Dynamic model of hysteretic elastic systems

A model for the dynamical behavior of a hysteretic elastic system is introduced and studied numerically. This model consists of a chain of hysteretic elastic elements. Each elastic element is a spring with properties that depend on an Ising-like state variable having Brownian dynamics in an energy landscape with structure that is sensitive to the forces which the elastic element must support. A single elastic element is studied carefully, numerically in order to establish its basic behavior. A one dimensional chain of N = 500 elastic elements, driven like a resonant bar, is studied numerically. The data from this study are analyzed by the methods employed in analyzing similar experimental data. The behavior of the numerical model compares well with the behavior of physical realizations of hysteretic elastic systems.