Fractional time-dependent deformation component models for characterizing viscoelastic Poisson's ratio

• Fractional and spring deformation elements are presented through analogy.
• Three fractional deformation models are obtained by connecting the two deformation elements.
• The fractional deformation models can represent accurately the viscoelastic Poisson's ratio.
• The fractional deformation models enjoy the advantage of having few parameters and simple form.

There is the complex relationship between Poisson's ratio and time in viscoelastic solids. Hence, using a simple model to characterize accurately the viscoelastic Poisson's 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 Poisson's 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 Poisson's ratio.