Geometrically Nonlinear Continuum Thermomechanics Coupled to Diffusion: A Framework for Case II Diffusion

  • Andrew T. McBride
  • Swantje Bargmann
  • Paul Steinmann
Part of the Lecture Notes in Applied and Computational Mechanics book series (LNACM, volume 59)


This chapter introduces a geometrically nonlinear, continuum thermomechanical framework for case II diffusion: a type of non-Fickian diffusion characterized by the wave-like propagation of a low-molecular weight solvent in a polymeric solid. The key objective of this contribution is to derive the coupled system of governing equations describing case II diffusion from fundamental balance principles. A general form for the Helmholtz energy is proposed and the resulting constitutive laws are derived from logical, thermodynamically consistent argumentation. The chapter concludes by comparing the model developed here to various others in the literature. The approach adopted to derive the governing equations is not specific to case II diffusion, rather it encompasses a wide range of applications wherein heat conduction, species diffusion and finite inelastic effects are coupled. The presentation is thus applicable to the generality of models for non-Fickian diffusion: an area of increasing research interest.


Constitutive Relation Glassy Polymer Deborah Number Species Mass Helmholtz Energy 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Andrew T. McBride
    • 1
  • Swantje Bargmann
    • 2
  • Paul Steinmann
    • 1
  1. 1.Applied MechanicsUniversity of Erlangen-NurembergErlangenGermany
  2. 2.Institute of MechanicsTU Dortmund UniversityDortmundGermany

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