Macroscopic material properties from quasi-static, microscopic simulations of a two-dimensional shear-cell |
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Authors: | Marc Lätzel Stefan Luding Hans J Herrmann |
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Affiliation: | (1) Institute for Computer Applications 1, Pfaffenwaldring 27, 70569 Stuttgart, GERMANY, DE |
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Abstract: | One of the essential questions in the area of granular matter is, how to obtain macroscopic tensorial quantities like stress
and strain from “microscopic” quantities like the contact forces in a granular assembly. Different averaging strategies are
introduced, tested, and used to obtain volume fractions, coordination numbers, and fabric properties. We derive anew the non-trivial
relation for the stress tensor that allows a straightforward calculation of the mean stress from discrete element simulations
and comment on the applicability. Furthermore, we derive “elastic” (reversible) mean displacement gradient, based on a best-fit
hypothesis. Finally, different combinations of the tensorial quantities are used to compute some material properties.
The bulk modulus, i.e. the stiffness of the granulate, is a linear function of the trace of the fabric tensor which itself
is proportional to the density and the coordination number. The fabric, the stress and strain tensors are not co-linear so that a more refined analysis than a classical elasticity theory is required.
Received: 23 July 1999 |
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Keywords: | micro-macro transition homegenization DEM modelling continuum theory stress anisotropy shear-all |
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