Comparison of fractional derivative models for finite deformation with experiments of impulse response

Abstract

In constructing a three-dimensional fractional derivative model for viscoelastic materials, difference of interpretation of strain in the fractional derivative results in many types of nonlinear models. In this paper, some nonlinear models are compared with experimental results of a polymer gel. In the experiment a weight was collided in the vertical direction on the upper free surface of a cylindrically shaped gel with the bottom side fixed. Then, the acceleration and the displacement of the contact surface between the weight and the gel are observed. In the models, deformation of the gel is approximated by the uniaxial compression of incompressible materials. Each model considered in this paper reproduces well the acceleration data in the early stage. However, differences between the calculated responses among the models begin to appear around the maximum point of the acceleration when the compression speed slows down. It is shown that incompressible models based on the weakly compressible approximations give good fits.