Fractional time-dependent deformation component models for characterizing viscoelastic Poissonʹs ratio

There is the complex relationship between Poissonʹs ratio and time in viscoelastic solids. Hence, using a simple model to characterize accurately the viscoelastic Poissonʹs ratio is important for the analysis of viscoelastic behaviors. We put forward two deformation elements, fractional and spring deformation element, and obtain three fractional deformation models through connecting the two deformation elements in parallel or series. The functions of viscoelastic Poissonʹs ratio are also derived for stress relaxation and constant-longitudinal-strain loading. Further comparisons between tests and fitting results reveal that the fractional deformation models can represent reasonably the viscoelastic Poissonʹs ratio.