A normal contact force model for viscoelastic bodies and its finite element modeling verification

A novel normal contact force model considering the energy dissipation for viscoelastic bodies is presented. By solving the differential equation through applying Laplace transform and its inverse transform, the relationship of the stress and strain is established. The model is transformed from the stress-strain relation using the Stieltjes convolution. The proposed model involves the viscosity and relaxation time which represent dominating characteristics of viscoelastic bodies. A means to verify the model using the finite element method (FEM) is performed with a specify two sphere model for FEM simulations and a user material subroutine applied to define viscoelastic material properties. The validity of the novel model is verified with FEM simulations by comparing the force-time and force-displacement relations. The comparisons indicate that results obtained by the model agree well with the outcomes of FEM simulations. In addition, results of the proposed model are compared with the former experimental data and results obtained by other viscoelastic contact models, which manifests that results predicted by this model fit the experimental data well in general, especially in the restitution phase.