Characterization of hysteretic stress–strain behavior using the integrated Preisach density

In this paper, we introduce the concept of Integrated Preisach–Mayergoyz (IPM) density to analyze static uniaxial compression tests at values well below the critical strength, and to characterize the elasticity of materials with hysteresis in their stress–strain relationship. The IPM density can be deduced from a particular force protocol following basic data treatment. The advantage of the IPM density over prior approaches is that no second order differentiation of the data is required which reduces the errors and uncertainties typical for past practice in the specific context of rock elasticity using scanning curves and PM density analysis. The characterization of the elasticity of the material is established in terms of a non-hysteretic strain contribution in the form of a non-linear but reversible equation of state, and a hysteretic contribution represented by the IPM density. The IPM inversion procedure is tested for simulated stress–strain data subjected to additive noise, and the results are compared to the traditional methodology. In addition, we analyze the hysteretic and non-hysteretic characteristics of five natural building stones, and show evidence for a classification based on the inferred properties.