Hierarchical Lattice Structures Research Articles

Multi-feature bionic gradient hierarchical lattice metamaterials with multi-synergistic crushing mechanisms

A persistent challenge of the checkerboard lattice metamaterials has been the trade-off between the controllability in crushing process and the enhancement of mechanical properties, where high stability and customizability tend to yield relatively low energy absorption capacity. To breakthrough this challenge, a design strategy based on a multi-feature bio-inspired gradient hierarchical lattice is presented, drawing from the microstructure characteristics of biological tissue. Experimental results and finite element analysis demonstrate the efficient and strong crushing performances and low oscillatory responses of the proposed gradient hierarchical lattice structures, featured by the designable multi-plateau crushing characteristics due to the multi-synergistic mechanisms of multi-biomimetic incentives. Specifically, its initial peak crushing stress is reduced by 162.69 %, and the energy absorption efficiency is improved by 62.19 % relative to the original square lattice with the same relative density. Moreover, the 1st plateau width of multi-feature bio-inspired gradient hierarchical lattice is determined by the size ratio of the unit cells, while the 1st and 2nd plateau stresses are mainly tailored by the wall-thickness and the relative density, respectively. The multi-bionic gradient hierarchical design paves an exemplary pathway to enhance the crushing performance and mechanical controllability of the checkerboard lattices.

Analytical model of mechanical properties for a hierarchical lattice structure based on hierarchical body-centered cubic unit cell

Hierarchical structure features complex geometric topology and excellent mechanical properties. In this work, analytical models are developed to predict the mechanical properties as Young's modulus, Poisson's ratio, and yield stress of a lattice structure composed of hierarchical body-centered cubic. Analytical results were validated by finite element simulations. The compressed experiments of lattice samples fabricated by powder bed fusion were conducted to examine mechanical properties. The analytical model agrees well with the simulation results and experimental results. The largest discrepancy from the analytical model to the finite element simulations for Young's modulus of lattice structures is 7.5%. Regarding Poisson's ratio and yield stress, the largest discrepancy are 0.05% and 13.1%, respectively. Furthermore, the Young's modulus shows an increasing trend as the relative density of lattices increases and geometrical ratio λ decreases. Moreover, the influence of shear deformation on the mechanical properties of the lattice structures decreases with the gradual increase of geometrical ratio λ. The Young's modulus and yield stress for the lattices increase as geometrical ratio λ decreases with increasing relative density. The Poisson's ratio shows an opposite trend to the Young's modulus as well as the yield stress. Finally, the degree of anisotropy of Young's modulus for the lattice structure is investigated. The range of anisotropy values for the lattice structure is large, i.e., 2.98∼745. The anisotropy value of Young's modulus decreases with the relative density increasing. And, the anisotropy value of lattices decreases with increasing relative density, i.e., the monotonic trend. This work provides guidance for future designs of the hierarchical lattice structures from the aspects of theoretical prediction.

Fabrication of hierarchical lattice structures from zirconia stabilized ceramics by micro-SLA 3D printing approach

The need for the new materials and advanced manufacturing techniques for achieving the highest characteristics of energy devices is an obvious trend. One of the possible ways to create structures for energy applications is to introduce complex geometries and promising features with additive manufacturing (AM). Using this approach, it is possible to create complex geometry and moreover decrease the weight of materials. In this paper, we developed the layer-by-layer fabrication approach of ceramic hierarchical lattice structures via the (micro-SLA) technology. As a feedstock material, the novel composition of partly stabilized-zirconia ceramics (6ScSZ, 8YSZ) was developed. Materials were selected as a solid slurry component due to high ionic conductivity at the working temperature of modern solid oxide fuel cells (SOFCs). For the sintering, the green body heat treatment process was optimized to one step, which decrease the time and production cost. The data from scanning electron microscopy and micro-CT shows that 112-layer samples of the octet truss did not show any critical defects, and the achieved relative density was close to the theoretical one. Totally, 22 samples with the total size of 6.5 mm * 6.5 mm * 2.8 mm and the diameter of struts in the range of 240–250 μm were fabricated at a rate of only 56 min per sample, using two modifications of advanced doped zirconia-ceramics. This study opens new opportunities for the development and transfer to the production of additive manufacturing of ceramics to build energy systems devices such as solid oxide fuel cells.

Mechanical Properties of Internally Hierarchical Multiphase Lattices Inspired by Precipitation Strengthening Mechanisms.

In metal metallurgy, precipitation strengthening is widely used to increase material strength by utilizing the impediment effect of the second-phase particles on dislocation movements. Inspired by this mechanism, in this paper, novel multiphase heterogeneous lattice materials are developed with enhanced mechanical properties utilizing a similar hindering effect of second-phase lattice cells on the shear band propagation. For this purpose, biphase and triphase lattice samples are fabricated using high-speed multi jet fusion (MJF) and digital light processing (DLP) additive manufacturing techniques, and a parametric study is carried out to investigate their mechanical properties. Different from the conventional random distribution, the second-phase and third-phase cells in this work are continuously distributed along the regular pattern of a larger-scale lattice to form internal hierarchical lattice structures. The results show that the triphase lattices possess balanced mechanical properties. Interestingly, this indicates that introducing a relatively weak phase also has the potential to improve the stiffness and plateau stress, which is distinct from the common mixed rule. This work is aimed at providing new references for the heterogeneous lattice design with outstanding mechanical properties through material microstructure inspiration.

Design of hierarchical lattice structures attainable by additive manufacturing techniques

Readiness of new materials that are simultaneously lightweight, damage-resistant, multifunctional, and sustainable is a primary need for many technology sectors. Thanks to additive manufacturing, lattice materials appear to be ideal candidates to meet this challenge. By designing their unit cells and structural organization, multiscale materials with unique combinations of properties can be obtained. Nevertheless, many gaps remain to be filled for their effective and efficient design. Nature, exploiting hierarchical architectures on a material scale, actually amplifies the properties of biological materials and combines them in ways we cannot achieve yet in synthetic materials. In materials design, we are still far from such a level of perfection. To narrow this gap and expand the current knowledge on the effects of hierarchy on the mechanical behaviour of materials, we numerically studied the mechanical response of 3D hierarchical lattice specimens under a four-point bending loading scenario. For this, we selected two types of unit cells with different structural behaviour and combined them together into different specimen topologies. The results show that, through hierarchy, it is possible to tailor lattice material performances, achieving benefits in terms of both specific mechanical properties and multifunctionality. The evidence found opens new horizons for applications such as heat exchangers, mechanical filters, scaffolds, energy storage, and packaging.

Dynamics of hierarchical beam lattice structures by an exact reduced-order dynamic-stiffness model

An exact reduced-order dynamic-stiffness model is proposed to study the dynamics of two-dimensional hierarchical beam lattices. Upon modelling every member of the lattice by a single exact two-node beam element, the model retains a few primary nodes of the unit cell and involves an exact dynamic condensation of the nodal degrees of freedom of the lattice structure internal to the unit cell and connected to the primary nodes. It is shown that the modes of the reduced-order model exhibit two orthogonality conditions, with dynamic-stiffness terms pertinent to the condensed lattice structures. The orthogonality conditions are the basis to decouple the motion equations and derive the exact modal response to external loading, in both time and frequency domains, under the assumption of proportional damping. The modal response is obtained in simple and elegant analytical form for the whole lattice, including the condensed lattice structures internal to the unit cells. Moreover, it can be calculated very expeditiously thanks to an exact representation of the eigenfunctions based on frequency dependent shape functions, which applies regardless of geometry and complexity of the hierarchical lattice structure. Numerical results confirm the exactness of the proposed reduced-order dynamic-stiffness model by comparison with standard finite-element solutions in ABAQUS.

Architecting materials for extremal stiffness, yield, and buckling strength

Abstract This paper proposes a methodology for architecting microstructures with extremal stiffness, yield, and buckling strength using topology optimisation. The optimised microstructures reveal an interesting transition from simple lattice-like structures for yield-dominated situations to hierarchical lattice structures for buckling-dominated situations. The transition from simple to hierarchical is governed by the relative yield strength of the constituent base material as well as the volume fraction. The overall performances of the optimised microstructures indicate that maximum strength is determined by the buckling strength at low-volume fractions and yield strength at higher-volume fractions, regardless of the base material’s relative yield strength. The non-normalised properties of the optimised microstructures show that higher base material Young’s modulus leads to both higher Young’s modulus and strength of the architected microstructures. Furthermore, the polynomial order of the maximum strength lines with respect to mass density obtained from the optimised microstructures reduces as base material relative yield strength decreases, reducing from 2.3 for buckling-dominated thermoplastic polyurethane to 1 for yield-dominated steel microstructures.

Hierarchical bioinspired architected materials and structures

Designing new materials that are both lightweight, damage-tolerant, and sustainable is a primary requirement for the advancement of many technological fields. To date, lattice materials appear to be ideal candidates for achieving such multifunctionality at the material scale and leveraging the structural hierarchy can pave the way to amplify their performance. Nature teaches us that, by designing multiscale architectures through a “bottom-up” logic, it is possible to improve and fine-tune the properties of biological building blocks to get robust and multifunctional materials. Yet, we are still far from achieving such a level of perfection that Nature has. In an attempt to narrow this gap and understand the role of hierarchical strategies in lattice structures, we studied, by finite element modeling, 3D hierarchical lattice structures formed by “beam-based” elementary units. Specifically, we selected two types of unit cells with different mechanical behaviors, we combined them into different topological configurations – through hierarchy and engineering approach – and we studied their mechanical behavior under four-point bending loading. The results of this study are twofold: introducing structural heterogeneity by mixing different unit cell types can be beneficial in terms of mechanical properties, while introducing structural hierarchy does not lead to significant improvements in the deformation behavior of the lattice structures analyzed. The latter, however, significantly changes the surface-to-volume ratios of the lattice structures and thus extends their functionality. The evidence found may open new horizons for applications such as heat exchangers, mechanical filters, tissue regeneration scaffolds, energy storage systems, and packaging.

Study on mechanical properties of lattice structures strengthened by synergistic hierarchical arrangement

To study the synergistic hierarchical arrangement effect, three hierarchical cubic lattice structures and six kinds of hybrid hierarchical lattice structures are designed based on the synergistic hierarchical arrangement concept. While studying the synergistic hierarchical arrangement effect on the structural protection characteristics, the prediction function of structural properties and the constitutive relation of lattice structures are derived. The structural properties are accurately predicted, and the errors are within 5%. In terms of mechanical properties of lattice structures, 941 hybrid hierarchical lattice structure, similar to the hybrid hierarchical arrangement inside the femur, presents the best mechanical behavior, followed by 194 and 419 hybrid hierarchical lattice structure. The bearing capacity, specific energy absorption, and energy absorption of 941 are more than 100% of those of other hierarchical or synergistic hybrid hierarchical lattice structures. The results show that the hierarchical and synergistic hybrid hierarchical lattice structure can effectively improve the mechanical properties of the lattice structure in different directions, especially the femur-like synergistic hybrid hierarchical structure. To better determine the excellent performance of the hybrid hierarchical structure, combined with the car seat, the performance of the hybrid hierarchical structure is further studied. Ideas are provided for the subsequent application of energy-absorbing engineering.

Mechanical performance of bio-inspired hierarchical honeycomb metamaterials

Natural materials with hierarchical structures usually have superior mechanical properties. Herein, inspired by the macro–micro coupling deformation characteristics of biomaterials, novel hierarchical auxetic-hexagonal honeycombs (AuxHex) metamaterials with various substructures, including equilateral triangles and double arrowheads lattice cells, were constructed. A universal analysis model of the plastic collapse stress was first established, considering the deformation behavior of both the primary and secondary structures. This mechanism-based method gets rid of redundant numerical fitting parameters, and is applicable to different hierarchical lattice structures. Typical hierarchical AuxHex specimens were prepared using selected laser melting and stainless steel. In-plane compression tests and finite element simulation results demonstrated that, in contrast to the regular structures, hierarchical honeycombs exhibit enhancement in their load-bearing capacities and energy absorption ability. The specific modulus of T-AuxHex and A-AuxHex were increased by about 180% and 45%, the specific strength rose by approximately 50% and 15%, and the specific energy absorption was improved by about 160% and 50%. The effects of geometrical parameters were systematically discussed to reveal the mechanisms underlying the enhancement of the above mechanical characteristics. The proposed theoretical model provides a new method for designing the mechanical properties of hierarchical metamaterials by tailoring the type and distribution of secondary structures.

Thermo-mechanical performance of 3D-printed TC4 hierarchical lattice-truss-core sandwich structures in high temperature conditions

Hierarchical lattice-truss-core sandwich structures have attracted increasing attention by virtue of superior performance in both mechanical properties and lightweight hierarchy topology. However, little work has been reported about the thermo-mechanical responses of such emerging structures. In this research, the effects of high temperature on the out-of-plane compressive properties and failure mechanisms of 3D-printed hierarchical lattice structures are experimentally and numerically investigated. Based on a single-stage pyramidal sandwich structure (P), two kinds of sandwich structures consisting of hierarchical pyramidal truss cores are designed: pyramidal-hollow (PH) and pyramidal-cylinder (PC), all kinds of the structures are integrally fabricated by 3D printing technique of titanium alloy (TC4). The thermo-mechanical coupling and responses during compression are experimentally evaluated from 25 °C to a high temperature of 350 °C. The relevant numerical simulations are carried out by finite element analysis (FEA), which are in well agreement with experimental measurements. It is evident that, compared with the single-stage lattice plate with a same weight, the 3D printed PC-1 type hierarchical configuration has a 131.93% increment in the internal heat-transfer area. Meanwhile, it has a 19.31% and a 26.58% increment in bearing capacity at room and high temperature, respectively. The superior integrated load-bearing and heat shielding efficiency are elucidated through the systematical analysis of the influence of hierarchical design on detrimental failure modes under high temperature: buckling and mixed buckling-plastic fracture of the basic and secondary hierarchy. This work could provide a fundamental knowledge for the future design of lightweight structures with thermo-mechanical superiority in high temperature conditions, such as hypersonic flight vehicles scenarios.

Compression behaviors of the bio-inspired hierarchical lattice structure with improved mechanical properties and energy absorption capacity

Nature materials usually possess unique hierarchical structures, like spongy bone, tendon and bamboo, and often exhibit remarkable mechanical properties. In this paper, inspired by the structural hierarchy of biological materials, the novel configuration design of unit cell with inner hierarchy was developed. The new lattice configuration takes advantage of the space filling and volume utilization of original BCC structure. The hierarchical lattices with 5 × 5 × 5 unit cells were manufactured by digital light processing (DLP) printing technique, using a hard-tough resin material. Numerical simulation and quasi-static experiment were performed to investigate the mechanical performance and deformation mechanisms of the lattice structures. The novel lattice configuration exhibits superior mechanical properties and enhanced energy absorption capacity with respect to conventional BCC lattice, e.g. when loading along x-axis, the improvement can be 38.9% for specific stiffness, 36.5% for specific energy absorption (SEA) and 73.1% for the crash load efficiency (CLE). Besides, the enhancement of mechanical performance and energy absorption capacity is more strong when loading along the z-axis. The mechanical interaction effect between structural hierarchy, e.g. master and slave cells, is proved to be the main reason that contributes to the enhancement of mechanical properties of hierarchical lattices. The designed novel configuration of hierarchical lattice will enrich the current lattice systems and promote the development of multifunctional applications in the future.

Synergistic effects of crystalline microstructure, architected mesostructure, and processing defects on the mechanical behaviour of Ti6Al4V meta-crystals

The mimicry of crystalline microstructure at the meso-scale creates a new class of architected materials, termed meta-crystals, and offers effective ways of significantly improving the toughness and eliminating the post-yield collapse of architected materials. The application of meta-crystal approach to crystalline alloys provides exciting opportunities for high strength structural components. This study investigated the mechanical behaviour of polycrystal-like meta-crystals fabricated from a widely used alloy, Ti6Al4V, by laser powder bed fusion (LPBF). The use of Ti6Al4V in fabricating meta-crystals created materials containing hierarchical lattice structures across length-scales: the atomic lattice, the intrinsic crystalline microstructure, and the architected polycrystal-like mesostructure, with each hierarchical feature playing an influential role in the mechanical behaviour of meta-crystals. This present study examined the hierarchical lattice structures at different lengthscales and their contribution to the behaviour of meta-crystals. In particular, the presence of acicular α’ martensitic microstructure was responsible for low ductility in the as-printed meta-crystals. Although heat-treatment was able to transform the martensitic microstructure to a typical α+β microstructure thus increasing the ductility, it was found that notch-like defects from lack of fusion at the free surface of struts were significantly detrimental. The study subsequently altered the meso-structural parameters to reduce the influence of the process defects and explored the effects of the heat treatment on the altered meta-crystals. Such alternations of structural design and crystalline microstructure appeared to be successful in minimising the processing effect, enabling the crystal-mimicry approach to effectively improve the toughness of Ti6Al4V meta-crystals.

Elastic wave propagation in self-similar and non-self-similar hierarchical two-dimensional square lattices

In this talk, we examine the elastic wave propagation behavior of infinite two-dimensional self-similar and non-self-similar hierarchical square periodic lattices. Using finite element analysis, we calculate the dispersion curves of different hierarchical lattice structures along their irreducible Brillouin zone (IBZ) paths. The effects of similarity, geometrical symmetry, and material symmetry on bandgap generation are studied. The mechanisms responsible for bandgap generation are explained by studying the mode shapes for different characteristic length ratios. We show that material symmetry can help induce wave attenuation bandgaps at low frequencies. Further, we classify the P- and S-wave propagation modes and study the effect of similarity on the generation of polarized bandgaps. We demonstrate that controlling the hierarchical similarity provides a robust method for tailoring the dispersion characteristics of periodic lattice structures.

Micro-Structured Patches for Dermal Regeneration Obtained via Electrophoretic Replica Deposition

Artificial substrates supporting the healing of skin wounds require specific structural and chemical architectures that promote a recapitulation of the complexity of the native organ. Bottom-up fabrication technologies are emerging as effective strategies to fine tune biochemical, morphological, and structural features intended for regenerative applications. Here, we proposed an electrophoretic replica deposition (EPrD) approach to realize chitosan three-dimensional structures specifically designed to treat patients with serious cutaneous damages or losses. The EPrD process has been optimized to consistently obtain random porosity vs. hierarchical lattice structures, showing mechanical properties in the range of skin tissue (E = 0.2–20 MPa). The obtained patches were tested in vivo via a one-stage grafting procedure in a full thickness skin wound rat model. Chitosan patches showed no adverse reactions throughout the experimental period (14 days). Hair follicles and sebaceous glands were observed in histological sections, indicating the regeneration of a thin epidermal layer with more skin appendages. Immunohistochemistry results demonstrated that keratin 10 was mostly expressed in basal and suprabasal layers, like normal skin, in structures with random porosity and with smaller lattice structures. The obtained results show the potential of EPrD to innovate the design of artificial substrates in skin healing therapies.

Substructure-Based Topology Optimization for Symmetric Hierarchical Lattice Structures

This work presents a topology optimization method for symmetric hierarchical lattice structures with substructuring. In this method, we define two types of symmetric lattice substructures, each of which contains many finite elements. By controlling the materials distribution of these elements, the configuration of substructure can be changed. And then each substructure is condensed into a super-element. A surrogate model based on a series of super-elements can be built using the cubic B-spline interpolation. Here, the relative density of substructure is set as the design variable. The optimality criteria method is used for the updating of design variables on two scales. In the process of topology optimization, the symmetry of microstructure is determined by self-defined microstructure configuration, while the symmetry of macro structure is determined by boundary conditions. In this proposed method, because of the educing number of degree of freedoms on macrostructure, the proposed method has high efficiency in optimization. Numerical examples show that both the size and the number of substructures have essential influences on macro structure, indicating the effectiveness of the presented method.

The substructuring‐based topology optimization for maximizing the first eigenvalue of hierarchical lattice structure

SummaryThis work presents a generalized substructuring‐based topology optimization method for the design hierarchical lattice structures to maximize the first eigenvalue. In this method, the macrostructure is assumed to be composed of substructures with a common artificial lattice geometry pattern. And two different yet connected scales are considered through a lattice geometry feature parameter. The feature parameter, which can control the material distribution of the substructure, determines the relative density of corresponding substructure. Each substructure is condensed into a super‐element to obtain the associated density‐related matrices. A surrogate model using cubic spline interpolation has been particularly built to map the density to stiffness and mass matrices of condensed super‐elements. The derivatives of super‐element matrices to the associated densities can be evaluated efficiently and accurately. Here, an augmented penalized density for this surrogate model is introduced. And the conventional optimality criteria method is selected as updating method of the density design variables. Numerical examples under two lattice patterns of substructures are shown to validate the correctness and superiority of this substructure‐based topology optimization method.

Compression property of hierarchical pyramid lattice

Hierarchical lattice structures have excellent mechanical and multi-functional properties. A novel hierarchical pyramid lattice structure was designed and the mechanical behaviours were studied using a finite element method. In order to reflect the advantages of hierarchical pyramid lattice structure, the compression simulation of the traditional pyramid lattice structure with the same relative density was also carried out. The results showed that the designed hierarchical pyramid lattice structure increased the buckling resistance, reduced the stress concentration at the joint of panel and core, and increased the energy absorption performance and specific strength. The designed hierarchical pyramid lattice structure contributes to the expansion of hierarchical lattice structure.

Topology optimization for concurrent design of layer-wise graded lattice materials and structures

Mechanical properties of hierarchical lattice structures depend not only on their overall shapes and topologies, but also on their microstructural configurations. This paper proposes a new method for concurrent topology optimization of structures composed of layer-wise graded lattice microstructures. Both macroscale design variables representing the distribution of different lattice materials and microscale design variables defining the topologies of the microstructural unit cells are to be simultaneously optimized. This formulation thus integrates the microstructure design into the structural design, instead of pursuing a grey macroscale design and then interpreting the intermediate densities into certain microstructures. The proposed method also enlarges the design space by allowing for graded microstructures. Two new design constraints, namely the structural coverage constraint and the average porosity constraint, are introduced into the proposed optimization formulation to reduce the complexity of the constraints in the layer-wise graded design. The macroscale and microscale designs are linked by using the Asymptotic homogenization method to compute the effective elastic properties of the microstructured materials. Numerical examples show validity of the proposed method. It is also found that layer-wise graded lattice structures outperform those with uniform lattice microstructures in terms of structural stiffness. Finite element simulations of constructed models of the optimized designs suggest that graded lattice structures exhibit higher buckling resistance and ultimate load bearing capacity than single-scale solid material structures or uniform lattice structures under the same material usage.

Topology optimization of hierarchical lattice structures with substructuring

This work presents a generalized topology optimization approach for the design of hierarchical lattice structures with the development of an Approximation of Reduced Substructure with Penalization (ARSP) model. The structure is assumed to be composed of substructures with a common lattice geometry pattern. Unlike conventional homogenization-based designs assuming the separation of scales, this work considers two different yet connected scales. Each substructure is condensed first into a super-element with a reduced degrees of freedom and is associated with a density design variable indicating the material volume fraction. The density design variable is linked to a lattice geometry feature parameter. A surrogate model is particularly built with the aid of proper orthogonal decomposition and diffuse approximation, mapping the density to super-element stiffness matrix. The derivative of super-element matrix with respect to the associated density can therefore be evaluated efficiently and explicitly. The super-element matrix is further augmented with a penalized density to control the structural complexity. The optimality criteria method is used for the update of design variables. Numerical examples show that both the size and the lattice pattern of substructure have essential influences on the design, indicating the necessity of performing connected hierarchical modeling and design.