Fractional derivative constitutive models, developed by the present authors (CND, vol.10, 061002, 2015), are implemented into a commercial finite element (FE) software, abaqus (referred to as a computational model) for solving dynamic problems of gel-like materials. This software is used to solve impact responses of gels, and the solutions are compared with the experimental results. The FE results reproduce well the experimental acceleration and displacement data from different types of gels whose properties are characterized by the fractional order and material parameters. Thus, the computational model presented here was validated. The fractional derivative model is compared with the Simo model (Computer Method in Applied Mechanics and Engineering, 60:153–173, 1987), which is an integer order derivative model. The response of the fractional derivative model can be approximated well when appropriate parameters of the Simo model are used. In the finite element method (FEM), compressibility is introduced artificially for simulations. Interpretations are given on the compressibility of materials in the FEM.
Modeling ramp-hold indentation measurements based on Kelvin–Voigt fractional derivative model
