# Mechanical Characterisation and Modelling of Elastomeric Shockpads
## 4 Results  
The microfoam material model showed good overall agreement with the experimental data for both the Berleburger and Holywell shockpads and all drop heights (Figure 8). The FE simulations met the accuracy criteria for both shockpads and all drop heights, except for the Berleburger 15 mm drop height where the strain RMSE was slightly above the threshold at 18% (Table 3).  
The FE simulations under-estimated shock absorption for the Berleburger shockpad by a consistent 3-4% across drop heights, corresponding to an over-estimation in peak force. Agreement was better for the Holywell shockpad with the difference within 2% throughout. The FE simulations over-estimated vertical deformation for the Berleburger shockpad, by up to 0.3 mm, while agreement was again better for the Holywell shockpad with the difference being no more than 0.2 mm throughout. In all cases if shock absorption was under-estimated then vertical deformation was over-estimated and vice versa, suggesting that for both shockpads the overall loading stiffness response was better estimated than the two loading extreme measures of shock absorption and vertical deformation. The FE simulations over-estimated energy restitution by up to 8% suggesting that more energy was returned to the impactor than was observed experimentally. These differences were larger than those for shock absorption and vertical deformation which was not unexpected given that both the loading and unloading phases contributed to this variable [20]. Interestingly, for both shockpads, the difference in energy restitution decreased with decreasing drop height; from 6 to 8% for the 55 mm drop height to only 0-1% for the 15 mm drop height. This trend suggests that the loading-unloading response  
Figure 7: Flow chart showing the steps involved in material model development.  
is accurately captured by the simulations for low strains, but less so for higher strains that reach the hyperelastic region of the stress-strain curve (Figure 5). For low strains, the compression and recovery are dominated by air voids, while for higher strains the compression and recovery includes not only air voids but also the rubber shreds/granules. This poorer performance may, therefore, represent a limitation of using a microfoam model to estimate compression and recovery of a granular/shredded rubber held together by a polyurethane binder (Table 1).  
Strain RMSEs were also larger than those for shock absorption and vertical deformation, on average similar between shockpads, but showed no consistent trend with drop height. For the Berleburger shockpad the strain RMSE increased with decreasing drop height (from 6 to 18%) and appeared linked to an increasing offset in the unloading curves between the experimental data and simulation output. In contrast, for the Holywell shockpad the strain RMSE decreased with decreasing drop height (from 14% to 6%) and appeared to be linked to the simulation output exhibiting undulations during the loading phase that, as noted above, were not present in the experimental data for this shockpad, with the undulations being of greater magnitude for the higher drop heights (Figure 8).  
Although some of these differences will be due to inaccuracies in the material models and FE simulations, there will also be a contribution related to uncertainties in the experimental data itself. These include: inconsistency in the shockpad thicknesses (Table 1) due to construction method and granular nature; errors introduced through numerical integration of the accelerometer data to generate the velocity and displacement data [20]; and in the use of this calculated velocity data to identify the instant of impact and impact conditions.  
Figure 8: Comparison of stress-strain experimental data against FE simulation outputs across the three drop heights for (**a**) Berleburger and (**b**) Holywell shockpads.