Effects of layer thickness on impact contact in functionally graded-equivalent layered plates: An experimental, FE and semi-analytical study of table-tennis ball impact

Elastic contact of layered elastic plates is common in sports equipment and engineering systems, yet most impact-contact analyses of elastic spheres still rely on classical Hertzian theory based on homogeneous half-spaces. For a table-tennis racket, however, the impact occurs on a strongly heterogeneous layered plate composed of a rubber top-sheet, a sponge layer, and a stiff wooden blade, for which the applicability of Hertzian theory is limited. In this study, a closed-loop framework is established by coupling free-fall rebound experiments, finite element (FE) simulation, Hertzian baseline analysis, and a semi-analytical discrete-convolution fast Fourier transform (DC-FFT) solver for functionally graded-equivalent layered plates. The measured rebound height is used for baseline FE calibration, whereas the contact duration and the contact radius at the maximum compression instant are reserved for validation of the transient contact response. Hertzian theory is then used as a homogeneous-reference estimate, so that the magnitude and direction of its deviation from the calibrated and experimentally checked FE response can be discussed. The DC-FFT framework is used for response-level forward reconstruction of the peak-compression contact state and for generating thickness-dependent maps of maximum compression, peak contact pressure, and contact radius by independently varying the rubber and sponge thicknesses. The results show that sponge thickness is the dominant structural variable governing the global compliance of the layered covering, while rubber thickness mainly provides a secondary near-surface tuning effect. The proposed framework also enables thickness-allocation screening and identifies a favorable rubber–sponge thickness combination for the racket considered. The experiment–FE–DC-FFT framework provides a practical and mechanically interpretable route for thickness design of layered plates under elastic impact. The optimized thickness pair is therefore reported as a model-based design recommendation.