This work provides an extension of previous works, dating back some thirty years on more, on maximum-entropy estimates for the micromechanics of granular assemblies. The focus here is on the statistical distribution of contact forces or particle displacements in quasi-static deformations.
The precise form obtained for probability density is shown to depend on the statistical weight assigned to elements in the state space of contact forces or particle displacements, a point overlooked in previous treatments. Comparisons are given with experiment and computer simulations for various assumed weightings.
A synthesis is given of previous descriptions of granular microstructure and micromechanics in terms of Delaunay-Voronoi tesselations. Based on this unified description, the formal methods of statistical thermodynamics are employed to establish a virtual thermomechanics, with no formal requirement of a granular temperature. This leads to an elastoplastic work function, of the type appearing in various phenomenological models of complex solids and fluids. The possibility of non-convexity leading to continuum- and meso-scale material instability is briefly discussed.
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