On the inadequacy of rate-dependent models in simulating asymmetric rate-independent hysteretic phenomena

Aim of this paper is to establish the limits of the common approach according to which, in oscillating systems, dissipative phenomena, often having an asymmetric rate-independent nature, are simulated by means of equivalent rate-dependent models relating forces and velocities. To this end we compare the time evolution of the generalized work and energy components of a Single Degree of Freedom (SDoF) hysteretic mechanical system including both conservative and non-conservative forces; in addition the generalized work of the non-conservative forces is related to the generalized internal energy of the system. To achieve such a result, we provide (closed-form) expression(s) to compute the path-dependent work performed by generalized rate-dependent (rate-independent) hysteretic forces, simulated by using the Seleemah and Constantinou (Asymmetric Bilinear) model. For the latter, we also provide a closed-form expression for the variation in internal energy associated with the generalized rate-independent work when a complete cycle of generalized displacement is applied. Such results are exploited to describe the behavior of symmetric, and asymmetric rate-independent hysteretic systems under loads of arbitrary nature, e.g., free vibration, harmonic load, and random load. Finally, the inadequacy of rate-dependent models in simulating asymmetric rate-independent hysteretic behaviors is assessed by showing that calibrating the former model according to the methodology usually suggested in the literature yields inaccurate results in terms of displacement and dissipated energy of the system.