Some Remarks on the Equilibrium of Granular Materials Described by Constitutive Relations That Depend on the Gradients of the Density or Volume Fraction

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Abstract One of the ways of determining the properties of granular materials is to subject the material to a tri-axial state of stress with three distinct eigenvalues, in a cubical tri-axial testing equipment, the material tested being in a static state. A constitutive relation for granular materials that does not allow the body to be in tri-axial static equilibrium would not be a reasonable model as experiments clearly show that granular materials can exist in such tri-axial states. In this short note, we observe that a large class of models that have been developed and used to describe the response of granular materials will not allow them to be in a static tri-axial state of stress with three different principal stresses.