Modelling a viscoelastic gymnastics landing mat during impact

Landing mats that 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 runtime. 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, through to a 3 layer mass-spring-damper system, Model 4, were constructed using Matlab to model the mat’s behaviour during impact. A fifth model compromised 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 one 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, inter-peak minima and initial rates of loading and could be incorporated into a gymnast-mat model.