A non-linear model for elastic hysteresis in the time domain: Computational procedure

Hysteretic damping of a material or structure loaded within its elastic region is the dissipation of mechanical energy at a rate independent of the frequency of vibration while at the same time directly proportional to the square of the displacement. Generally, reproducing this frequency-independent damping can be computationally complex and requires prior knowledge of the system’s natural frequencies or the full time history of the system’s response. In this paper, a new model and numerical procedure are proposed whereby hysteretic material damping is achieved in the time domain. The proposed procedure is developed based on modifying the viscous model through a correction factor calculated exclusively using the local response. The superiority of the proposed approach lies in its ability to capture material hysteresis without any knowledge of the eigen- or modal frequencies of the system and without knowledge of the past time history of the system’s response or the characteristics of any excitation forces. A numerical procedure is also presented for implementing the proposed model in vibration analysis. The simplicity of the approach enables its generalisation to continuous systems and to systems of multi-degrees of freedom as demonstrated herein. The proposed model is presented as a correction to the viscous damping model which makes it attractive to implement into commercial finite element package using user-defined element subroutines as demonstrated in this study.