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An Extended Continuum Theory for Granular Media

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Mathematical Models of Granular Matter

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1937))

In a dilatant granular material with rotating grains the kinetic energy in addition to the usual translational one consists of three terms owing to the microstructural motion; in particular, it includes the rotation of granules and the dilatational expansion and contraction of the individual (compressible) grains and of the grains relative to one another. Therefore the balance and constitutive equations of the medium are obtained by considering it as a continuum with a constrained affine microstructure. Moreover, the balance of granular energy is demonstrated to be a direct consequence of the balance of micromomentum, while the dilatational and the rotational microstresses are turned out to be of different physical nature. Finally, a kinetic energy theorem implies that, locally, the power of all inertial forces is the opposite of the time-rate of change of kinetic energy plus the divergence of a flux through the boundary. The peculiar case of a suspension of rotating rigid granules puts in evidence the possibility for granular materials of supporting shear stresses through the generation of microrotational gradients.

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Author information

Authors and Affiliations

  1. Dipartimento di Meccanica e Materiali, Università “Mediterranea”, via Graziella, Località Feo di Vito, 89127, Reggio Calabria, Italy

    Pasquale Giovine

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  1. Pasquale Giovine
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Editors and Affiliations

  1. Department of Mathematics, University of Pisa, largo Bruno Pontecorvo 5, 56127, Pisa, Italy

    Gianfranco Capriz

  2. Accademia Nazionale dei Lincei, via della Lungara 10, 00165, Roma, Italy

    Gianfranco Capriz

  3. DICeA, University of Florence, via Santa Marta 3, 50139, Firenze, Italy

    Paolo Maria Mariano

  4. Dipartimento di Meccanica e Materiali, Università “Mediterranea” di Reggio Calabria, via Graziella, località Feo di Vito, 89060, Reggio Calabria, Italy

    Pasquale Giovine

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Giovine, P. (2008). An Extended Continuum Theory for Granular Media. In: Capriz, G., Mariano, P.M., Giovine, P. (eds) Mathematical Models of Granular Matter. Lecture Notes in Mathematics, vol 1937. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78277-3_8

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