Been Living in the Past? Hysteresis in the Equation of State of Granular Media

Granular media, from unconsolidated to consolidated, are supported by a complex contact set. In their quasi-static response granular media exhibit stress-strain hysteresis with end-point memory. They often show slow dynamics in transient response (release of an applied stress) and in dynamic response (under AC drive). To model granular media successfully one steps to the mesoscopic scale and employs continuum elastic elements that couple to their neighbors through a contact set having prescribed properties. Important among these properties is a state variable that is sensitive to the local stress history of each contact. This state variable is tracked in a Preisach bookkeeping space. Preliminary to investigations of the dynamics of these systems we have undertaken studies of the quasi-static response of a model that has the flexibility to go from unconsolidated (sand) to consolidated (sandstone). Initial findings, in the consolidated granular media limit, will be reported.