Continua described by a microstructural field

  • Eliot Fried
Brief Reports


Using a balance law for microforces and an appropriate statement of the second law of thermodynamics, a framework is provided for continuum theories that involve a microstructural variable. Examples of specific physical theories that fall within that framework—spanning internal state-variable theories for plasticity and polymeric solutions, order-parameter based theories for phase transitions, and various theories for liquid crystals-are given.


Phase Transition Mathematical Method Polymeric Solution Base Theory Physical Theory 


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  1. [1]
    A. Gordon and J. Genossar,Precursor order clusters at ferroelectric phase transitions, Physica B125, 53–62 (1984).Google Scholar
  2. [2]
    J. L. Ericksen,Liquid crystals with variable degree of orientation, Arch. Rat. Mech. Analysis113, 97–120 (1991).Google Scholar
  3. [3]
    B. D. Coleman and W. Noll,The thermodynamics of elastic materials with heat conduction and viscosity, Arch. Rat. Mech. Analysis13, 167–178 (1963).Google Scholar
  4. [4]
    M. E. Gurtin and P. W. Voorhees,The continuum mechanics of coherent two-phase elastic solids with mass transport, Proc. Roy. Soc, London A 440, 323–343 (1993).Google Scholar
  5. [5]
    B. D. Coleman and M. E. Gurtin,Thermodynamics with internal state variables, J. Chem. Phys.47, 597–613 (1967).Google Scholar
  6. [6]
    J. Kratochvil and O. W. Dillon,Thermodynamics of elastic-plastic materials as a theory of internal state variables, J. Appl. Phys.40, 3207–3218 (1969).Google Scholar
  7. [7]
    J. Lubliner,On fading memory in materials of evolutionary type, Acta Mech.8, 75–78 (1969).Google Scholar
  8. [8]
    J. R. Rice,Inelastic constitutive relations for solids: an internal-variable theory and its application to metal plasticity. J. Mech. Phys. Solids19, 433–455 (1971).Google Scholar
  9. [9]
    G. L. Hand,A theory of anisotropic fluids, J. Fluid Mech.13, 33–46 (1962).Google Scholar
  10. [10]
    P. A. Dashner and W. E. Varnarsdale,A phenomenological theory for elastic fluids, J. Non-Newtonian Fluid Mech.8, 59–67 (1981).Google Scholar
  11. [11]
    G. A. Maughin and R. Drouot,Internal variables and the thermodynamics of macromolecule solutions, Int. J. Eng. Sci.21, 705–724 (1983).Google Scholar
  12. [12]
    Th. de Donder and P. van Rysselberghe,Thermodynamic Theory of Affinity, Oxford University Press, London 1936.Google Scholar
  13. [13]
    S.-K. Chan,Steady-state kinetics of diffusionless first order phase transformations, J. Chem. Phys.67, 5755–5762 (1977).Google Scholar
  14. [14]
    S. M. Alien and J. W. Cahn,A macroscopic theory for antiphase boundary motion and its application to antiphase domain coarsening, Acta Metall. 27, 1085–1095 (1979).Google Scholar
  15. [15]
    E. Fried and M. E. Gurtin,Continuum theory of thermally induced phase transitions based on an order parameter, Physics D68, 326–343 (1993).Google Scholar
  16. [16]
    E. Fried and M. E. Gurtin,Dynamic solid-solid transitions with phase characterized by an order parameter, Physica D72, 287–308 (1994).Google Scholar
  17. [17]
    M. E. Gurtin, D. A. Polignone and J. Viñals,Two-phase binary fluids and immiscible fluids described by an order parameter, Math. Models Methods Appl. Sci., to appear.Google Scholar
  18. [18]
    E. G. Virga,Defects in nematic liquid crystals with variable degree of orientation, in:Nematics (Eds. J.-M. Coron, J.-M. Ghidaglia and F. Hélein), Kluwer Academic Publ., Dordrecht 1991.Google Scholar
  19. [19]
    P. G. de Gennes.Short range order effects in the isotropic phase of nematics and cholesterics, Mol. Cryst. Liquid Cryst.12, 193–214 (1971).Google Scholar

Copyright information

© Birkhäuser Verlag 1996

Authors and Affiliations

  • Eliot Fried
    • 1
  1. 1.Dept of Theoretical and Applied MechanicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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