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Macroscopic strains in granular materials accounting for grain rotations

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Abstract

Granular materials are special materials, from the continuum-mechanical viewpoint, in the sense that they possess a clear microstructure of grains and intergrain contacts. In addition, the grains have translational as well as rotational degrees of freedom. Here a micromechanical expression is formulated for the average displacement gradient tensor in terms of the grain displacements and rotations for the two-dimensional case. It is based on a tessellation of the granular assembly into closed loops, along whose boundary the displacement field is defined in terms of the grain displacements and rotations. An important consideration for this expression is that it must satisfy the surface-additivity property, according to which the average displacement gradient of a combined two-dimensional surface is determined by the average displacement gradients of the constituent surfaces (and weighted by their areas). The developed micromechanical expression is verified by comparing its results with the macroscopic deformation as determined from the displacements at the boundary. Results of DEM simulations of a biaxial test (where the average rotation is equal to zero) and a shear test (where the average rotation is not equal to zero) are employed for this verification. The developed micromechanical expression for the displacement gradient is subsequently used to study deformation patterns in a complex case of a biaxial test where a shear band is formed.

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Notes

  1. This definition involves not only contact forces between grains, but also inertia forces in dynamical situations (see also [20] for the associated DEM simulations).

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Acknowledgments

The authors acknowledge data shown in Sect. 6 that was kindly provided by N. Hadda (previously with Irstea, France; currently with the Department of Civil Engineering of the University of Calgary, Alberta, Canada). NK acknowledges hospitality at Université de La Rochelle.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Twente, Enschede, The Netherlands

    N. P. Kruyt

  2. LaSIE-UMR CNRS 7356, La Rochelle University, La Rochelle, France

    O. Millet

  3. Irstea, Grenoble, France

    F. Nicot

Authors
  1. N. P. Kruyt
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  2. O. Millet
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  3. F. Nicot
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Correspondence to N. P. Kruyt.

Additional information

This study is an extended version of that presented by the authors [26].

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Kruyt, N.P., Millet, O. & Nicot, F. Macroscopic strains in granular materials accounting for grain rotations. Granular Matter 16, 933–944 (2014). https://doi.org/10.1007/s10035-014-0523-3

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