The Clausius-Duhem Inequality, an Interesting and Productive Inequality

  • Michel Frémond
Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 12)


The Clausius-Duhem inequality which appears in continuum mechanics when combining the momentum balance law and the two laws of thermodynamics may be thought as an interesting inequality or as a productive relation to derive constitutive laws. We recall that it gathers most of the quantities which intervene when deriving constitutive laws. In some circumstances it may be much more than a summary: the duality pairings of the inequality give precious information on the quantities which are to be related in predictive theories and to be measured in experiments. Examples are given in various problems of solid mechanics.


Clausius-Duhem inequality constitutive laws damage phase change shape memory alloys collisions fracture 


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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  • Michel Frémond
    • 1
  1. 1.Laboratoire LagrangeLCPCParis Cedex 15France

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