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Abstract Emerging polymeric foams exhibiting unique microstructure of microspherical shells with reinforcing dense microspheres creates a new opportunity for impact-tolerant foam paddings in sport gears applications. This paper describes the static response of reinforced microcell consisting of an outer spherical shell and uniformly distributed microspheres while quantifying the stiffening effect. The distribution of the microspheres is illustrated using the Fourier series, allowing tuning of the reinforcing strategy. Expressions of the external and internal works are derived, whereas the Ritz energy method is adopted to calculate the deformations due to a compressive load distributed over a range of areas. Emphasis is given to the effect of the geometrical attributes of the microcell and the reinforcing microspheres on the resulting deformation response and stiffening effect. The framework is used to investigate the response of several case studies to elucidate the effects of relative radii ratio, reinforcement density, microcell wall thickness, and loading configurations on the stiffness. A new normalized strain energy parameter is introduced to simplify and accelerate the analysis while providing insights on the underpinnings of the observed buckling response. The results strongly suggest the viability of the newly discovered foam microstructure in managing static loads while providing an opportunity to strategically tune the mechanical response using the analytical framework presented herein. 

This paper reports the unique microstructure of polyurea foams that combines the advantages of open and closed cell polymeric foams, which were synthesized through a self-foaming process. The latter was the result of aggressive mechanical mixing of diamine curative, isocyanate, and deionized water at ambient conditions, which can be adjusted on-demand to produce variable density polyurea foam. The spherical, semi-closed microcellular structure has large perforations on the cell surface resulting from the concurrent expansion of neighboring cells and small holes at the bottom surface of the cells. This resulted in a partially perforated microcellular structure of polyurea foam. As a byproduct of the manufacturing process, polyurea microspheres nucleate and deposit on the inner cell walls of the foam, acting as a reinforcement. Since cell walls and the microspheres are made of polyurea, the resulting reinforcement effect overcomes the fundamental interfacial issue of different adjacent materials. The partially perforated, self-reinforced polyurea foam is compared to the performance of traditional counterparts in biomechanical impact scenarios. An analytical model was developed to explicate the stiffening effect associated with the reinforcing microspheres. The model results indicate that the reinforced microcell exhibited, on average, ~30% higher stiffness than its barren counterpart.