Fractional Derivative Consideration on Nonlinear Viscoelastic Statical and Dynamical Behavior under Large Pre-Displacement

The nonlinear force-displacement relations of a viscoelastic cylindrical column under uniaxial monotonic slow compressive displacement with a constant speed, and under uniaxial rapid sinusoidal displacement with a constant compressive predisplacement were experimentally and theoretically investigated to describe fractional derivative models for these relations. They were separately extracted from the slow compressive and the rapid sinusoidal experiments. These fractional derivative models were combined to construct a unified nonlinear viscoelastic model to cover from slow to rapid phenomenon appeared in the test specimen. This model successfully reproduced the slow and the rapid phenomena in the experiment.