Leveraging the Equivalence of Hysteresis Models From Different Fields for Analysis and Numerical Simulation of Jointed Structures

An important problem that spans across many types of systems (e.g. mechanical and biological) is how to model the dynamics of joints or interfaces in built-up structures in such a way that the complex dynamic and energy dissipative behavior that depends on micro-scale phenomena at the joint/interface is accurately captured, yet in a framework that is amenable to efficient computational analyses of the larger macro-scale system of which the joint or interface is a (spatially) small part. Simulating joint behavior in finite element analysis by meshing the joint regions finely enough to capture relevant micromechanics is impractical for large-scale structural systems due to the prohibitively small time steps required and/or resulting matrix ill-conditioning. A more practical approach is to devise constitutive models for the overall behavior of individual joints that accurately capture their nonlinear and energy-dissipative behavior and to incorporate the constitutive response locally into the otherwise often-linear structural model. Recent studies have successfully captured and simulated mechanical joint dynamics using computationally simple phenomenological models of combined elasticity and slip with associated friction and energy dissipation, known as Iwan models. In the present article, the author reviews the relationship, and in some cases exact equivalence, of one type of Iwan model to several other models of hysteretic behavior that have been used to simulate a wide range of physical phenomena. Specifically, it is shown that the “parallel-series” Iwan model has been referred to in other fields by different names, including “Maxwell Resistive-Capacitor” and “Ishlinskii”. Given this, the author establishes the relationship of this Iwan model to several other hysteresis models, most significantly the classical Preisach model. Having established these relationships, it is then possible to extend analytical tools developed for a specific hysteresis model to all of the models with which it is related. Such analytical tools include experimental identification, inversion and analysis of vibratory energy flow and dissipation. A numerical case study of a simple system that includes an Iwan-modeled joint illustrates these points.