Application of local elasticity continuum damping models in nonlinear dynamic analysis

In nonlinear dynamic analysis, damping models are used to represent the un-modelled dissipation. Till now, majority of nonlinear dynamic analysis tools for seismic engineering uses the classical Rayleigh damping and its variations. Though these models perform well in linear dynamic analysis, their adaptation to nonlinear dynamic analysis is accompanied with severe penalties. In quest of developing a better modelling approach to mimic the so observed un-modelled dissipation phenomenon in nonlinear dynamic analysis, the authors have recently proposed a new approach of inherent damping modelling by formulating the damping matrix at an element level. In this paper, the new approach is further applied into more mathematically rigorous continuum damping models based on local elasticity. In the present paper, these models are called local continuum damping models mainly because the damping stress at a point in space is a function of the strain history at that point only. Semi-discretization procedures and time domain implementation schemes are outlined in detail. It has been shown that these models can be easily incorporated into the existing commercial software framework with minor modifications. The performance of the proposed adaptations of these models is illustrated by conducting nonlinear dynamic analysis on a four-story RC frame designed to Eurocodes. The incremental dynamic analysis study presented outlines the fact that the proposed models perform in a more reliable manner in comparison to the classical damping models in capturing the damping phenomenon.