Abstract: We show the hysteretic nonlinear behavior of discrete memory, hysteresis loop and “X” shape tangent elastic moduli (Young’s modulus and Poisson’s ratio) in uniaxial cyclic loading experiments, and further clarify it using hysteretic quasi-static stress-strain equation of state in Preisach-Mayergoyz model (PM model) proposed by McCall and Guyer. Detailed curves of stress-axial strain, stress-radial strain, tangent modulus-axial strain and tangent Poisson’s ratio-axial strain are determined by space density and elastic property of hysteretic mesoscopic units (HMU) in PM model. In the equation of state, stress is proportional to the fraction of closed elastic units to total units, and the closed elastic units are related to applied pressure history, especially at the turn of pressure reversal. The response of strain is related to the stress path, and the model emphasizes the importance of stress history in determination of the elastic state of rock, hence the model can be used to simulate discrete memory. In this sense, hysteresis might be the cause of discrete memory in rock. By the simulation, we demonstrate the quantitative relationships between the parameters of PM model and elastic moduli of rock.

Key words: simulation, hysteresis, discrete memory, elastic moduli