Modeling a Viscoelastic Gymnastics Landing Mat during Impact

Landing mats that can undergo a large amount of area deformation are now essential for the safe completion of landings in gymnastics. The objective of this study was to develop an analytical model of a landing mat that reproduces the key characteristics of the mat-ground force during impact with minimal simulation run time. A force plate and two high-speed video cameras were used to record the mat deformation during vertical drop testing of a 24-kg impactor. Four increasingly complex point mass spring-damper models, from a single mass spring-damper system, Model 1, to a 3-layer mass spring-damper system, Model 4, were constructed using Matlab to model the mat's behavior during impact. A fifth model composed of a 3-layer mass spring-damper system was developed using visual Nastran 4D. The results showed that Models 4 and 5 were able to match the loading phase of the impact with simulation times of less than 1 second for Model 4 and 28 seconds for Model 5. Both Models 4 and 5 successfully reproduced the key force-time characteristics of the mat-ground interface, such as peak forces, time of peak forces, interpeak minima and initial rates of loading, and could be incorporated into a gymnast-mat model.

Simulation of the influence of sports surfaces on vertical ground reaction forces during landing

In many biomechanical analyses, the vertical ground reaction force (GRF) is measured by force plates. However, if force plates are fixed on elastic surfaces, the force signals have low-frequency oscillations superimposed. The question arises, as to whether this oscillation results from the response of the athlete to the surface properties or from the fixation of the force plate on the elastic surface. For the simulation of the vertical GRF, a mechanical model was developed that combines three submodels representing the surface, the athlete and the force plate. The simulations were carried out for landings on concrete and wooden elastic surfaces, without and with the force plate, respectively. Comparison of the two surfaces showed that, on the elastic surface, the passive peak of the vertical GRF was lower and was reached later than on the concrete surface. Thus a lower force rate was possible during the landing on the elastic surface (concrete: 186 body weight per second; wooden: 164 body weight per second), which can reduce the risk of damaging the joint cartilage. The simulations also showed that the time course of the GRF was changed by a rippling effect when the force plate was fixed on the elastic surface. The rippling was not the result of a change in the athlete's movements, because the parameters of the athlete submodel were not changed. The rippling induced by the force plate hinders the analysis of the GRF time course involving the real peak force and the force rate.