Finite element analysis of the contact forces between a viscoelastic sphere and rigid plane

The normal and tangential force–displacement (NFD and TFD) relationships between a viscoelastic sphere and a rigid plane are analysed using the finite element method (FEM). The normal force models commonly used in the literature are carefully examined in terms of the viscous stress profile at the contact patch, and are found to exhibit discrepancy with the FEM outcome. There are also problems in the tangential force models in the literature. Based on the theoretical analysis and FEM results, a new set of semi-analytical models for both the normal and tangential forces is proposed and shown to be effective in simulating a host of oblique collisions. The new models have an advantage that their parameters can all be directly determined from the material properties for viscoelastic spheres.

Graphical abstractThe normal and tangential force–displacement relationships (NFD and TFD) between a viscoelastic sphere and a rigid plane are analysed using finite element method (FEM). A new set of semi-analytical models for both the normal and tangential forces is proposed and shown to be effective in simulating a host of oblique collisions.Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► New theories are developed to calculate the collision between viscoelastic spheres. ► The resulting models overcome the theoretical problems of the previous models. ► All parameters in the models can be evaluated as a function of material properties. ► The approach has been tested from oblique impacts of viscoelastic sphere.