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

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.