Nonsmooth Mechanics and Analysis

Volume 12 of the series Advances in Mechanics and Mathematics pp 107-118

The Clausius-Duhem Inequality, an Interesting and Productive Inequality

  • Michel FrémondAffiliated withLaboratoire Lagrange, LCPC

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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