Summary
In this paper, we present a micro-structured model for describing global deformations of heterogeneous mixtures. In particular, for a saturated solid-fluid mixture, we regard the solid volume fraction as a microstructural parameter so as to enlarge the space of admissible deformations with respect to the classical theory of mixtures. According to the variational approach, the governing equations are obtained as the stationarity of a suitable action functional. The micro-structured model is then forced to establish a second-gradient mixture theory, by introducing among the considered state parameters a suitable internal constraint. Finally, we determine under which (integrability) conditions the additional balance laws, typically employed to close the theory of porous media endowed with the volume fraction, can fit the variational framework.
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The authors wish to thank Prof. Francesco dell'Isola from University of Rome “La Sapienza” for his constructive criticism about the variational approach to continuum mechanics and the interpretation of the volume-fraction balance law.
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Sciarra, G., Hutter, K. & Maugin, G. A variational approach to a micro-structured theory of solid-fluid mixtures. Archive of Applied Mechanics 73, 199–224 (2003). https://doi.org/10.1007/s00419-003-0279-4
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DOI: https://doi.org/10.1007/s00419-003-0279-4