Modification of Goodman-Cowin Theory and Its Application to the Constitutive Models of Flowing Granular Materials

Goodman and Cowin proposed in 1972 a continuum theory of a dry cohesionless granular material in which the solid volume fraction ν is treated as an independent kinematical field for which an additional balance law of equilibrated force is postulated. In the derivation of said balance of equilibrated of force there exists some logical inconsistency and it results in the incorrect explanation of this balance equation and the incorrect balance of internal energy. It is demonstrated that the balance of equilibrated force can be modified by a simple dimensionalanalysis. The resulted modified Goodman-Cowin theory is then applied to investigate the constitutive models of flowing granular materials. A complete thermodynamic analysis based upon Müller-Liu approach is performed and the constitutive responses of a granular material in thermodynamic equilibrium are obtained. From the theoretical investigations it shows that the results are more general than those obtained from the original theory and for simple shearing flow problems the current theory can reproduce all results from previous works based on the original theory.