WIAS Preprint No. 465, (1998)

Note on the notion of incompressibility in theories of porous and granular materials


  • Wilmański, Krzysztof

2010 Mathematics Subject Classification

  • 73B30


  • incompressibility, porous and granular materials, second law of thermodynamics




We present a simple two-component model of a porous material based on the constraint assumption that the so-called true components are incompressible. In my previous work on this subject [1] I pointed out that many such models are not thermodynamically admissible. Namely the second law of thermodynamics led to the conclusion that an additional field of reaction force on the constraint cannot be introduced, and, consequently, the set of field equations was overdetermined. However I speculated as well that an extension of the set of variables may lead to thermodynamic admissibility. Indeed an example presented in this paper supports this speculation. According to results of this work it seems to be neccessary to introduce higher gradients to multicomponent models with constraints in order to satisfy the second law of thermodynamics.

Appeared in

  • Z. Angew. Mathem. Mech., 81(2001), pp. 37-42

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