Hierarchical Cellular Structures Research Articles

3D-printed thermoplastic polyurethane/polyvinylidene fluoride gradient stiffness and hierarchical cellular structures with tailored energy absorption behavior

Currently, designing materials and structures is the main means of improving their energy-absorption properties; however, optimization methods based on structural design can only be applied to specific structures. In this study, two optimization methods of energy-absorbing structures (EASs) are proposed from the material system and manufacturing method for fabricating gradient stiffness and hierarchical cellular structures, respectively. The gradient stiffness structure was prepared using different ratios of thermoplastic polyurethane (TPU)/polyvinylidene fluoride (PVDF) filaments in different locations in the EAS. The gradient stiffness structure exhibited energy-absorption behavior corresponding to the strength of the printed material; this behavior decreased in the order of material strength from low to high, thus achieving controlled yield deformation behavior. Hierarchical honeycomb structures were prepared by combining three-dimensional (3D) printing with supercritical CO2 foaming technology, which facilitated the simultaneous formation of both centimeter and micron-scale cellular structures. When the PVDF content was 30%, the average cellular size of the microcellular structure was only 3 μm, and the prepared hierarchical honeycomb structures exhibited higher energy-absorption efficiencies compared with the general honeycomb structure. The energy absorption per unit mass values in three different compression directions of the hierarchical honeycomb structures were 152.75%, 67.33%, and 56.91% higher, respectively, than that of the TPU honeycomb without foaming. Therefore, the gradient stiffness and hierarchical honeycomb structures prepared from TPU/PVDF blends have various applications in energy absorption, personal protection, and transportation.

Hierarchically Interpenetrated and Reentrant Microcellular Frameworks for Stretchable Lithium Metal Batteries.

With the rapid development of human-friendly wearable devices, energy storage components are required to have skin-like stretchability or free-form to fit closer and more comfortably to the human body. This study introduces a hierarchically interpenetrated reentrant microcellular structure combined with 2D cellular graphene/MXene/carbon nanotubes (CNTs) and 3D cellular melamine foam. This composite structure works as a stretchable framework of lithium metal composite electrodes to provide stretchability for lithium metal electrodes, which are promising as next-generation energy storage systems. The interpenetrated but independent cellular structures successfully obtain stable structural deformability from the nonconductive and deformable melamine foam, while at the same time, high electrical conductivity, lithiophilicity, and mechanical stability of the graphene/CNT/MXene network serve as a lithium deposition support during the electrodeposition of lithium. The reentrant structure is fabricated by radial compressing the hierarchical cellular structures to take advantage of the structural stretchability of the accordion-like reentrant frameworks. The lithium-deposited composite electrodes exhibit much lower overpotential during Li stripping and plating than lithium metal foil anodes and show stable electrochemical performances under 30% of mechanical strain. The reentrant microcellular electrodes offer great potential for advanced designs of lithium metal electrodes for stretchable batteries with high energy density.

Lightweight and large-scale rGO reinforced SiBCN aerogels with hierarchical cellular structures exposed to high-temperature environments

SiBCN ceramic aerogel is an ideal potential candidate for ultra-high temperature thermal insulation due to its unique microscopic pore structure combined with the excellent thermal stability of SiBCN ceramic. Here, reduced graphene oxide (rGO) modified SiBCN aerogels (rGO/SiBCN) were prepared through solvothermal, freeze-casting and pyrolysis, and the dimension of the aerogel is up to Φ130 mm × 28 mm. The density of the rGO/SiBCN aerogel is as low as 0.024 g/cm3 and the microstructural regulation is achieved by controlling the rGO content in the aerogel. The hierarchical cellular structure endows the aerogel with a high specific surface area (148.6 m2/g) and low thermal conductivity (0.057 W m−1 K−1). The 10 mm-thick sample exhibits excellent thermal insulation and ablation resistance, as evidenced by its ability to reduce the temperature from ∼1100 °C to ∼180 °C under the intense heat of a butane flame. Moreover, benefiting from the ultrahigh-temperature stability of SiBCN, the rGO/SiBCN aerogel exhibits good thermal stability up to 1200 °C in argon and short-oxidation resistance at 800 °C in air. Therefore, the rGO/SiBCN aerogel with superior overall performance could expand its practical application in high-temperature thermal insulation under extreme environments.

Mechanical properties of a novel hierarchical cellular structure architectured with minimal surfaces and Voronoi-tessellation

Hierarchical structures are commonly found in nature due to their combination of low density, exceptional specific properties, and multifunctionality. Inspired by this, we proposed a novel hierarchical cellular structure based on triply periodic minimal surface (TPMS) by connecting two topologically identical and parallel sheets with a series of connecting ribs. A conformal design guideline was provided by describing the mathematical principles behind the generation of such hierarchical cellular structures. Then the designed structures with different configurations were fabricated via laser powder bed fusion (LPBF). Finally, the mechanical performance of the hierarchical cellular structures was analyzed by both experiment and numerical simulation. The dynamic compressive behavior was investigated using a Split Hopkinson pressure bar (SPHB) at a strain rate of 650 s−1, and the temperature distribution during tests was monitored using a high-speed infrared camera. As for quasi-static compression tests, it is found that the hierarchical cellular structure had good energy absorption characteristics and relatively low first peak stresses. These results showed that the structure could reduce strain rate hardening effects under dynamic loading, thereby mitigating the increase in first peak stress. The proposed hierarchical cellular structures showed good potential for efficient energy absorption under quasi-static and dynamic compression loadings.

Crushing behavior and energy absorption of the thousands-of-eyes-Bodhi-inspired novel hierarchical cellular structure

Natural hierarchical materials are proved to have excellent mechanical properties and have been widely applied in the design concept of engineering materials. In this study, inspired by the hierarchical structure of the thousands-of-eyes-Bodhi (TEB), a novel biomimetic hierarchical cellular structure is designed and fabricated using 3D printing technology. The crushing resistance capability and deformation mode of TEB-inspired hierarchical cellular structure are investigated by experiments and simulation methods. Meanwhile the deformation processes are recorded by the compression experiments, and the strain field distributions are analyzed by the digital image correlation (DIC) method. Comparing the mechanical behaviors of square tube, second-order and TEB-inspired hierarchical cellular structures, it is found that the structure hierarchy affects the deformation mode, improves the strain field distribution, delays the strain concentration, and enhances the crashworthiness. It is also noted that the TEB-inspired hierarchical cellular structure exhibits different deformation modes and strain field distributions in the transverse and longitudinal directions, and shows better crushing resistance in the longitudinal direction. In addition, compared with other typical natural materials and engineering materials, the TEB-inspired hierarchical cellular structure possesses superior specific energy absorption and specific strength. These findings provide a new perspective for the application of biomimetic engineering materials.

Manufacturing of scaffolds with interconnected internal open porosity and surface roughness.

Manufacturing of three-dimensional scaffolds with multiple levels of porosity are an advantage in tissue regeneration approaches to influence cell behavior. Three-dimensional scaffolds with surface roughness and intra-filament open porosity were successfully fabricated by additive manufacturing combined with chemical foaming and porogen leaching without the need of toxic solvents. The decomposition of sodium citrate, a chemical blowing agent, generated pores within the scaffold filaments, which were interconnected and opened to the external environment by leaching of a water-soluble sacrificial phase, as confirmed by micro-CT and buoyancy measurements. The additional porosity did not result in lower elastic modulus, but in higher strain at maximum load, i.e. scaffold ductility. Human mesenchymal stromal cells cultured for 24 h adhered in greater numbers on these scaffolds when compared to plain additive-manufactured ones, irrespectively of the scaffold pre-treatment method. Additionally, they showed a more spread and random morphology, which is known to influence cell fate. Cells cultured for a longer period exhibited enhanced metabolic activity while secreting higher osteogenic markers after 7 days in culture. STATEMENT OF SIGNIFICANCE: Inspired by the function of hierarchical cellular structures in natural materials, this work elucidates the development of scaffolds with multiscale porosity by combining in-situ foaming and additive manufacturing, and successive porogen leaching. The resulting scaffolds displayed enhanced mechanical toughness and multiscale pore network interconnectivity, combined with early differentiation of adult mesenchymal stromal cells into the osteogenic lineage.

Ultralight, super thermal insulation, and fire-resistant cellular cement fabricated with Janus nanoparticle stabilized ultra-stable aqueous foam

Bubble-templated advanced cellular materials with ultralight and superior thermal insulation properties have shown great potential in energy-saving related applications. However, insufficient bubble stability severely limits the generation of such highly porous structures. Herein, we present an efficient method to produce ultra-stable aqueous foams by combing the amphiphilic Janus nanoparticle (Janus-SiO2) with the surface-active polymer (hydroxypropyl methylcellulose). The life of aqueous foams is dramatically increased from 4 h to over 5 days with 5 wt% Janus-SiO2 concentration. The dense adsorbed layer formed by the efficient adsorption of Janus-SiO2 on the bubble film is the main factor for the outstanding foam stability. Owing to the greatly enhanced foam stability, we successfully produce ultralight cellular cement with hierarchical cellular structures and a density as low as 80 kg/m3. The ultralight cellular cement exhibits superior mechanical strength, robust fire resistance and excellent thermal insulation with a thermal conductivity as low as 0.038 W·m−1·K−1. This work provides a practical approach for fabricating various advanced porous materials that employ bubbles as templates.

Impact analysis of hierarchical honeycomb core sandwich structures

Cellular structures are light weight structures with high specific, impact, flexural strength and stiffness. Hierarchical structures offer higher load-bearing capacity compared to their conventional counter parts. In this study, performance of enhanced hierarchical honeycomb core cellular structures under compression and impact loads is investigated. The hierarchy is proposed by varying the order and the level of the cells. Hierarchical patterns are developed by replacing the vertex cells of regular hexagonal honeycomb with circular cells. The local arrangement of the proposed hierarchical cellular structures is improved to withstand higher loads. The out-of-plane performance of honeycomb structure is enhanced by a hierarchical scheme. As a result, a novel hierarchical second order second level hexagon based hybrid cell has been developed. Furthermore, the influence of sandwiching the cellular structures between face sheets against impact loads is also studied using numerical simulations. In order to transfer the loads efficiently from the top and bottom ends to the mid walls of the unit cell, the structural angle β is introduced as the angle between the normal of the face-sheet and the axis of the unit cell. Such an arrangement is observed to enhance the load distribution in the cellular structures.

Supercritical CO2 utilization for development of graded cellular structures in semicrystalline polymers

Carbon dioxide (CO2) in a supercritical condition is utilized to develop hierarchical cellular structures in injection molding. Polypropylene is used as sample semicrystalline polymer. First, a single-phase CO2-charged melt was produced under pressure. Then, a gradient cell structure was induced onto the polymer melt by pressure reduction and crystal-induced shrinkage. A visualization mold was employed to monitor real-time nucleation of CO2 cells within the mold cavity. Distinctive cell nucleation behaviour was visualized for the first time in which a myriad of ultra-fine cells nucleated rapidly inside the system in an abnormal manner. This type of cell nucleation was different from that occurring due to a pressure drop during foam processing. This mode of cell nucleation was likely driven by the crystallization of the polypropylene chains in the presence of the supercritical CO2. The crystallization behaviour of polypropylene was then investigated within the mold cavity and in the presence of dissolved CO2 by wide-angle X-ray diffraction (WAXD) and differential scanning calorimetry (DSC). The presence of supercritical CO2 affected the size of α and β crystals. Furthermore, γ crystals were detected in the core regions of samples. The formed crystals served as effective nucleating sites which promoted the nucleation of large number of fine cells and produced structurally graded foams. The effects of CO2 content, melt packing, and melt temperature on the cell structure development was studied. It was concluded that these parameters can be regulated to design cellular structures with desired cell size and cell morphologies.

A direct foaming approach for carbon nanotube aerogels with ultra-low thermal conductivity and high mechanical stability.

Thermally insulating materials (TIMs) with ultra-low thermal conductivity, fire-retardancy, and mechanical stability are demanded to improve energy efficiency in many fields, such as petrochemical plants, energy-saving buildings, and aerospace. However, traditional polymer-based TIMs could not meet these demands. Herein, we propose a direct foaming strategy for obtaining carbon nanotube (CNT) aerogels by the gradual expansion of CNT films with H2O2 as a foaming agent at room temperature. The obtained CNT aerogels have hierarchical cellular structures and possess an ultra-low density (4.6 mg cm-3) and thermal conductivity (16.5 mW m-1 K-1) as well as excellent mechanical robustness and fire-resistance. Our results show that such CNT aerogels have promising applications in the field of thermal insulation and present a facile pathway for the design of thermally insulating, fire-retardant materials based on CNTs.

Influence of a novel hierarchical cellular structure on the mechanical behavior: The thousands of eyes bobhi material

The thousands of eyes Bobhis (TEB) is a natural cellular material and has ingeniously evolved hierarchical structures to resist the damage from external environment. In this study, the relationship between cellular structure and mechanical properties of the TEBs is first investigated. SEM studies reveal that the TEB hierarchically exhibit three distinct cellular structures, the filled-cells, novel-closed-cells and open-cells, which is ranging from the macroscopic (>10−3 m) to the microcosmic scale (10−4-10−6 m) respectively. Compression and shear tests indicate that such hierarchical cellular structure has intimate influence on the mechanical properties of TEB. The loads of TEB samples are decomposed through the three hierarchical cellular structures. Microscopically, the multiple micro-cracks are firstly generated from the open-cells, and the novel-closed-cells are deformed and crushed in which the multiple micro shear bands and cell walls interlocking phenomenon can be found in the tests. Macroscopically, the filled-cells are stretched and damaged with the extrusion of filler. The hierarchical cellular structure of TEB possesses excellent mechanical properties, which hinder the catastrophic failure and increase the toughness and strength. The distinct hierarchical cellular structure of TEB provides a new pathway to design bio-inspired engineering materials.

A Novel Bionic Structure Inspired by Luffa Sponge and Its Cushion Properties

The luffa sponge shows excellent cushion properties. This paper presents a bio-inspired structure of the luffa sponge. The geometry of the bionic structure was built based on the fractal theory by Python programming language and prepared by a 3D printer. Then a series of quasi-static compression tests and finite element analysis were carried out to determine the cushion properties. An optimization design was adopted to determine the best design parameter. The results showed that the influence of length ( a ) on specific energy absorption was more important than the degree ( θ ). The best parameter was found to be length less than 4 mm and angle around 11 degrees. The bionic structure of luffa sponge may show a novel perspective on natural cellular material. The findings demonstrate the great potential for designing hierarchical cellular structures and broad application prospects in the field of cushioning and energy absorption.

3D Printing of Ultralight Biomimetic Hierarchical Graphene Materials with Exceptional Stiffness and Resilience.

Biological materials with hierarchical architectures (e.g., a macroscopic hollow structure and a microscopic cellular structure) offer unique inspiration for designing and manufacturing advanced biomimetic materials with outstanding mechanical performance and low density. Most conventional biomimetic materials only benefit from bioinspired architecture at a single length scale (e.g., microscopic material structure), which largely limits the mechanical performance of the resulting materials. There exists great potential to maxime the mechanical performance of biomimetic materials by leveraging a bioinspired hierarchical structure. An ink-based three-dimensional (3D) printing strategy to manufacture an ultralight biomimetic hierarchical graphene material (BHGMs) with exceptionally high stiffness and resilience is demonstrated. By simultaneously engineering 3D-printed macroscopic hollow structures and constructing an ice-crystal-induced cellular microstructure, BHGMs can achieve ultrahigh elasticity and stability at compressive strains up to 95%. Multiscale finite element analyses indicate that the hierarchical structures of BHGMs effectively reduce the macroscopic strain and transform the microscopic compressive deformation into the rotation and bending of the interconnected graphene flakes. This 3D printing strategy demonstrates the great potential that exists for the assembly of other functional materials into hierarchical cellular structures for various applications where high stiffness and resilience at low density are simultaneously required.

Concurrent two-scale topological design of multiple unit cells and structure using combined velocity field level set and density model

This paper studies concurrent two-scale design optimization of composite structures filled with multiple microstructural unit cells. The task of the design problem is to simultaneously optimize microstructural configurations of the unit cells and their spatial distribution in the macroscale. To this end, a new topology optimization framework based on combined topology representation of the density model and the level set model is proposed. The homogenization method is used to link the material microstructural design and the macroscale design by evaluating the effective properties of the microstructures. In the microscale, topology optimization of multiple microstructural unit cells is performed with the density-based method. In the macroscale design, the distribution of multiple microstructural unit cells is optimized by the velocity field level set method, which inherits advantages of the implicit geometrical representation of the conventional level set model (relatively clear and smooth material boundaries/interfaces, more natural description of topological evolution). Moreover, the velocity field level set method maps the variational boundary shape optimization problem into a finite-dimensional design space, thus making it relatively easy and efficient to employ general mathematical programming algorithms to handle the multiple constraints and two types of design variables in the concurrent two-scale design problem. Numerical examples show that the present concurrent two-scale design method can generate meaningful designs of hierarchical cellular structures with well-defined boundaries and material interfaces.

Mechanical behaviors of hierarchical cellular structures with negative Poisson’s ratio

An investigation of the mechanical behaviors on hierarchical re-entrant honeycomb structures was undertaken using finite element method. The hierarchical structure with a hierarchy order n (n ≥ 1) was constructed by replacing each vertex of a re-entrant hexagonal structure of hierarchy order n − 1 with a smaller re-entrant hexagon with identical geometry aspect ratio. The Poisson’s ratio and energy absorption capacity of re-entrant structures of different hierarchy orders were studied under various compression velocities. The minimum Poisson’s ratios of the first-order (n = 1) and second-order (n = 2) hierarchical re-entrant structures were − 1.581 and − 1.823, respectively; they were 32.9 and 53.2% lower than that of a zeroth-order hierarchical structure (i.e., conventional re-entrant hexagon). The second-order hierarchical structure exhibited the highest rate of increase in energy absorption capacity with an increasing compression velocity. The plateau stresses of the first- and second-order hierarchical structures were lower than that of the zeroth-order hierarchical structure; however, the second-order hierarchical structure exhibited the highest energy absorption capacity at high compression velocity rate (v > 40 m/s). The energy absorption capacities of the first- and second-order hierarchical structures proposed in the present study are 1.5 and 1.8 times, respectively, higher than those of the hierarchical re-entrant structures proposed in our previous work (Li et al. in Smart Mater Struct 26:025014, 2017).

Oriented Crystallization of Barium Sulfate Confined in Hierarchical Cellular Structures

Biomineralization involves the controlled formation of inorganic matter within hierarchical biological scaffolds. Mimicking the crystallization of biominerals in such confinement is an important goal in the field of crystal engineering. Natural porous materials offer an interesting platform for studying mineral morphogenesis and texturing through template-directed mineralization. In this paper, we precipitate barium sulfate from aqueous salt solutions in the constrained micro- and nanoenvironment of pristine wood cells and cell walls. By employing spatially resolved characterization techniques, such as scanning electron microscopy (SEM), Raman spectroscopic imaging, and scanning wide-angle X-ray scattering (WAXS), we gain important insights into the deposition pattern, morphology, and crystallographic orientation of Barite crystals in the plant cell anatomy. The experimental findings suggest directed crystallization of BaSO4 at different hierarchical levels. SEM shows elongated, dendritic BaSO4 crystals g...

Numerical analysis on mechanical behaviors of hierarchical cellular structures with negative Poisson’s ratio

Two-dimensional hierarchical re-entrant honeycomb structures were designed and the mechanical behaviors of the structures were studied using a finite element method. Hierarchical re-entrant structure of order n (n ≥ 1) was constructed by replacing each vertex of a lower order (n − 1) hierarchical re-entrant structure with a smaller re-entrant hexagon with identical strut aspect ratio. The Poisson’s ratio and energy absorption capacity of re-entrant structures of different hierarchical orders were studied under different compression velocities. The results showed that the Poisson’s ratio of the first and second order hierarchical structures can reach −1.36 and −1.33 with appropriate aspect ratio, 13.8% and 12.1% lower than that of the zeroth order hierarchical structure. The energy absorption capacity of the three models increased with an increasing compression velocity; the second order hierarchical structure exhibited the highest rate of increase in energy absorption capacity with an increasing compression velocity. The plateau stresses of the first and second order hierarchical structures were slightly lower than that of the zeroth order hierarchical structure; however the second order hierarchical structure exhibited the highest energy absorption capacity at high compression velocity (60 m s−1).

The twist-to-bend compliance of the Rheum rhabarbarum petiole: integrated computations and experiments

Plant petioles can be considered as hierarchical cellular structures, displaying geometric features defined at multiple length scales. Their macroscopic mechanical properties are the cumulative outcome of structural properties attained at each level of the structural hierarchy. This work appraises the compliance of a rhubarb stalk by determining the stalk’s bending and torsional stiffness both computationally and experimentally. In our model, the irregular cross-sectional shape of the petiole and the layers of the constituent tissues are considered to evaluate the stiffness properties at the structural level. The arbitrary shape contour of the petiole is generated with reasonable accuracy by the Gielis superformula. The stiffness and architecture of the constituent layered tissues are modeled by using the concept of shape transformers so as to obtain the computational twist-to-bend ratio for the petiole. The rhubarb stalk exhibits a ratio of flexural to torsional stiffness 4.04 (computational) and 3.83 (experimental) in comparison with 1.5 for isotropic, incompressible, circular cylinders, values that demonstrate the relative structural compliance to flexure and torsion.

Hybrid design and energy absorption of luffa-sponge-like hierarchical cellular structures

Luffa sponge has hierarchical cellular structure with macro-pores and micro-pores. Its strength is greatly enhanced by the stiff inner-surface layer around the macro-pores. This hierarchical bio-cellular structure was mimicked to construct a hierarchical aluminum foam cylinder reinforced by stiff thin-walled carbon fiber reinforced plastic (CFRP) tubes. Compression behaviors of the luffa-sponge-like hierarchical foam cylindrical structures were revealed and it is found that the specific energy absorption (SEA) of the hierarchical structure is greatly improved compared with the pure aluminum foam cylinder. Interaction between the CFRP tube and the aluminum foam lets the SEA of the hierarchical cylinder is greater than the linear summation of the SEA of each component in the hierarchical foam. Through hybrid and hierarchical design, an ultra-light composite cellular structure with excellent energy absorption was developed.

Computational study of the elastic properties of Rheum rhabarbarum tissues via surrogate models of tissue geometry

Plant petioles and stems are hierarchical cellular structures, displaying geometrical features defined at multiple length scales. One or more of the intermediate hierarchical levels consists of tissues in which the cellular distribution is quasi-random, a factor that affects the elastic properties of the tissues. The current work focuses on the finite element analysis (FEA) of the constituent tissues of the plant Rheum rhabarbarum (rhubarb). The geometric model is generated via a recently introduced method: the finite edge centroidal Voronoi tessellation (FECVT), which is capable to capture the gradients of cellularity and diversified pattern of cellular materials, as opposed to current approaches in literature. The effective stiffness of the tissues is obtained by using an accurate numerical homogenization technique via detailed finite element analysis of the models of sub-regions of the tissues. As opposed to a large-scale representative volume element (RVE), statistical volume elements (SVE) are considered in this work to model tissue microstructures that are highly random. 2D finite element analyses demonstrate that the distribution of cells in collenchyma and parenchyma tissue make them stiffer in two different directions, while the overall effect of the combined tissues results in approximately equal stiffness in both directions. The rhubarb tissues, on the other hand, are more compliant than periodic and quasi-uniform random cellular materials by a factor of up to 47% and 44%, respectively. The variations of the stiffness shows the stiffening role that cell shape, size, and graded cellular distribution play in the mechanics of the rhubarb tissue.