First-principles mesoscopic dynamics in heterogeneous materials

Abstract

A systematic link between microscopic and macroscopic theories of matter has been lacking in the case of heterogeneous materials (polycrystals, composites, etc.). The properties of such materials are largely determined by their collective microstructure, which defines several intermediate or mesoscopic length scales. A microscopic description is presented and the principles of statistical mechanics are used to derive a set of mesoscopic field dynamical equations that describe microstructure evolution under external stresses, temperature gradients, or electric current. The macroscopic dynamical equations of continuum mechanics are recovered. The cross-coupled phenomena of elastic deformations and inelastic diffusive and slip processes are present, setting the stage for a first-principles theory of dislocation dynamics and plasticity.