A constitutive model for wet granular materials

Abstract

Wet granular materials develop both shear stresses and normal stresses during simple shear. Over a certain range of shear rate levels, both the shear stress and the normal stress that develop are linearly proportional to the shear rate. In addition, such materials exhibit permanent increase in volume during simple shear. In this article, a model is developed to capture these features of the mechanical behavior of such wet granular materials. The model is developed within a Gibbs-potential-based thermodynamic framework utilizing the notion of the body possessing multiple natural configurations. Specific functional forms are assumed for the Gibbs potential and the rate of dissipation and the constitutive relations are obtained by the maximizing the rate of dissipation (rate of entropy production). Dilatant behavior is captured by coupling the dissipation due to volume changes to the dissipation associated with the distortion of the material.

Keywords:

• Wet granular materials
• Gibbs potential
• natural configurations
• normal stresses
• dilatancy

Acknowledgments

KRR thanks the Office of Naval Research for support of this work.

Notes

1 Maximization requires us to take the second derivative and show that it is negative. We do not do so here though it can be show that the choice we have made does indeed lead to a maximum.