Acta Mechanica Sinica

, Volume 31, Issue 2, pp 162–172 | Cite as

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

  • Svyatoslav Gladkov
  • Bob SvendsenEmail author


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.


Continuum thermodynamics Material inhomogeneity Conservative Non-conservative phase fields 



Financial support of Subproject M03 in the Transregional Collaborative Research Center SFB/TRR 136 by the German Science Foundation (DFG) is gratefully acknowledged.


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Copyright information

© The Chinese Society of Theoretical and Applied Mechanics; Institute of Mechanics, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Material MechanicsRWTH AachenAachenGermany
  2. 2.Microstructure Physics and Alloy DesignMax-Planck-Institut für EisenforschungDüsseldorfGermany

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