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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Hendy, S.C. (2005). Towards a theory of granular plasticity. In: Hill, J.M., Selvadurai, A. (eds) Mathematics and Mechanics of Granular Materials. Springer, Dordrecht. https://doi.org/10.1007/1-4020-4183-7_8
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DOI: https://doi.org/10.1007/1-4020-4183-7_8
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