Cellular solids have gained extensive popularity in different areas of engineering due to their unique physical and mechanical properties. Recent advancements in manufacturing technologies have led to the development of cellular solids with highly controllable microstructures and properties modulated for multiple functionalities at low structural weights. The concept of density gradation in cellular solids has recently gained attention due to its potentials in opening new doors to the development of lightweight structures that offer optimal physical and mechanical properties without compromising their favorable characteristics. Herein, a comprehensive insight into the fundamental concepts, fabrication, and current and potential applications of density‐graded cellular solids in various areas of science and engineering is provided. Cellular solids are broadly classified into two main categories: foams and lattice structures. An overview of the fundamental concepts in each category is presented, followed by details on the characterization approaches and some of the most novel processing techniques utilized in fabricating the structures. The uses of density‐graded structures in load‐bearing, acoustic, and biomedical applications are highlighted. The state of the art in each category and the current trends in application‐specific optimization of density‐graded structures are discussed. The review concludes with an outlook of the future directions in this exciting field.

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Elastomeric polymer foams are widely used in sports and other protective padding applications due to their unique properties, such as excellent cushioning and relatively high‐energy absorption to weight ratio. This work investigates the mechanical and energy absorption performance of an elastomeric hybrid structure polyurea foam in response to low‐velocity impact. The examined polyurea foams are synthesized using a novel self‐foaming process that leads to the development of a semi‐closed cellular structure. The quasi‐static response of the foam is first characterized by measuring the global stress–strain and energy absorption characteristics. The evolution of the foam's Poisson's ratio is also characterized by in situ digital image correlation (DIC) measurements. The same properties are also studied in dynamic loading conditions by subjecting the foam samples to controlled impact tests. A strain‐dependent rate sensitivity parameter is used to quantify differences between the quasi‐static and dynamic strength and energy absorption responses of the foam. The examined foam shows significant enhancement in strength at increased strain rates while retaining its excellent energy absorption capacity. This unique characteristic of the examined foam is discussed in terms of the concurrent effects of entrapped gas and the rate sensitivity of the parent polymer.

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This research investigates the dynamic response of a novel polyurea foam with different densities by separately submitting samples to single and multiple impacts at different energies ranging from 1.77 to 7.09 J. The impact and transmitted force‐time histories are acquired during the impact events. Deformation of the samples is also recorded using high‐speed photography and analyzed using digital image correlation (DIC) to characterize density‐dependent strain rate and Poisson's ratio. The analyses of the force‐time histories highlight the interrelationship between the incoming impact energy and force characteristics, including amplitude and durations. The experimental results reveal that polyurea foams can absorb nearly 50% of the incoming impact energy irrespective of their density. The dynamic impact efficacy of the foam persists even after sequential impact events are imparted on the same samples, with only a 20% drop in the load‐bearing capacity after seven consecutive impacts. Furthermore, as verified via electron microscopy observations, the higher‐density foam does not exhibit any permanent damage. This high‐density polyurea foam shows reversible auxetic transition at all impact energies considered herein. The outcomes of this research indicate the suitability of polyurea foams for cushioning and impact mitigation applications, especially in repeated biomechanical impact scenarios.

The concept of density-graded foams has been proposed to simultaneously enhance strain energy dissipation and the load-bearing capacities at a reduced structural weight. From a practical perspective, the fabrication of density-graded foams is often achieved by stacking different foam densities. Under such conditions, the adhesive interlayer significantly affects the mechanical performance and failure modes of the structure. This work investigates the role of different adhesive layers on the mechanical and energy absorption behaviors of graded flexible foams with distinct density layers. Three adhesive candidates with different chemical, physical, and mechanical characteristics are used to assemble density-graded polyurea foam structures. The mechanical load-bearing and energy absorption performances of the structures are evaluated under quasi-static and dynamic loading conditions. Mechanical tests are accompanied by digital image correlation (DIC) analyses to study the local strain fields developed in the vicinity of the interface. Experimental measurements are also supplemented by model predictions that reveal the interplay between the mechanical properties of an adhesive interlayer and the macroscale mechanical performance of the graded foam structures. The results obtained herein demonstrate that the deformation patterns and macroscale properties of graded foam composites can be tuned by selecting different bonding agents. It is also shown that the proper selection of an adhesive can be a practical way to address the strength–energy dissipation dichotomy in graded structures.

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