapter, we will derive explicitly a candidate form of the flow-evolutionary law as a possible embodiment of the duality, which is followed by application examples.