Including Plastic Strain Into the Discrete Preisach-Mayergoyz Space: Application to Granular Media

The Preisach-Mayergoyz (PM) model describes hysteretic behavior in several fields. For fractured rocks, a discretized version of the PM model successfully models nonlinear hysteretic elasticity under multiple loading cycles. In addition to hysteresis, granular media are subjected to large irreversible (plastic) deformation. To account for plastic deformation, we propose a modification of the PM density matrix, in which we include negative opening pressure. We associate negative opening pressure with rearrangements of the contact network. We apply the model to three sand samples undergoing multiple isotropic loading cycles. Calibrating the model parameters from quasi-static measurements of volumetric deformation, we estimate the quality of prediction of the dynamic bulk modulus. When this elastoplastic PM model is compared to the classic PM model, strong improvements are found both in matching the strain path and in the estimation of the dynamic bulk modulus.