Cellular Materials Research Articles

The role of unit cell topology in modulating the compaction response of additively manufactured cellular materials using simulations and validation experiments

Abstract Additive manufacturing has enabled a transformational ability to create cellular structures (or foams) with tailored topology. Compared to their monolithic polymer counterparts, cellular structures are potentially suitable for systems requiring materials with high specific energy-absorbing capability to provide enhanced damping. In this work, we demonstrate the utility of controlling unit-cell topology with the intent of obtaining a desired stress-strain response and energy density. Using mesoscale simulations that resolve the unit-cell sub-structures, we validate the role of unit-cell topology in selectively activating a buckling mode and thereby modulating the characteristic stress-strain response. Simulations incorporate a linear viscoelastic constitutive model and a hyperelastic model for simulating large deformation of the polymer under both tension and compression. Simulated results for nine different cellular structures are compared with experimental data to gain insights into three different modes of buckling and the corresponding stress-strain response.

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.

Characterization of flexural fatigue behaviour of additively manufactured (PBF–LB) gyroid structures

AbstractAdditive manufacturing (AM) holds remarkable potential for producing cellular materials with intricate structures and tailored mechanical properties. The study investigates the flexural fatigue behaviour of additively manufactured triply periodic minimal surface (TPMS) gyroid structures using laser powder bed fusion (PBF–LB) technique. The fatigue properties, especially the bending fatigue properties, of additively manufactured cellular structures are not well understood to date. The research aims to enhance understanding of bending fatigue in complex cellular geometries and assess the suitability of rotating bending tests. The PBF–LB process parameters were modified to study their impact on the specimen’s fatigue properties. The modified parameters led to increased surface roughness but significantly improved fatigue behaviour. This enhancement is attributed to a reduction in build defects, namely pores and finer grain size in thin-walled structures. The study also includes analysis of microstructure, hardness, surface roughness, and porosity of the specimens. The results indicate that optimizing process parameters for thin walled cellular structures can lead to substantial improvements in fatigue strength, at the expense of increased surface roughness. This finding offers practical insights for applications in which a rough surface finish may not be critical or even intentionally desired by the application. The research contributes to the understanding of additive manufacturing, cellular structures, and material testing, with potential implications for materials science and engineering applications.

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 wave 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 capacity, 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.

Development of decellularization protocols for female cat reproductive organs

Decellularization is an innovative method to create natural scaffolds by removing all cellular materials while preserving the composition and three-dimensional ultrastructure of the extracellular matrix (ECM). The obtention of decellularized reproductive organs in cats might facilitate the development of assisted reproductive techniques not only in this species but also in other felids. The aim was to compare the efficiency of three decellularization protocols on reproductive organs (ovary, oviduct, and uterine horn) in domestic cats. The decellularization protocol involved 0.1% sodium dodecyl sulfate and 1%Triton X-100. Protocol 1 (P1) entailed 2-cycles of decellularization using these detergents. Protocol 2 (P2) was like P1 but included 3-cycles. Protocol 3 (P3) was similar to P2, with the addition of deoxyribonuclease incubation. Reproductive organs from nine cats were separated into two sides. One side served as the control (non-decellularized organ) while the contralateral side was the treated group (decellularized organ). The treated organs were subdivided into 3 groups (n = 3 per group) for each protocol. Both control and treated samples were individually analyzed for DNA content, histology (nuclear and ECM (collagen, elastin, and glycosaminoglycans (GAGs)) density), and evaluating ultrastructure by electron microscopy. The results of the study showed that P3 was the only protocol that displayed no nucleus residue and significantly reduced DNA content in decellularized samples (in all the studied organs) compared to the control (P < 0.05). The ECM content in the ovaries remained similar across all protocols compared with controls (P > 0.05). However, elastic fibers and GAGs decreased in decellularized oviducts (P < 0.05), while collagen levels remained unchanged (P > 0.05). Regarding the uterus, the ECM content decreased in decellularized uterine horns from P3 (P < 0.05). Electron microscopy revealed that the microarchitecture of the decellularized samples was maintained compared to controls. The decellularized tissues, upon being washed for 24 h, showed cytocompatibility following co-incubation with sperm. In conclusion, when comparing different decellularization methods, P3 proved to be the most efficient in removing nuclear material from reproductive organs compared to P1 and P2. P3 demonstrated its success in decellularizing ovarian samples by significantly decreasing DNA content while maintaining ECM components and tissue microarchitecture. However, P3 was less effective in maintaining ECM contents in decellularized oviducts and uterine horns.

Autophagosome biogenesis and organelle homeostasis in plant cells.

Autophagy is one of the major highly inducible degradation processes in response to plant developmental and environmental signals. In response to different stimuli, cellular materials, including proteins and organelles, can be sequestered into a double membrane autophagosome structure either selectively or non-selectively. The formation of an autophagosome as well as its delivery into the vacuole involves complex and dynamic membrane processes. The identification and characterization of the conserved autophagy-related (ATG) proteins and their related regulators have greatly advanced our understanding of the molecular mechanism underlying autophagosome biogenesis and function in plant cells. Autophagosome biogenesis is tightly regulated by the coordination of multiple ATG and non-ATG proteins, and selective cargo recruitment. This review updates our current knowledge of autophagosome biogenesis, with special emphasis on the core molecular machinery that drives autophagosome formation, and autophagosome-organelle interactions under abiotic stress conditions.

Compression properties of cellular iron lattice structures used to mimic bone characteristics

Recently, cellular materials made by the repetition of unit cells, that is, iron lattices have become appealing to mimic the structure of bone. The aim of the study is to choose the most adequate lattice structures, which have the compressive mechanical properties closer to the ones of bone, in the perspective of their use as temporary implants. Five types of unit cells were selected, such as, cubic (C), truncated octahedron (TO), truncated cubic (TC), rhombicuboctahedron (RCO), and rhombitrucated cuboctahedron (RTCO). The mechanical properties were assessed by numerical simulations with a finite-element analysis. The size effect was studied with the comparison of results among samples with different numbers of unit cells. Simulations covered a wide range of relative densities. Graded dense-in and dense-out configurations were constructed with lattices of types RTCO and TO, being the unit cells, themselves graded. Lattice structures RTCO and TO were found to be stable at every relative density studied, while C, TC and RCO lattices are unstable at low densities. The evaluation of size effects was not conclusive, which could be biased by other factors. The Young's modulus of RTCO and TO lattices enable to reproduce the properties of both trabecular and cortical bone, with an appropriate choice of the relative density. To mimic trabecular bone, only RTCO and TO structures with low relative densities, can be used, while arrangements of C, TC and RCO cells can only replicate the properties of cortical bone. Graded cells may have the same properties as non-graded with lower density.

Three-dimensional elastic properties of open-cell porous structures: Analytic and finite element modelling

The current paper introduces a three-dimensional micromechanical model of open-cell cellular solid materials and presents the homogenization of the model to an orthotropic continuum. An orthotropic microstructural beam model was created and tested under pure stretch and pure angular distortion to identify the dominant deformation modes by mapping the contributions of normal-, bending- and torsional stiffness to the total strain energy. In the case of unidirectional tension, the deformation mode was dependent primarily on the proportion of normal- and bending stiffnesses, except for the cases with similarly small bending- and torsional stiffness values, where the contribution of torsion was significant. In the case of the pure angular distortion, the key deformation mode was defined by the ratio of bending- and torsional stiffness values, except for the case of large normal- and torsional stiffness values, which resulted in normal-deformation-driven behaviour.The homogenization of the micromodel was conducted by creating an equivalent spring model, by means of which the equivalent elastic modulus values for the main directions of orthotropy have been derived as functions of the geometric and elastic properties of the beams. With the aid of the equivalent spring models, the relative density dependence of Young’s modulus and shear modulus have been examined. The typical second-degree relationship was found to become inaccurate in the range of lower porosity. In the case of increasing relative density values, the exponent of the elastic modulus function decreased while the exponent of the shear modulus increased.

Modelling and characterization of novel honeycomb structures with mass gradient produced by additive manufacturing

The dissemination of additive manufacturing methods has facilitated the design and production of complex structures which have a high strength-to-weight ratio. Cellular materials such as honeycombs have low-weight and high capacity to absorb energy which makes them desirable for the aerospace and automotive industries. The present work covers the study and comparison of metal-based regular honeycombs and functionally graded honeycombs. The latter encompass radial and linear/longitudinal gradients. Three repeating unit cells were studied: regular hexagons, Plateau and lotus. The structures were produced in aluminium using the laser powder bed fusion technique. Selected samples were submitted to a stress-relieving heat treatment. Numerical and experimental methods were used to assess the in-plane compressive properties. Finite element analysis was used to obtain the simulated force–displacement curves of each structure, allowing for the calculation of specific stiffness, absorbed energy and yield strength. The experimental method consisted of the compression of three specimens of three types of regular structures with and without stress-relieving heat treatment. The heat treatment reduced the yield strength and stiffness whilst increasing the ductility of the samples. The mechanical behaviour of the structures was found to depend upon a combined effect of the type of gradient, relative density, and unit cell structure. The results showed that an increase in the relative density would enhance the specific mechanical properties. The lotus configuration displayed the highest specific mechanical properties, as its geometry reduces the stress concentrations. The numerical results showed a reasonable match with the experimental results.

DLP printed 3D gyroid structure: Mechanical response at meso and macro scale

Rapid prototyping (RP) technology enables the fabrication of complex geometries, making lattice structures increasingly popular. Lattice structures, known as cellular materials, have garnered significant attention over the past two decades due to their ability to optimise mass distribution in components. These structures excel in mechanical properties, catering to energy absorption (bending-dominated structures) and structural performance (stretch-dominated structures). In this paper, we investigate the behaviour of stretch-dominated lattice structures using periodic surface models, specifically focusing on sheet-based Gyroid cells, to allow for a more efficient macroscale modelling. We study cells and scaffolds of different sizes, considering various triply periodic minimal surface thicknesses and relative densities ranging from approximately 0.2 to 0.65. We explore load applications in directions different from the unit cell's principal axes and analyse the strain rate effect on both bulk and cellular material. The lattice structures are manufactured using epoxy resin and digital light processing (DLP) technology. In the range of relative density investigated, both in quasi-static and dynamic conditions, a linear trend is observed for Young's modulus and compression yield strength. To extend the quasi-static results to the dynamic regime, we employ a more generalized normalization technique. This approach divides Young's modulus and compression yield strength by the behaviour of the base material at a specific strain rate, facilitating the correlation of mechanical properties across the two loading regimes. Based on experimental findings, we implemented and calibrated a bi-linear material model for describing, in macroscale, triply periodic minimal surface (TPMS) Gyroid structures. The model coefficients are parameterized with respect to relative density. In addition, the presented material law was compared with that proposed by Gibson-Ashby. Furthermore, we evaluated the anisotropy of both the base material and the unit cell. The first one is done by testing the 3D printed samples in directions different from the printing one, the latter by using the Zener factor. The anisotropy evaluation confirmed the isotropic behaviour of the unit cell within the range of relative density and test conditions investigated. Finally, we perform linear elastic 3D macroscopic and mesoscopic model simulations for combined shear-compression tests using the implemented bi-linear material model and the anisotropic stiffness matrix (obtained through the homogeneous formulation) for the macroscale, and the base material for the mesoscopic one. The results demonstrate the suitability of the proposed equivalent material model for studying the TPMS Gyroid structure in the elastic regime, both in quasi-static and dynamic states. This allows for an efficient FE modelling process of complex lattice structures.

Contact mechanics of open-cell foams with macroscopic asperities

Poroelastic materials mounted against rigid surfaces often result in partial contact between the two, affecting their mechanical interaction. The surface roughness of cellular materials introduces complexity in predicting their behavior due to the interface with partial contact. This interface exhibits a stiffness distinct from the bulk material, which is driven by the surface asperities and the preload. This study conducts compression experiments on an open-cell poroelastic melamine foam, and compares them to finite elements simulations and analytic predictions. The material’s intrinsic stress–strain nonlinearity is accounted for, and an original hyperelastic aging model is proposed to achieve accurate predictions of its compression stiffness across multiple time scales. Predicting the compression stiffness of a macroscopic pyramidal asperity demonstrates a good agreement with the simple analytic solution for an elastic pyramidal geometry. Using a Greenwood–Williamson-like model based on the distribution of asperities of different heights, we propose a method to predict the contact stiffness of a rough surface. Our findings have important implications for understanding and optimizing efficient vibration barriers, resulting from the simple stacking of layers and screens of raw poroelastic materials, a configuration widely adopted in the transportation and civil engineering industries.

Comparison of batch, fed-batch and continuous operation modes for scalable polyhydroxyalkanoate (PHA) production and carbon sequestration from phenol

Polyhydroxyalkanoates (PHA) are biodegradable intracellular polymers, and a renewable alternative to conventional plastics. To reduce PHA's cost, this study combined an unconventional carbon source, i.e. a toxic aromatics phenol, with an acclimated consortium, to develop a scalable PHA production process. The resultant process performance was systematically compared across three operational modes: batch, fed-batch, and continuous. Phenol toxicity caused inhibition in the batch mode, reducing the PHA synthesis rate but resulting in a high PHA content in cells (PHA% > 50 %). Fed-batch feeding alleviated such inhibition, facilitating a high PHA titer and yield from the substrate. Interestingly, a higher feeding rate in the fed-batch reactor improved its performance, probably by providing a suitable food-to-microbe ratio for the biomass. Using a continuous mode also reduced phenol toxicity, but resulted in more synthesis of non-PHA cellular materials (NPCM). The difference might have been caused by different metabolic states and the presence of intermediates in the reactors. Comparing all 14 conditions under the three modes, feeding phenol more gradually tended to channel substrate away from PHA to NPCM synthesis. The volumetric productivity generally ranged from 3 to 12 mg L−1 min−1, while the biomass productivity was between 2 and 11 mg g initial CDW−1 min−1. A 3-stage, production-harvest and starvation-production process was then designed to simulate real industrialized manufacturing, where the operational modes had a long-term effect on biomass' productivity. Fed-batch mode performed the best, as it fixed 1/3 of phenol's organic carbon in PHA product, suggesting high potential for future application.

Evidence of nonlinearity tailoring in static and dynamic responses of honeycomb and auxetic hourglass lattice metastructures

Nature’s morphology and optimal energetic solutions remain the key motivation for designing cellular-based lattice structures. Understanding the nonlinear dynamical behaviors that arise from different lattice topologies of such structures in the metastructure framework is crucial for their successful implementation in various novel designs and technologies related to vibration and shape control. This paper presents a study of the static and dynamic response of auxetic and honeycomb lattices with hourglass or dome-shaped metastructures. The potential tailoring of nonlinearity of such responses through various design parameters that play a vital role in shaping the dynamic properties of such structures is discussed here. The impact of cell design parameters on the resulting macroscopic behavior is assessed using both numerical simulations and experimental studies. The transition from softening to hardening nonlinear dynamic responses is reported with cell topologies ranging from the regular honeycomb to auxetic topologies that are widely used as fundamental cells of cellular materials design. The experimental study is based on the time responses measured to verify the numerical predictions. The experimental system consists of different 3D printed hourglass samples based on the auxetic and honeycomb lattices on which dynamic testing using a laser Doppler vibrometer is performed. The design strategies proposed in this paper can be integrated into a wide range of lattice-based materials for noise and vibration control applications and biomedical devices.

Evaluation of a Local Acoustic Resonance Method for Coating Thickness Determination on Stochastic Metal Hybrid Foams

Novel cellular materials promise a combination of high strength and low specific weight for sustainable and energy‐efficient material design. Inhomogeneities of the materials, such as varying coating thickness, are inherent to the production process but require advanced characterization in order to better understand mechanical properties. Herein, global and local acoustic analysis for nondestructive characterization of local coating thickness on an open‐porous hybrid metal foam system is studied. Experiments and numerical simulations are carried out to evaluate vibration behavior stimulated by a low‐energy impact. The novelty of the work is the use of local excitation and analysis of decay times to determine coating thickness gradients. This qualitative measurement can inform and speed up the material development process due to its simplicity, speed, and low cost. Furthermore, it provides a basis for quality control when scaling up the technology of metal hybrid foams for industrial applications.

Compression fatigue of elastomeric foams used in midsoles of running shoes

Due to their excellent specific mechanical properties, closed cell elastomeric foams are the main element in the soles of running shoes to absorb repetitive shocks from strides and to release a maximum of the absorbed energy. However, these cellular materials are gradually damaged. To enhance their mechanical durability by slowing their damage kinetics, it is critical to understand their mechanical behaviour in fatigue. The objective of this work is thus to clarify the link between the microstructure and the fatigue properties of five commercial elastomeric foams used in the midsoles of running shoes. The 3D cellular structures of each foam were finely analysed using X-ray microtomography. Foam samples were then subjected to cyclic compression which were close to running conditions. During cycling, samples exhibited a rapid densification associated with noticeable decreases of (i) the stress levels required to deform them as well as (ii) the cushioning and (iii) the rebound properties. We show that the two midsoles filled with micro-sized mineral fillers present the highest specific mechanical properties during the first compression cycle and during fatigue. However, their damage kinetics and rebound properties could probably be improved by tuning the fillers-matrix compatibility. The lightest foam, being very porous and presenting process-induced tortuous cell walls, is the best cushioning system but exhibits high damage kinetics. The densest foam presents poor specific mechanical properties, but very slow damage kinetics. Its double hierarchical architecture probably prevents the occurrence of micro-cracks in the cell walls.