Modelling small and large displacements of a sphere on an elastic half-space exposed to a dynamic force

Spheres at medium interfaces are encountered in many applications, including atomic force microscopy or indentation tests. Although the Hertz theory describes contact mechanics between an elastic sphere and half-space for static loading small deformations very well, there is a need to consider density of medium, mass radiation damping dynamic obtain reliable results. In this study, analytical model predicting large displacements on exposed developed. For purpose, after summarizing mathematical that has recently been proposed interface, finite element interface Based comparison models, improved addition considering properties size sphere, developed here takes into account damping, valid displacements. The can be used understand responses spherical objects practical applications. Furthermore, remarkable tool undergraduate graduate students researchers fields engineering, materials science physics gain insight spheres interfaces.