Modeling dry granular mass flows as elasto-visco-hypoplastic continua with microstructural effects. I. Thermodynamically consistent constitutive model

Abstract

On the basis of the revised Goodman–Cowin theory, dry granular mass flows are modeled as elasto-visco-plastic continua with microstructural effects. In particular, hypoplasticity is incorporated to account for the plastic deformations and internal-friction characteristics of the material. The constitutive equations comprise of the equilibrium and non-equilibrium parts. A thermodynamic analysis, based on the Muller–Liu entropy principle, is performed to derive the ultimate equilibrium expressions of the constitutive variables, while the non-equilibrium responses are postulated by use of a quasi-linear theory. Results show that the revised Goodman–Cowin theory can appropriately be extended to take the frictional and plastic effects into account. These are revealed in the additonal plastic contributions in the equilibrium expressions of the Cauchy stress tensor and the balance equations of two internal variables. It is also shown that the present model is capable of describing the complex elasto-viscous-plastic behaviour of granular materials in static/quasi-static as well as in dynamic situations. This paper is devoted to the derivation of the thermodynamically consistent constitutive model. Its applications to benchmark problems and the justified evaluation of its performance and limitations are deferred to the other further paper.