Cellular Materials Research Articles

Influence of the cell size and wall thickness on the compressive behaviour of fused filament fabricated PLA gyroid structures

The development of Additive Manufacturing (AM) has greatly facilitated the fabrication of cellular and lattice materials. Gyroid-based lattice structures, known for their distinctive properties such as interconnected porosity, high surface-to-volume ratio, and remarkable structural stiffness combined with specific energy absorption, have been extensively explored. Many studies examining the impact of design parameters on the mechanical properties of Gyroid lattice materials have utilized metal AM techniques. This research aims to evaluate the influence of two design parameters on the compressive properties of Gyroid structures obtained by fused filament fabrication (FFF). A full factorial analysis was employed to assess the effects of cell size and wall thickness on the compressive properties of polylactic acid (PLA) Gyroid lattices. Cell sizes were varied between 4 mm, 5 mm, and 10 mm, while wall thickness ranged from 0.4 mm, 0.6 mm, to 0.8 mm. After 3D printing, the print quality was assessed, samples were weighted and then subjected to compression testing. During compression, the lattices with 10 mm cells exhibited successive layer collapse, whereas the lattice with 4 mm and 5 mm cells displayed plastic deformation, marked by a plateau in the stress-strain curve. These behaviours were mostly independent of wall thickness, except for the 5 mm cell lattice with 0.4 mm wall thickness. The elastic modulus, yield stress and absorbed energy per volume aligned with the apparent density of the lattices, ranging between 1% and 12% of the bulk 3D printed material for both the stiffness and yield stress, and between 1% and 22% for the energy absorbed. Analysis of the fitted means indicated that doubling the cell size had a more significant impact on the measured properties than doubling the wall thickness, while doubling both the cell size and wall thickness exerted a more pronounced influence on the yield stress and strain. Notably, under the conditions of this study, the 3D printed PLA Gyroids behaved similarly to closed cell foams, despite their interconnected channels. Their compressive mechanical properties comparable to those of rigid polyurethane foams with closed cells.

Multiaxial yield behavior of 2D re-entrant auxetic cellular materials

A series of re-entrant honeycombs (RH) with different off-axis angles and perturbation parameters are constructed and utilized to numerically explore the multiaxial yield behavior for 2D auxetic cellular materials. The off-axis angle significantly affects the anisotropic properties and Poisson's ratio of RH. The effects of microstructural irregularity on the multiaxial yield surfaces are also evaluated for all of the topologies. Simulation results under principal stress space, mean stress-effective stress space and normal stress-shear stress space reveal that the unique microstructure of auxetic cellular materials makes its mechanical properties significantly different from conventional cellular materials with positive Poisson's ratio. Furthermore, a pressure-dependent anisotropic phenomenological yield criterion is proposed for 2D auxetic cellular materials, which can effectively capture the multiaxial yield behavior of RH with different topologies in principal stress space. The present conclusions provide fresh insights into the microstructural design of auxetic cellular materials and pave the way for their future engineering applications.

Shape-Versatile Fixed Cellular Materials for Multiple Target Immunomodulation.

Therapeutic cells are usually administered as living agents, despite the risks of undesired cell migration and acquisition of unpredictable phenotypes. Additionally, most cell-based therapies rely on the administration of single cells, often associated with rapid in vivo clearance. 3D cellular materials may be useful to prolong the effect of cellular therapies and offer the possibility of creating structural volumetric constructs. Here, the manufacturing of shape-versatile fixed cell-based materials with immunomodulatory properties is reported. Living cell aggregates with different shapes (spheres and centimeter-long fibers) are fixed using a method compatible with maintenance of structural integrity, robustness, and flexibility of 3D constructs.The biological properties of living cells can be modulated before fixation, renderingan in vitroanti-inflammatory effect toward human macrophages, in line with a decreased activation of the nuclear factor kappa B (NF-κB) pathway that preponderantly correlated with the surface area of the materials. These findings are further corroborated in vivo in mouse skin wounds. Contact with fixed materials also reduces the proliferation ofactivated primary T lymphocytes, while promotingregulatory populations. The fixation of cellular constructs is proposed as a versatile phenotypic stabilization method that can be easily implemented to prepare immunomodulatory materials with therapeutic potential.

In-plane and out-of-plane compressive properties of regular and graded cellular cores of sandwich panels fabricated by additive manufacturing

Cellular materials with a gradient of properties become appealing as cores of the sandwich panels due to the possibility of improving strength and absorbed energy in lightweight components. 2D cellular structures designated by honeycombs have an anisotropic behaviour when loaded under in- and out-plane. Thus, when proposing new designs, it is essential to analyse how the in-plane arrangement with a gradient in cell wall thickness affects in-plane and out-of-plane mechanical properties. This work aims to study graded cellular structures in comparison with regular hexagonal honeycombs. Structures were manufactured by laser powder bed fusion using an aluminium alloy. Regular arrangements were formed with cells with the same thickness, while graded structures possessed a radial gradient of cell thickness. Three types of innovative gradients, where cell length varies radially along concentric layers, were analysed. The compressive properties of regular and graded structures were evaluated when loaded both under in-plane and out-of-plane conditions. Compression behaviour was assessed, both experimentally and by numerical modelling. Even though there is a mismatch between numerical and experimental results, they exhibit the same trends. All graded samples showed an increased mechanical performance when loaded under out-of-plane conditions in comparison with the results from tests under in-plane loading with values, for example, of stiffness four hundred times larger, absorbed energy around thirty times higher and with yield stress four times larger. The results showed that the graded samples attain higher values of strength, stiffness and absorbed energy in comparison with regular hexagonal honeycombs, for the same relative density.

Aircraft Wing Morphing Using Auxetic Structures

Cellular materials exhibit two key properties: structures and mechanisms. This allows for the design of structures using cellular materials while effectively controlling both stiffness and flexibility, based on the connectivity of the struts. This study aims to explore the in-plane flexible properties of cellular materials dominated by bending under macroscopic deformation. Additionally, it seeks to establish a method for designing a passive morphing airfoil with flexible cellular cores. The investigation focuses on airfoils featuring re-entrant and S-shaped cellular cores, analyzing their behavior under static loads by examining the deformation of the cellular cores subjected to aerostatic loads. In the context of the airfoil's deformation with flexible cellular cores under aerostatic loading, shear emerges as the predominant deformation mode for the cores of the airfoil. Wings of conventional aircraft are optimized for only a few conditions, not for the entire flight envelope. Therefore, it is necessary to develop the morphing airfoil with smart structures for the next generation of excellent aircraft. In this project, this was made possible using, re-entrant and S-shaped auxetic structures as a member of the meta- material family, with negative Poisson's ratio to enable an effortless passive morphing mechanism as it has high flexibility along in-plane direction (chord-wise). The 3D CAD Models of Re-entrant and S-shaped auxetic airframes were designed and analyzed. Initially, Static Structural analysis is performed on both airframes to observe the structure’s behavior, and design modification and optimization are performed in different iterations. With a reduction in maximum equivalent stress by 20%, the Re-entrant airframe exhibits lower stress and hence more flexibility. The wings were modeled with a span of 1m using auxetic airframes, air pressure was generated using CFD analysis with MACH 0.45. Finally, the fluid-structure interaction was done by importing the air pressure and performing static structural analysis for the structural performance of wings using auxetic airframes. It was found that Re-entrant auxetic wing showed an increase of 9.99% in load carrying capacity, accompanied by a decrease of 389 grams of weight when compared to S-shaped auxetic wing. Considering the deformation of the airframe with flexible cellular cores under a load, the re-entrant honeycomb core shows the highest flexibility in shear and causes lower stress than the S-auxetic cores. This implies that the re-entrant honeycomb core has the potential for passive morphing.

Modeling Density Waves and Circulations in Vertical Cross-Section in Adhesive Contacts

This work continues the study of the process of friction between a steel spherical indenter and a soft elastic elastomer previously published in our paper. It is done in the context of our previous experimental results obtained on systems with strongly pronounced adhesive interaction between the surfaces of contacting bodies during the process of friction between a steel spherical indenter and a soft elastic elastomer. In the present paper, we concentrate on the theoretical study of the processes developing in a vertical cross-section of the system. For continuity, here the case of indenter motion at a low speed at different indentation depths is considered as before. The analysis of the evolution of normal and tangential contact forces, mean normal pressure, tangential stresses, as well as the size of the contact area is performed. Despite its relative simplicity, a numerical two-dimensional (2D = 1 + 1) model, which is used here, satisfactorily reproduces experimentally observed effects. Furthermore, it allows direct visualization of the motion in the vertical cross-section of the system, which is currently invisible experimentally. Partially, it recalls two-dimensional (2D = 1 + 1) models recently proposed to describe the “turbulent” shear flow of solids under torsion and in cellular materials. The observations extracted from the model help us to understand better the adhesive processes that underlie the experimental results.

3D-printing of architected calcium silicate binders with enhanced and in-situ carbonation

ABSTRACT This paper investigates the use of architected cellular and solid designs of materials via additive manufacturing and in-situ CO2 circulation to augment the carbonation and mechanical properties of a calcium silicate-based cement (CSC) binder. A wollastonite-based binder was formulated for extrusion-based 3D-printing. Solid and cellular lamellar architectures were designed to probe the role of layered interfaces and higher surface area on the degree of carbonation (DOC), respectively. Two carbonation exposure scenarios, with and without in-situ carbonation were employed. The DOC, microstructural phases, and flexural strength were characterised using TGA, modified over-flow image analysis technique, and three-point-bending, respectively. By exploiting 3D-printing and harnessing the higher surface area of cellular architecture, the material obtained a significantly higher DOC (by 8.9-folds) and flexural strength (by 5.7-folds) compared to reference cast. In-situ carbonation of cellular architected materials can additionally improve early-stage deformation, DOC (by 12.9-folds) and flexural strength (by 16.5-folds), compared to cast.

Lightweight Potential of Anisotropic Plate Lattice Metamaterials

Additive manufacturing enables the production of lattice structures, which have been proven to be a superior class of lightweight mechanical metamaterials whose specific stiffness can reach the theoretical limit of the upper Hashin–Shtrikman bound for isotropic cellular materials. To achieve isotropy, complex structures are required, which can be challenging in powder bed additive manufacturing, especially with regard to subsequent powder removal. The present study focuses on the Finite Element Method simulation of 2,5D anisotropic plate lattice metamaterials and the investigation of their lightweight potential. The intentional use of anisotropic structures allows the production of a cell architecture that is easily manufacturable via Laser Powder Bed Fusion (LPBF) while also enabling straightforward optimization for specific load cases. The work demonstrates that the considered anisotropic plate lattices exhibit high weight-specific stiffnesses, superior to those of honeycomb structures, and, simultaneously, a good de-powdering capability. A significant increase in stiffness and the associated surpassing of the upper Hashin–Shtrikman bound due to anisotropy is achievable by optimizing wall thicknesses depending on specific load cases. A stability analysis reveals that, in all lattice structures, plastic deformation is initiated before linear buckling occurs. An analysis of stress concentrations indicates that the introduction of radii at the plate intersections reduces stress peaks and simultaneously increases the weight-specific stiffnesses and thus the lightweight potential. Exemplary samples illustrate the feasibility of manufacturing the analyzed metamaterials within the LPBF process.

Crystal-Inspired Cellular Metamaterials and Triply Periodic Minimal Surfaces.

Triply periodic minimal surfaces (TPMSs) are found in many natural objects including butterfly wings, sea urchins, and biological membranes. They simultaneously have zero mean curvature at every point and a crystallographic group symmetry. A metamaterial can be created from such periodic surfaces or used as a reinforcement of a composite material. While a TPMS as a mathematical object has been known since 1865, only novel additive manufacturing (AM) technology made it possible to fabricate cellular materials with complex TPMS shapes. Cellular TPMS-based metamaterials have remarkable properties related to wetting/liquid penetration, shock absorption, and the absence of stress concentrators. Recent studies showed that TPMSs are also found in natural crystals when electron surfaces are considered. Artificial crystal-inspired metamaterials mimic such crystals including zeolites and schwarzites. These metamaterials are used for shock, acoustic waves, and vibration absorption, and as structural materials, heat exchangers, and for other applications. The choice of the crystalline cell of a material, as well as its microstructure, plays a decisive role in its properties. The new area of crystal-inspired materials has many common features with traditional biomimetics with models being borrowed from nature and adjusted for engineering applications.

Modeling non-uniform aluminum foams as sacrificial layers for blast mitigation of protected structures — A theoretical approach

Aluminum Foams (AFs) are cellular materials that exhibit energy absorption capabilities, making them desirable to use as sacrificial protective cladding applied on structural members. Thereby, the structural resistance to blast loads is increased. During the foam compaction, inner and local buckling of the material walls occur. The described phenomenon reduces the peak overpressure of the blast load and increases its positive duration while maintaining the impulse and transmitting the plateau stress of the foam to the Protected Structure (PS). The plateau stress is commonly significantly lower than the peak overpressure of the blast load. Available analysis approaches typically neglect the coupling between AF and PS and mostly consider uniform-density foams. Moreover, the efficiency of adding AF has been commonly evaluated by comparing the structural response with and without AF. However, such a comparison may not be adequate for studying energy absorption due to the role that the added mass affects the behavior of the structural system due to inertia forces. In this study, using the shock front theory, a numerical solution to a non-uniform density foam as protective cladding is developed, considering both the foam densification and the PS response. A parametric study is performed using this approach to investigate the efficiency of non-uniform density foam compared to a uniform density foam. Calculation and discussion of the efficiency of uniform and non-uniform foams are presented using a more adequate proposed approach, mainly concluding that under loads considered to be impulsive, the non-uniform AF with certain specimens considerably reduce the Peak Displacement (PD) of the PS significantly more than uniform AF.

Design, Manufacturing, and Analysis of Periodic Three-Dimensional Cellular Materials for Energy Absorption Applications: A Critical Review.

Cellular materials offer industries the ability to close gaps in the material selection design space with properties not otherwise achievable by bulk, monolithic counterparts. Their superior specific strength, stiffness, and energy absorption, as well as their multi-functionality, makes them desirable for a wide range of applications. The objective of this paper is to compile and present a review of the open literature focusing on the energy absorption of periodic three-dimensional cellular materials. The review begins with the methodical cataloging of qualitative and quantitative elements from 100 papers in the available literature and then provides readers with a thorough overview of the state of this research field, discussing areas such as parent material(s), manufacturing methods, cell topologies, cross-section shapes for truss topologies, analysis methods, loading types, and test strain rates. Based on these collected data, areas of great and limited research are identified and future avenues of interest are suggested for the continued maturation and growth of this field, such as the development of a consistent naming and classification system for topologies; the creation of test standards considering additive manufacturing processes; further investigation of non-uniform and non-cylindrical struts on the performance of truss lattices; and further investigation into the performance of lattice materials under the impact of non-flat surfaces and projectiles. Finally, the numerical energy absorption (by mass and by volume) data of 76 papers are presented across multiple property selection charts, highlighting various materials, manufacturing methods, and topology groups. While there are noticeable differences at certain densities, the graphs show that the categorical differences within those groups have large overlap in terms of energy absorption performance and can be referenced to identify areas for further investigation and to help in the preliminary design process by researchers and industry professionals alike.

Impact behavior of periodic, stochastic, and anisotropic minimal surface-lattice sandwich structures

Recent advancements in 3D printing technologies have made it possible to fabricate intricate lattice architectures with high precision. These lattices can now be utilized to design lightweight sandwich structures that serve multiple functions. To enhance the impact loading performance of these structures, it is crucial to understand how the lattice's topological properties, particularly those with minimal surface attributes like periodic or stochastic Primitive and Gyroid triply periodic minimal surfaces (TPMS) and spinodal-like stochastic cellular materials, associate with the mechanical properties of sandwich structures while keeping the skin thickness fixed. Thus, this paper explores the low-velocity impact behavior of various sheet/shell-based minimal surface-latticed cores of sandwich structures with woven composite skins. The elasto-plastic-damage numerical simulations consider lattice core periodicity, randomness, and anisotropy while keeping the relative density constant. Core lattice randomness and anisotropy are designed using the Gaussian Random Field (GRF) method for spinodal-based stochastic cellular materials and stochastic TPMS. The simulation results showed that the periodic Primitive-lattice core exhibits high out-of-plane shearing strength, enabling the sandwich structure to demonstrate the highest perforation limit. GRF spinodal-based core achieved the highest peak load due to its anisotropic mechanical properties. However, the post-yielding bending of the lattice sheet limited its ability to resist perforation, and absorb and dissipated energy. Interestingly, the stochastic Gyroid TPMS topology, with its inherent densely-distributed microstructure, showed high sensitivity to loading rate, resulting in enhanced energy absorption and dissipation of the sandwich structure. These findings offer valuable insights for optimizing multifunctional sandwich structures with superior impact performance and their design for additive manufacturing.

Development of a low-cost flutter test bed with an EPS foam model for preliminary wing design

This paper discusses a novel, low-cost approach for the design and testing of a flutter test article made out of expanded polystyrene (EPS) foam. The low mass of this test article makes it especially suitable for serving as a test bed for similar low structure-to-fluid mass ratio wing configurations, though it could just as easily be used as the first step in the flutter testing of any structure with complex shape and mechanical properties. The material properties of EPS foam were tested using two different approaches: a 3-point bending test based on ASTM Standards for cellular materials and a new finite element model updating approach that used experimental data collected from simple ground vibration tests (GVT). It was found that the second approach provided material properties that were the most representative of the behavior of the specimen under flutter loads. That information was then used in a computational aeroelastic flutter model of the EPS foam wing. Wind tunnel flutter tests were performed for the EPS foam model. The computational frequency domain decomposition (CFDD) method was used to identify modal parameters and the damping trend extrapolating method was used to predict the critical flutter speed from pre-flutter experimental data. The flutter results from the aeroelastic model were in good agreement with the test data.

Keep it Simple: Ceramic Kelvin Cells via Liquid Crystal Display‐Stereolithography Printing

Additive manufacturing is the state‐of‐the‐art method for producing complex ceramic parts. For cellular materials, the freedom of design is particularly advantageous, as pore networks and shapes can be tailored. Herein, the direct printing of complex parts with high porosity using the cost‐effective manufacturing method of Liquid Crystal Display‐based stereolithography on low‐cost printers is determined. It is investigated how the architecture of the alumina Kelvin cells topology, their fabrication process, the printing parameters, and the microstructure affect the accuracy and mechanical properties of the printed samples. A notable reduction to a strut thickness of Kelvin cells down to 0.20 mm is achieved corresponding to a reduction of 1.5 compared with the state‐of‐the‐art literature (min. 0.35 mm). Ultrahigh porosities between 89.5% and 97.2% and a maximum compressive strength of 1.84 ± 0.17 MPa are reached due to the dense struts of the structure. Low‐cost and simple vat ceramic photopolymerization with high accuracy printing proves to be a promising candidate for the rapid and cost‐effective fabrication of highly porous and complex ceramic structures.

Tailorable Energy Absorbing Cellular Materials via Sintering of Dry Powder Printed Hollow Glass Microspheres

This article examines amorphous glass-based foams as lightweight core materials for crash-resistant structures that offer tailorable energy absorption capabilities. Hollow glass microspheres (HGMs) of different densities are layered using dry powder print- ing (DPP), an additive manufacturing process, and subsequently sintered to consolidate these microspheres into a cellular foam structure. The tuning of energy absorption is achieved in these foams by layering hollow microspheres with different densities and different thickness ratios of the layers. The mechanical response to quasi-static uniax- ial compression of the bilayer foams is also investigated. Bilayer samples a distinctive two-step stress-strain profile that includes first and second plateau stress, as opposed to a single constant density which does not. The strain at which the second plateau occurs can be tuned by adjusting the thickness ratio of the two layers. The resulting tailorable stress-strain profile demonstrates tailorable energy absorption. Tailorability is found to be more significant if the density values of each layer differ greatly. For comparison, bilayer samples are fabricated using epoxy at the interface instead of the co-sintering process. Epoxy-bonded samples show a different mechanical response from the co-sintered sample with a different stress-strain profile. Designing the bilayer foams enables tailoring of the stress-strain profile, so that energy-absorption requirements can be met for a specific impact condition. The implementation of these materials for energy absorption, crashworthiness, and buoyancy applications will be discussed.

Porous Melt Blown Poly(butylene terephthalate) Fibers with High Ductility and High-Temperature Structural Stability.

In this study, porous poly(butylene terephthalate) (PBT) fibers were produced by melt blowing cocontinuous blends of PBT and polystyrene (PS) and selectively extracting the interconnected PS domains. Small amounts of hydroxyl terminated PS additives that can undergo transesterification with the ester units in PBT were added to stabilize the cocontinuous structure during melt processing. The resulting fibers are highly ductile and display fine porous structural features, which persist at temperatures over 150 °C. Single fiber tensile testing and electron microscopy are presented to demonstrate the role of rapid quenching and drawing of the melt blowing process in defining the fiber properties. The templated highly aligned pore structure, which is not easily produced in solvent-based fiber spinning methods, leads to remarkable mechanical properties of the porous fibers and overcomes the notoriously poor tensile properties common to other cellular materials like foams.

An analytical representation of the 2d generalized balanced power diagram

Tessellations are an important tool to model the microstructure of cellular and polycrystalline materials. Classical tessellation models include the Voronoi diagram and the Laguerre tessellation whose cells are polyhedra. Due to the convexity of their cells, those models may be too restrictive to describe data that includes possibly anisotropic grains with curved boundaries. Several generalizations exist. The cells of the generalized balanced power diagram are induced by elliptic distances leading to more diverse structures. So far, methods for computing the generalized balanced power diagram are restricted to discretized versions in the form of label images. In this work, we derive an analytic representation of the vertices and edges of the generalized balanced power diagram in 2d. Based on that, we propose a novel algorithm to compute the whole diagram.

Low-cycle compression-compression fatigue behavior of MEX-printed PLA parts

Due to cyclic loads, additively manufactured (AM) parts can collapse at lower stress values than the strength corresponding to static loads. To date, there is limited research on the fatigue life of AM polymers. The present work investigates the fatigue behavior of material extrusion (MEX) printed Polylactic acid (PLA) parts. In this regard, the low-cycle fatigue (LCF) domain was studied and a compression-compression fatigue test setup was adopted. Initially, before the experimental tests, the MEX-printed samples were subjected to physical assessments. The printed fatigue samples presented a high accuracy with dimensional relative errors below 0.04%, while 6.66% was noted as their mass relative error. Subsequently, quasi-static and cyclic tests were performed in order to determine the mechanical behavior of the AM parts, with special focus on the low-cycle domain of the S-N (or Wöhler) curve. The quasi-static compression behavior of the PLA samples is typical of cellular materials, the samples highlighting a shear band as a failure mechanism. Five load levels were used to plot the low-cycle domain of the S-N (or Wöhler) curve with its 95% level confidence bands. The tests were performed in force-controlled mode with the stress asymmetry ratio R = 0.1 and at the test frequency of f = 10 Hz. An exponential relationship was also found between the strain at break and the number of cycles until failure. The failure of the samples in fatigue load occurred suddenly.

Efficient design of sandwich panels with cellular truss cores and large phononic band gaps using surrogate modeling and global optimization

Recent advancements in additive manufacturing technologies and topology optimization techniques have catalyzed a transformative shift in the design of architected materials, enabling increasingly complex and customized configurations. This study delves into the realm of engineered cellular materials, spotlighting their capacity to modulate the propagation of mechanical waves through the strategic creation of phononic band gaps. Focusing on the design of sandwich panels with cellular truss cores, we aim to harness these band gaps to achieve pronounced wave suppression within specific frequency ranges. Our methodology combines surrogate modeling with a comprehensive global optimization strategy, employing three machine learning algorithms—k-Nearest Neighbors (kNN), Random Forest Regression (RFR), and Artificial Neural Networks (ANN)—to construct predictive models from parameterized finite element (FE) analyses. These models, once trained, are integrated with Particle Swarm Optimization (PSO) to refine the panel designs. This approach not only facilitates the discovery of optimal truss core configurations for targeted phononic band gaps but also showcases a marked increase in computational efficiency over traditional optimization methods, particularly in the context of designing for diverse target frequencies.

Dynamic characteristics of density-graded cellular materials for impact mitigation

Due to their exceptional impact resistance capabilities, density-graded cellular materials have immense potential in applications where crashworthiness requirements are of prime importance. Under impact loading, the deformation in these materials is characterized by compaction front propagation. Previous studies have utilized numerical techniques to solve the equations governing compaction shock propagation for cellular materials with density gradation. In this study, analytical solutions are formulated using compaction front position as the independent variable. The expressions for the velocity of the impinging rigid mass, energy absorption, incident stress, and transmitted stress are determined. The analytical solutions are shown to be in excellent agreement with the cell-based finite element solutions. The effect of density gradient on energy absorption and stresses is studied. The impact resistance factor is employed to assess different density-graded cellular materials for their effectiveness in impact mitigation. This study demonstrates that density-graded cellular materials can offer superior impact protection to objects at both the incident and transmitted ends. Lower density toward the incident end enhances impact resistance to objects located there, and likewise, lower density at the transmitted end offers more impact resistance to objects at that end.