Abstract

In this talk, I present a phase-field theory for enriched continua, exposing the geometry of gradient flows. We begin the theory with a set of postulate balances on nonsmooth open surfaces to characterize the fundamental fields. By considering nontrivial interactions inside the body, we characterize the existence of a hypermicrotraction field, a central aspect of this theory. Subject to thermodynamic constraints, we develop a general set of constitutive relations for a phase-field model where its free-energy density depends on second gradients of the phase field. To exemplify the usefulness of our theory, we generalize two commonly used phase-field equations. We propose a generalized Swift–Hohenberg equation-a second-grade phase-field equation-and its conserved version, the generalized phase-field crystal equation-a conserved second-grade phase-field equation. Furthermore, we derive the configurational fields arising in this theory. Configurational forces are a generalization of Newtonian forces to describe the kinetics and kinematics of manifolds. We conclude with the presentation of a comprehensive and thermodynamically consistent set of boundary conditions.

Based on: Espath & Calo, Phase-field gradient theory. 2021, ZAMP. DOI: 10.1007/s00033-020-01441-2.