Microstructural mechanics of granular media

A geometrically and physically linear micromechanical theory for elastic granular media is presented, based on the identification of the constituent grains with the nodes of a Bravais lattice. Adjacent particles are permitted to displace normally and transversely to each other, and to rotate with respect to the doublet axes. Thus, microstrains of the axial, torsional, and shear type are generated. The conjugate microstresses are then defined. Through a variational formulation, the microstress equations of motion are derived, together with natural boundary conditions and the transition from the microstresses to the macrostresses. The principles of thermodynamics are employed to derive the most general, invariant, and appropriately symmetric microconstitutive equations, and to close the system of field equations for the granular medium, subject to both adiabatic and non-adiabatic processes. The problem of a granular semispace loaded by compressive boundary force is solved as an application, and the existence of locally tensile microstresses is determined, while the associated macrostresses are computed to coincide with the well-known Flamant's solution and thus to be compressive everywhere.