www.mapeng.net 马棚网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" quan- tities like the contact forces in a granular assembly. Differ- ent 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 calcula- tion 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.
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http://www.mapeng.net/Files/paper/从准静态的宏观材料性质，到二维剪切单元的微观仿真
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