A class of uniaxial phenomenological models for simulating hysteretic phenomena in rate-independent mechanical systems and materials

We present a general formulation of a class of uniaxial phenomenological models, able to accurately simulate hysteretic phenomena in rate-independent mechanical systems and materials, which requires only one history variable and leads to the solution of a scalar equation for the evaluation of the generalized force. Two specific instances of the class, denominated Bilinear and Exponential Models, are developed as an example to illustrate the peculiar features of the formulation. The Bilinear Model, that is one of the simplest hysteretic models which can be emanated from the proposed class, is first described to clarify the physical meaning of the quantities adopted in the formulation. Specifically, the potentiality of the proposed class is witnessed by the Exponential Model, able to simulate more complex hysteretic behaviors of rate-independent mechanical systems and materials exhibiting either kinematic hardening or softening. The accuracy and the computational efficiency of this last model are assessed by carrying out nonlinear time history analyses, for a single degree of freedom mechanical system having a rate-independent kinematic hardening behavior, subjected either to a harmonic or to a random force. The relevant results are compared with those obtained by exploiting the widely used Bouc–Wen Model.