Viscoelasticity of granular materials

In a former work (V.T. Granik and M. Ferrari (1993), Microstructural mechanics of granular media, Mech. Mater. 15, 301-322) a micromechanical theory for elastic granular media was deduced on the basis of the identification of the constituent grains with the nodes of a Bravais lattice. The transition from the discrete structure to the continuum level was achieved through assumptions on the kinematical fields and through a variational formulation establishing the relationship between microstresses and macrostresses. In the present paper we extend this theory to the linear viscoelasticity domain. We formulate the general linear viscoelastic relations in terms of microstresses and microdeformations, deducing the boundary value problems for the microstresses and for macrostresses. Then we focus our attention on the links between constitutive equations governing the microscopic level (formulated following the general methods of linear viscoelasticity) and their macroscopic counterparts. Thus we directly relate microstructural information to the macroscopic constitutive laws. deducing classical macroscopic properties in terms of structural parameters. Finally the dynamical problem of plane waves propagation in a semi-infinite granular medium is analyzed and the influence that the arrangement of the particles exerts on the pulse propagation is discussed.