Für interessierte UnRAVeL Mitglieder: Weekly Seminar by RTG Eddy: Phase-Field Gradient Theory: the geometry of gradient flows and its configuration mechanics
Donnerstag, 22.04.2021, 10.15 Uhr
Ort: Online Session
Vortragender: Luis Espath (RWTH Aachen University)
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.
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