Including plastic behaviour in the Preisach-Mayergoyz space to find static and dynamic bulk moduli in granular media

We propose a modification of the Preisach-Mayergoyz (PM) space model to account for plastic deformation of a heterogeneous medium subjected to hysteretic non-linear elasticity. The PM space models the heterogeneous medium as a set of hysteretic nonlinear mesoscopic units which behave as switches that expand (turn on) and contract (turn off) at different pressures. The density distribution of these units describes the elastic behaviour of the medium. The PM model accounts for hysteresis but not for plastic deformation. We modify the model to include the plastic deformation by allowing the units to expand (turn on) at negative pressures. We implemented the elasto-plastic PM model using a discretized representation according to (Guyer et al. 1997). We tested this model on two loading cycles of a Gulf of Mexico beach-sand sample (Zimmer 2003). We compare the classical PM to our elasto-plastic PM and we highlight the increased ability to predict the dynamic bulk modulus as well as the enhancement in the representation of the effective stress-strain path, while being consistent with the original PM model.