Towards a theory of granular plasticity |
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Authors: | Shaun C Hendy |
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Affiliation: | (1) Applied Mathematics, Industrial Research Ltd, Lower Hutt, New Zealand |
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Abstract: | A theory of granular plasticity based on the time-averaged rigid-plastic flow equations is presented. Slow granular flows
in hoppers are often modeled as rigid-plastic flows with frictional yield conditions. However, such constitutive relations
lead to systems of partial differential equations that are ill-posed: they possess instabilities in the short-wavelength limit.
In addition, features of these flows clearly depend on microstructure in a way not modeled by such continuum models. Here
an attempt is made to address both short-comings by splitting variables into ‘fluctuating’ plus ‘average’ parts and time-averaging
the rigid-plastic flow equations to produce effective equations which depend on the ‘average’ variables and variances of the
‘fluctuating’ variables. Microstructural physics can be introduced by appealing to the kinetic theory of inelastic hard-spheres
to develop a constitutive relation for the new ‘fluctuating’ variables. The equations can then be closed by a suitable consitutive
equation, requiring that this system of equations be stable in the short-wavelength limit. In this way a granular length-scale
is introduced to the rigid-plastic flow equations. |
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Keywords: | granular flow granular temperature plasticity |
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