Amplitude- and frequency-dependent nonlinearities in the presence of thermally-induced transitions in the Preisach model of acoustic hysteresis

Contribution of hysteretic mechanical elements to the stress/strain relationship of microinhomogeneous material is analyzed within the framework of a model where the transitions between the different mechanical states of the individual elements in addition to acoustic loading can be induced by thermal fluctuations. The model provides explanation for the dependence of the type and order of the acoustic nonlinearity on the wave amplitude observed in experiments with microinhomogeneous materials, where, with increasing wave amplitude, transition from behavior characterized by the dominance of the quasinonhysteretic nonlinearity to another characterized by the dominance of hysteretic quadratic nonlinearity takes place. Analytical evaluation of the model for the acoustic hysteresis is shown to confirm the expectation that thermal relaxation effects are capable of inducing dispersion in both the linear and nonlinear acoustic properties of the material.