Summary
The problem of fairly densily packed particles with rate independent though otherwise arbitrary interaction is investigated in two dimensions. It is shown that slow changes in a statistically uniform medium in the pre-failure deformation state can be described by a stiffness tensor. An approximate expression for this tensor is obtained from first principles. The connection with the perfectly random heterogeneous medium is established. A simple example for round rough particles in an isotropic packing of four contacts is given.
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Koenders, M.A. The incremental stiffness of an assembly of particles. Acta Mechanica 70, 31–49 (1987). https://doi.org/10.1007/BF01174645
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DOI: https://doi.org/10.1007/BF01174645