# Partially-Perforated Self-Reinforced Polyurea Foams
## 1 Introduction  
Foams are generally an essential class of materials that are ubiquitous in impact mitigation applications, due to their inherent high-energy absorption ability. Such an ability is associated with its cellular structure through multiple deformations or failure mechanisms dependent on the classification of the foam structure, i.e., open-cell or closed-cell. In general, the reversible or irreversible deformations (e.g., elastic deformation, bulking, and densification) dissipate the incoming impact energy through the strain energy resulting from the shape change during the loading scenario. Another intrinsic property of foams is the significant reduction of weight compared to its base materials, since the solid is either orderly or randomly arranged in the three-dimensional space during the foaming process. A sub-class of the foam family of materials is polymeric foams, which are universally used in protective sports equipment to guard against low to moderate impacts such as those experienced by athletes. Polymeric foams strategically combine the fundamental properties of cellular solids by providing superior energy absorption to weight ratio, which is imperative for novel and innovative personal armors for athletic and military applications [1]. To further improve the performance of polymericfoams in dynamic loading scenarios, dense polymers with superior impact mitigation have been continuously sought by scientists and engineers to create the cellular microstructure of foams. The macroscale deformation response of polymeric foams is sensitive to the attributes of the loading conditions, including the duration and amplitude of the impact, as well as the strain rate. This sensitivity is an interplay between the properties of the base or parent polymer and the cellular microstructure [2; 3; 4; 5; 6; 7]. At the fundamental level, the mechanical behavior of foams is hinged on the interconnectivity of the solid forming the basic cell structure, which gives rise to different energy dissipation and shunting mechanisms that are tunable through the geometry of the cellular microstructure. [PERSON] and [PERSON] exhaustively treated the topic of the structure and properties of foams by generally classifying their microstructures as either open-cell or closed-cell, as well as partially-open/partially-closed cells [2]. The latter, if it exists, usually is a material with segregated regions of open-cells adjacent to regions of closed-cells, due to the difficulty in strategically controlling the dispersion of the blowing or foaming agent into the polymer melt during the manufacturing process. Open-cell foams are more desirable for energy-absorption applications, due to their horizontal plateau behavior, while closed-cell foams are more desirable for cushioning and load distribution applications [8; 9; 10]. Thus, combining the advantages of the open and closed microcellular structures would result in a foam material with tailorable properties explicitly designed for a target application. The material selection can be further improved if shape memory properties are intrinsically or extrinsically induced on the foam microstructure [11]. Recently, our group reported a manufacturing process that produced a hybrid structure foam encompassing the advantages of closed and open cells [5; 6; 12; 13]. A byproduct of the foaming process is the nucleation of dense microspheres, which get deposited on the inner walls of the cells during the final water drainage process, resulting in additional reinforcement. The latter is the focus on the research leading to this paper. It is important to note the difference between enhancing properties by tailoring the molecular structure through the combination of urethane and urea bonds [11], the addition of microparticles to form composite materials [3], and the approach reported here, where polyurea microspheres form during the mechanical mixing process and act a reinforcement.