On the Correspondence between Stored Energy Function and Helmholtz Free Energy Function of Granular Materials

Goodman and Cowin proposed a continuum theory of a dry cohesionless granular material in which the solid volume fraction ν is treated as an independent kinematical field. With their theory the most important phenomenon of granular materials, dilatancy, can well be simulated. The key point of their theory lies in the postulation of the balance of equilibrated force, which is a balance equation proposed for the evolution of ν. In derivation of this equation the existence of the stored energy function φ and its specific functional dependence have been assumed,and a variational analysis for φ is performed. In the current paper a complete thermodynamic analysis based upon Müller-Liu approach will be given, and the results show that the stored energy function φ corresponds to the Helmholtz free energy function Ψ in thermodynamic equilibrium under isothermal condition, which in turn, indicates that the specification of the functional dependence of φ in the derivation of the balance of equilibrated force is reasonable.