Entropy methods in the constitutive modeling of granular material

Granular materials provide uncertainties with respect to the geometric and material states of the grains and their arrangements. The use of Jaynes’ maximum entropy principle allows uncertainties to be resolved in such a way that evident information is retained and the unknown described in an unbiased manner. This paper presents the entropy approach with respect to granular materials where the grains are modeled as spheres of linear elastic material. Uncertainties dealt with include the random distribution of spheres and the elastic constants of the materials. Although the approach has been worked our for describing the bulk modulus of a material of like spheres, genuine problems exist in extending the ideas to materials of various sphere sizes and properties. These difficulties are considered in the paper and various modeling approaches using Jaynes’ principle are discussed.