The Preisach-Mayergoyz (PM) space models both static and dynamic elastic moduli of complex media subjected to hysteretic non-linear elasticity. The Guyer et al. discrete formulation of the PM space compactly represents the model parameters with a density matrix using a constant pressure step. A recently proposed modification of this model permits to account for irreversible plastic deformation by expanding the PM space to negative opening pressures. This modification is crucial in granular media for which irreversible deformation associated with grain rearrangement is macroscopic. In this work, we optimize the discretized elasto-plastic PM space by allowing a variable pressure step in the discretization. The size of the pressure step depends on the density of the observed data samples in a certain pressure range. We tested this model on two loading cycles of a Gulf of Mexico beach-sand sample. Using the elasto-plastic formulation, we compare the constant pressure step and the variable pressure step models, and we highlight the improvement of the latter in the prediction of the dynamic bulk modulus.


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