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Thermodynamic and rate variational formulation of models for inhomogeneous gradient materials with microstructure and application to phase field modeling

Thermodynamic and rate variational formulation of models for inhomogeneous gradient materials... Abstract In this work, thermodynamic models for the energetics and kinetics of inhomogeneous gradient materials with microstructure are formulated in the context of continuum thermodynamics and material theory. For simplicity, attention is restricted to isothermal conditions. The materials of interest here are characterized by (1) first- and second-order gradients of the deformation field and (2) a kinematic microstructure field and its gradient (e.g., in the sense of director, micromorphic or Cosserat microstructure). Material inhomogeneity takes the form of multiple phases and chemical constituents, modeled here with the help of corresponding phase fields. Invariance requirements together with the dissipation principle result in the reduced model field and constitutive relations. Special cases of these include the well-known Cahn–Hilliard and Ginzburg–Landau relations. In the last part of the work, initial boundary value problems for this class of materials are formulated with the help of rate variational methods. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png "Acta Mechanica Sinica" Springer Journals

Thermodynamic and rate variational formulation of models for inhomogeneous gradient materials with microstructure and application to phase field modeling

Gladkov, Svyatoslav; Svendsen, Bob
"Acta Mechanica Sinica" , Volume 31 (2): 11 – Apr 1, 2015
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References (83)

Publisher
Springer Journals
Copyright
2015 The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
ISSN
0567-7718
eISSN
1614-3116
DOI
10.1007/s10409-015-0406-9
Publisher site
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Abstract

Abstract In this work, thermodynamic models for the energetics and kinetics of inhomogeneous gradient materials with microstructure are formulated in the context of continuum thermodynamics and material theory. For simplicity, attention is restricted to isothermal conditions. The materials of interest here are characterized by (1) first- and second-order gradients of the deformation field and (2) a kinematic microstructure field and its gradient (e.g., in the sense of director, micromorphic or Cosserat microstructure). Material inhomogeneity takes the form of multiple phases and chemical constituents, modeled here with the help of corresponding phase fields. Invariance requirements together with the dissipation principle result in the reduced model field and constitutive relations. Special cases of these include the well-known Cahn–Hilliard and Ginzburg–Landau relations. In the last part of the work, initial boundary value problems for this class of materials are formulated with the help of rate variational methods.

Journal

"Acta Mechanica Sinica" – Springer Journals

Published: Apr 1, 2015

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