Continuum Mechanics and Thermodynamics

, Volume 29, Issue 6, pp 1335–1345 | Cite as

On the thermodynamics of the Swift–Hohenberg theory

  • L. F. R. Espath
  • A. F. Sarmiento
  • L. Dalcin
  • V. M. Calo
Original Article


We present the microbalance including the microforces, the first- and second-order microstresses for the Swift–Hohenberg equation concomitantly with their constitutive equations, which are consistent with the free-energy imbalance. We provide an explicit form for the microstress structure for a free-energy functional endowed with second-order spatial derivatives. Additionally, we generalize the Swift–Hohenberg theory via a proper constitutive process. Finally, we present one highly resolved three-dimensional numerical simulation to demonstrate the particular form of the resulting microstresses and their interactions in the evolution of the Swift–Hohenberg equation.


Phase-field Gradient theory Thermodynamics of continua Swift–Hohenberg theory 


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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • L. F. R. Espath
    • 1
  • A. F. Sarmiento
    • 1
  • L. Dalcin
    • 2
  • V. M. Calo
    • 3
    • 4
  1. 1.Computer, Electrical and Mathematical Sciences and EngineeringKing Abdullah University of Science and TechnologyThuwalSaudi Arabia
  2. 2.Extreme Computing Research Center, King Abdullah University of Science and TechnologyThuwalSaudi Arabia
  3. 3.Applied Geology, Western Australian School of Mines, Faculty of Science and EngineeringCurtin UniversityPerthAustralia
  4. 4.Mineral Resources, Commonwealth Scientific and Industrial Research Organisation (CSIRO)KensingtonAustralia

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