Kinematic variables bridging discrete and continuum granular mechanics |
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Authors: | Mingjing Jiang Hai-Sui Yu David Harris |
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Institution: | aNottingham Centre for Geomechanics, School of Civil Engineering, University of Nottingham, University Park, Nottingham NG7 2RD, UK;bSchool of Mathematics, University of Manchester, Manchester M60 1QD, UK |
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Abstract: | It is known that there is wide, and at present, unbridgeable, gap between discrete and continuum granular mechanics. In this contribution, first, microscopic kinematic variables neglected in classical continuum granular mechanics are investigated based on the kinematics of discs in contact. Then, a kinematic variable called the averaged pure rotation rate (APR) is proposed for an assembly of circular discs of different sizes, which is then used to produce another two kinematic tensors with one equal to the deformation rate tensor and the other unifying the spin tensor and the APR. As an example, the kinematic variables are incorporated into the unified double-slip plasticity model. Finally, these theoretical analyses are verified using a two-dimensional discrete element method. The study shows that these kinematic variables can be used to bridge discrete and continuum granular mechanics. |
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Keywords: | Kinematic variables Continuum granular mechanics Discrete granular mechanics Discrete element method Double-slip Rotation rate model |
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