Thermodynamically consistent variational principles with applications to electrically and magnetically active systems

TitleThermodynamically consistent variational principles with applications to electrically and magnetically active systems
Publication TypeJournal Article
Year of Publication2004
AuthorsGarcia, RE, Bishop, CM, Carter, WCraig
JournalActa Materialia
Volume52
Issue1
Pagination11 - 21
Date Published2004/01/05/
Abstract

We propose a theoretical framework to derive thermodynamically consistent equilibrium equations and kinetic driving forces to describe the time evolution for electrically and magnetically active materials. This procedure starts from the combined statement of the first and second laws of thermodynamics, naturally incorporates Maxwell's equations, and accommodates the description of continuous phase transformations for conserved and non-conserved order parameters. The kinetics of conserved and non-conserved ordered parameters are introduced, the adequate gradient flow is identified, thus the appropriate kinetics (e.g., Allen-Cahn, Cahn-Hilliard) are derived. Example applications of this theory include the electromechanical fields of piezoelectric materials and the wave equation in the limit of chemically homogeneous solids. Moreover, we derive a thermodynamically consistent set of partial differential equations which describe the transport of charged species in conductive, non-polarizable, magnetizable solids, and in polarizable, electrically insulating, non-magnetizable solids. (C) 2003 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.