Macroscopic material properties from quasi-static, microscopic simulations of a two-dimensional shear-cell

Marc Lätzel*, Stefan Luding, Hans J. Herrmann

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

149 Citations (Scopus)


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.

Original languageEnglish
Pages (from-to)123-135
Number of pages13
JournalGranular matter
Issue number3
Publication statusPublished - 1 Jun 2000
Externally publishedYes


  • Anisotropy shear-all
  • Continuum theory
  • DEM modelling
  • Homegenization
  • Micro-macro transition
  • Stress

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