# Mechanical Characterisation and Modelling of Elastomeric Shockpads
## 3 Finite Element Simulation of AAA
### Material Model Development  
Development of material models to represent the behaviour of the shockpads followed a systematic approach (Figure 7). From the experimental results, it was clear that hyperelastic material models were needed to match the non-linear deformation behaviour of the shockpads (Figure 5). Hysteresis was also seen for both shockpads meaning models capable of capturing viscoelasticity must be used. Taking these factors into account, two models were selected for initial calibration. The Bergstrom-Boyce model has been successful in representing solid rubber behaviour [19], however, due to the cellular nature of the shockpads a microfoam material model was also selected. Separate models were calibrated for each of the shockpads in order to capture their unique behaviour. MCalibration software (Version 4.6, Veryst Engineering, Needham, MA, USA) was used to calibrate models from the PolyUMod material database against stress-strain data from a single AAA drop from 55 mm for each of the shockpads (Table 2). The MCalibration software provides a more extensive library of material models compared to the inbuilt Abaqus materials library and gives the user more  
Figure 6: AAA FE model showing increased mesh density around impact area. The model was extruded to eight times the radius of the impact foot. control over the calibration. Each of the material coefficients were calibrated to the experimental data using equations including Lavenberg-Marquardt, NEWUOA and Nelder-Mead. Whilst this process fits the model to the data, the software does not understand relationships between variables often meaning further manual alterations must be done. Calibrated material models were imported into the FE simulation where the AAA drop from 55 mm was replicated and the results of the simulation subsequently compared to the experimental data. A number of variables were used as an indicator of the model accuracy, including the shock absorption, energy restitution, vertical deformation and contact time. The root mean square error (RMSE) was also calculated for the strain as the AAA impact was a stress controlled test. The model was deemed accurate if the mean error was less than 10% and no individual error was greater than 15%. If these criteria were not met the model coefficients were refined manually in MCalibration. Error was defined as the percentage difference between the experimental values and the FE simulated values with exception of the strain RMSE that was expressed as a percentage of the maximum strain. Refinement of the models was done using an intelligent trial and error approach, changing the appropriate coefficients to alter the material response based upon the results of the previous simulation. Both models calibrated well to the experimental data, however, the Bergstrom-Boyce model was unable to accurately represent the deformation response to an error lower than 15%. The microfoam material model performed much better, producing good initial results as the relative density was taken into consideration during the model calculations. This model was further refined to increase the accuracy for both shockpads before validation. Validation of the models was undertaken through the simulation of the lower drop heights of the AAA, with the results subsequently compared to the experimental data.