Power laws behavior in multi-state elastic models with different constraints in the statistical distribution of elements

• We analyze the properties of an adhesion model of elastic nonlinearity.
• We introduce a multistate statistical formulation.
• We link power law exponents and statistical properties of the model.
• We prove usefulness of bounded distribution of statistical properties.

Often materials exhibit nonlinearity and hysteresis in their response to an elastic excitation and the dependence of the nonlinear indicator on the excitation energy is a power law function. From the theoretical point of view, such behavior could be described using multistate elastic models based on a generalized Preisach–Mayergoyz (PM) approach. In these models a statistical distribution of transition parameters is usually introduced. We show in this paper the existence of a link between the power law exponent predicted by the model and the properties of the chosen distribution. Numerical results are discussed, based on an implementation in the PM formalism of an adhesion model.