# Partially-Perforated Self-Reinforced Polyurea Foams
## 3 Results and Discussion
The performance of foams in such impact scenarios can be evaluated from the results of quasi-static mechanical testing [8; 9; 10] to elucidate the ability of the foam to resist deformation, i.e., elastic modulus, as well as the amount of strain energy per unit volume represented by the area under the stress-strain curve. To draw a distinction between our polyurea foams and others currently available on the open market, 19.1 mm thick foam plugs with a diameter of 41.3 mm and 25.4 mm were extracted from EML227 and EML350, respectively. Alternatively, 25.4 mm Dia. \(\times\) 14.0 mm thick samples were extracted from a commercially available impact mitigating foam (\(\sim\)390 kg\(\cdot\)m\({}^{-3}\), closed-cell) used in motorcycle helmets and padding. The latter served as a benchmark control for comparison of performance, and the reduction in diameter for the higher density foam plugs was to accommodate the force limitations of the testing apparatus. Previously mechanical testing showed that the EML350 foam resulted in a density-normalized absorbed energy per unit volume of 991 Pa/kg\(\cdot\)m\({}^{-3}\), while EML227 and the control foams were found to be similar for this metric, resulting in density-normalized absorbed energies per unit volume of 536 Pa/kg\(\cdot\)m\({}^{-3}\) and 532 Pa/kg\(\cdot\)m\({}^{-3}\), respectively, with EML227 being 42.8% lighter. Moreover, the specific modulus (modulus per unit density) for both polyurea foam variations were found to be superior in comparison to the specific modulus of the control foam, where EML227 and EML350 have specific moduli of 2.52 and 2.81 Pa/kg\(\cdot\)m\({}^{-3}\), while the control reported only 1.73 Pa/kg\(\cdot\)m\({}^{-3}\). In a helmet impact scenario, the kinetic energy can be represented as, \(U=\ \frac{1}{2}m(at+\ v_{0})^{2}\), where \(m\) is the mass of the head (taken in subsequent calculations to be 5 kg [37]), \(a\) is the acceleration of the head, \(v_{0}\) is the initial velocity, and \(t\) is the duration of the impact (estimated to be 10 ms for biomechanical impact [37]). Thus, the kinetic energy (due to this impact) can be compared to the strain energy in the foam based on the quasi-static data reported in the previous paragraph to determine the effectiveness of EML350 and control foams in decelerating an incoming impact. EML227 foam was not included in the comparison, due to the large density difference with the other two types of  
Figure 4: SEM micrographs of the cured foam samples showing the polyurea microspheres on (**a**) EML227 and (**b**) EML350 internal cell walls leading to the reinforcement effect. foams. To estimate the strain energy, the density-normalized absorbed energy per unit volume is multiplied by the volume of the impact region and the density of the respective foam. The volume of the impact region was calculated based on an estimated 10 cm impact diameter and the thickness of a typical helmet foam liner (2 cm). The results show that EML350 can tolerate up to 47.6 g of acceleration, while the control foam (with comparable density) can only sustain an acceleration of 36.8 g. The estimated 29% increase in impact mitigation ability through tolerance to higher acceleration is attributed to the unique microstructure of our novel polyurea foam. Finally, a discussion about the reinforcing effect due to the nucleation and deposition of dense polyurea microspheres during the foam fabrication process is warranted to demonstrate the substantial change in the response upon reinforcing. The stiffening phenomenon is emphasized locally, due to the deposition of the microspheres on the inner surface of the microcell of the foam; hence, it is not conducive for experimental probing. Here, we alternatively leverage a newly developed analytical model by some of the current authors to elucidate the increase in stiffness, due to the presence of microspheres. In this model, the dense microspheres were modeled as uniformly distributed over the inner surface in both polar and azimuth directions.