Rhombic Dodecahedron Unit Cells Research Articles

Lattice structures in stainless steel 17-4PH manufactured via selective laser melting (SLM) process: dimensional accuracy, satellites formation, compressive response and printing parameters optimization

By the term, lattice structures are intended topologically ordered open-celled structures consisting of one or more repeating unit cells. Technological development and especially the growth of the additive manufacturing (AM) industry allows innovative structural design, including complex lattice structure. Selective laser melting (SLM) is an AM process that enables the manufacture of space filling structures. This work investigated the influence of the most important process parameter settings on lattices printability, focusing on the geometrical accuracy, the quantity of powders adhered to the main frame (satellites) and their compression behaviour. The process parameters such as the laser power, scan speed and layer height affect vigorously the design, quality and mechanical properties of the part. The aim of the paper is to evaluate how different parameter combinations affect the cellular structures’ printing. Twenty-four lattice structures with cubic and rhombic dodecahedron unit cells made of stainless steel 17-4PH (AISI-630) were printed using different combinations of SLM process parameters. Each structure was analysed considering its geometrical, topological and mechanical properties. Finally, the best parameter combination was evaluated comparing results achieved. Although this work investigated the 17-4PH stainless steel, physical principles related to the printing process described are generally true for the SLM process. Therefore, the adopted approach could still be suitable also for all the other materials commonly used with this AM technology.

The osteogenic effects of porous Tantalum and Titanium alloy scaffolds with different unit cell structure

Porous scaffolds have long been regarded as optimal substitute for bone tissue repairing. In order to explore the influence of unit cell structure and inherent material characteristics on the porous scaffolds in terms of mechanical and biological performance, selective laser melting (SLM) technology was used to fabricate porous tantalum (Ta) and titanium alloy (Ti6Al4V) with diamond (Di) or rhombic dodecahedron (Do) unit cell structure. The mechanical strength of all the porous scaffolds could match that of trabecular bone, while the biological performance of each scaffold was diverse from each other. Moreover, the ILK/ERK1/2/Runx2 signaling pathway had been verified to be involved in the osteogenic differentiation of rat bone mesenchymal stem cells (rBMSCs) cultured on those porous scaffolds. Unit cell structure and material characteristics of the porous Ta and Ti6Al4V scaffolds can synergistically modulate this axis and further impact on the osteogenic effects. Our results hence illustrate that porous Ta scaffold with diamond unit cell structure possesses excellent osteogenic effects and moderate mechanical strength and porous Ti6Al4V scaffold with rhombic dodecahedron unit cell structure has the highest mechanical strength and moderate osteogenic effects. Both porous Ta and Ti6Al4V can be applied in different settings requiring either better biological performance or higher mechanical demand.

Additively manufactured space-filling meta-implants

The unprecedented properties of meta-biomaterials could pave the way for the development of life-lasting orthopedic implants. Here, we used non-auxetic meta-biomaterials to address the shortcomings of the current treatment options in acetabular revision surgery. Due to the severe bone deficiencies and poor bone quality, it can be very challenging to acquire adequate initial implant stability and long-term fixation. More advanced treatments, such as patient-specific implants, do guarantee the initial stability, but are formidably expensive and may eventually fail due to stress shielding. We, therefore, developed meta-implants furnished with a deformable porous outer layer. Upon implantation, this layer plastically deforms into the defects, thereby improving the initial stability and homogeneously stimulating the surrounding bone. We first studied the space-filling behavior of additively manufactured pure titanium lattices, based on six different unit cells, in a compression test complemented with full-field strain measurements. The diamond, body-centered cubic, and rhombic dodecahedron unit cells were eventually selected for the design of the deformable porous outer layer. Each design came in three different relative density profiles, namely maximum (MAX), functionally graded (FG), and minimum (MIN). After their compression in bone-mimicking molds with simulated acetabular defects, the space-filling behavior of the implants was evaluated using load-displacement curves, micro-CT images, and 3D reconstructions. The meta-implants with an FG diamond infill exhibited the most promising space-filling behavior. However, the required push-in forces exceed the impact forces currently applied in surgery. Future research should, therefore, focus on design optimization, to improve the space-filling behavior and to facilitate the implantation process for orthopedic surgeons. Statement of significanceIdeally, orthopedic implants would last for the entire lifetime of the patient. Unfortunately, they rarely do. Critically sized defects are a common sight in the revision of acetabular cups, and rather difficult to treat. The permanent deformation of lattice structures can be used to create shape-morphing implants that would fill up the defect site, and thereby restore the physiological loading conditions. Bending-dominated structures were incorporated in the porous outer layer of the space-filling meta-implants for their considerable lateral expansion in response to axial compression. A functionally graded density offered structural integrity at the joint while enhancing the deformability at the bone-implant interface. With the use of a more ductile metal, CP-Ti, these meta-implants could be deformed without strut failure.

Investigation of the experimental, statistical and optimisation of 3D printed lattice core sandwich panel energy absorber with novel configuration using response surface method

This paper focuses on the energy absorption of additively manufactured or 3D printed lattice-core sandwich structures of different configurations. The compressive behavior of 3D lattice structures with rhombic dodecahedron unit cells is investigated at Quasi-static loading. A parametric analysis was performed, using a Box-Behnken design (BBD), as a method for design of experiments (DOE). Then, the influence of the angle between struts and their diameter were investigated. It was observed from experimental data that the angle between struts had the highest degree of influence on the specific energy absorption. The results showed that the diameter of struts has been the most influential parameter to increase mean and peak forces. The results from using the design expert software showed the optimal specific energy absorption and peak force to be 2.1014 J/gr and 2224.87 N, respectively.

Experimental and numerical study and multi-objective optimisation of quasi-static compressive test on three-dimensional printed lattice-core sandwich structures

This paper focuses on the energy absorption of additively-manufactured or 3D-printed lattice-core sandwich structures of different configurations. The rhombic dodecahedron lattice unit cell, which has been extensively investigated for energy absorption, is the starting point for this research. The compressive behaviour of 3D lattice structures with rhombic dodecahedron unit cells was examined at quasi-static loading along with the influence of the angle between struts, struts diameter, and the number of layers in the core. The angle between struts had the highest degree of influence on the specific energy absorption. The results showed that the diameter of struts has been the most influential parameter to increase mean and peak forces. The results of using the design expert software showed the optimal specific energy absorption and peak force to be 3.8779 J/gr and 3458.25 N, respectively.

Development of porous implants with non-uniform mechanical properties distribution based on CT images

In this study, the mechanical properties (elastic modulus, yield stress, and Poisson's ratio) of rhombic dodecahedron (RD) unit cell has been studied analytically and numerically. For the analytical study, two well-known beam theories, namely Euler Bernoulli and Timoshenko, have been implemented. For validating the analytical relationships, finite element model of unit cell with repetitive boundary condition has been created. Moreover, the experimental results of recent studies have been used for validation. The results showed that the presented analytical relationships for RD lattice structure have good agreement with numerical and experimental results in all the relative densities particularly in lower relative densities. Besides, the analytical relationships based on Timoshenko theory showed closer results with numerical/experimental data. The derived analytical relationships for RD as well as the data extracted from CT scan images of a femur bone, were combined and used to create a porous femur implant model. The stress and strain distributions of the porous femur model under typical static compressive load due to human weight as well as axial rigidity of the model in the same loading conditions have been obtained and compared with the experimental results from other studies. The stress and strain distributions of the porous femur implant model based on RD unit cells, as well as its axial rigidity, showed good agreement with the results obtained for human femur.

Subject-specific finite element analysis of a lumbar cage produced by electron beam melting.

The aim of this study was the analysis of the mechanical behaviour of a partially porous lumbar custom-made cage by means of a subject-specific finite element analysis (FEA). The cage, made of Ti6Al4V ELI alloy, was produced via electron beam melting (EBM) process and surgically implanted in a female subject, 50 years old. The novelty of this study was the customized design of the cage and of its internal structure, which is impossible to obtain with the traditional production techniques. The 3D model of the spine was obtained from the computed tomography (CT) of the patient. Moreover, high-resolution industrial CT was also used to reconstruct a 3D model of the cage, with its real (as-produced) features, such as superficial roughness, morphology of the bulk and of the porous structure. The workflow was divided in several steps: the main finite element analyses were non-linear and quasi-static regarding: the rhombic dodecahedron (RD) unit cell of the porous structure; the device; the whole L4-L5 motion segment with the implanted cage. Stress distribution was calculated under compression load for all models. For the RD unit cell, the maximum stress appeared at the connected cross nodes, where notch effect was present. For the cage subjected to a load of 1 kN, the porous structure did not present any functional failure. For the whole biomechanical system subjected to a physiological load of 360 N, the calculated stress in the bone was smaller than its yield strength value. On the axial view, a zone with higher compressive stresses was present on the L5 vertebral body. This was due to the contact stress between the cage and the vertebra. From the comparison between FE results and the CT images of the spine, bone remodelling was supposed, with the formation of new bone. Graphical abstract Workflow showing the phases of the research.

Compressive properties and micro-structural characteristics of Ti–6Al–4V fabricated by electron beam melting and selective laser melting

Bulk Ti–6Al–4V material and its lattice structures with rhombic dodecahedron unit cells are fabricated by electron beam melting (EBM) and selective laser melting (SLM) method respectively. The effect of part size on the compressive properties and failure modes of the material is taken into consideration. Electronic universal testing machine and Split Hopkinson pressure bar (SHPB) system are adopted for experiments, and the compressive behavior of the additively manufactured materials is investigated accordingly. Meanwhile, multiscale observations are conducted to reveal the macro- and microscopic deformation mechanism. The results showed that the mechanical response of the dense struts as well as micro-lattice structures manufactured by the two processes are quite different. The geometric imperfections are considered to reduce the strength of the undersized struts prepared by EBM. The specimens fabricated by both of the two approaches exhibit elastic-plastic deformation. Besides, the SLM made material is found to be more sensitive to strain rate especially for that below 1000/s than the EBM parts.

Deformation and failure modes of Ti-6Al-4V lattice-walled tubes under uniaxial compression

The compressive large deformation response of tubes, comprising walls made of rhombic dodecahedron unit cells, under quasi-static and dynamic loadings is investigated. Six types of tubes with cellular walls that vary with respect to cell density, tube cross-section and cellular tube wall thickness are manufactured by selective laser melting (SLM). The quasi-static and dynamic compression tests are conducted by using a universal testing machine, a drop hammer device and direct-impact Hopkinson pressure bar (DHPB), respectively, to determine the force-deformation responses of the different structures. In addition, the deformation modes and energy absorption capacity of the tubes are identified. The influence of the cross-sectional shape and cellular-walled density gradient on the energy absorption capacity of the various tube configurations is examined. The results indicate that the Ti-6Al-4V lattice-walled tubes with a density gradient exhibit the best absorption efficiency among the tubes studied. The collapse strength of the square cross section tube tested is more significant than that of its cylindrical counterparts.

Fatigue crack propagation in additively manufactured porous biomaterials

Additively manufactured porous titanium implants, in addition to preserving the excellent biocompatible properties of titanium, have very small stiffness values comparable to those of natural bones. Although usually loaded in compression, biomedical implants can also be under tensional, shear, and bending loads which leads to crack initiation and propagation in their critical points. In this study, the static and fatigue crack propagation in additively manufactured porous biomaterials with porosities between 66% and 84% is investigated using compact-tension (CT) samples. The samples were made using selective laser melting from Ti-6Al-4V and were loaded in tension (in static study) and tension-tension (in fatigue study) loadings. The results showed that displacement accumulation diagram obtained for different CT samples under cyclic loading had several similarities with the corresponding diagrams obtained for cylindrical samples under compression-compression cyclic loadings (in particular, it showed a two-stage behavior). For a load level equaling 50% of the yield load, both the CT specimens studied here and the cylindrical samples we had tested under compression-compression cyclic loading elsewhere exhibited similar fatigue lives of around 104 cycles. The test results also showed that for the same load level of 0.5Fy, the lower density porous structures demonstrate relatively longer lives than the higher-density ones. This is because the high bending stresses in high-density porous structures gives rise to local Mode-I crack opening in the rough external surface of the struts which leads to quicker formation and propagation of the cracks. Under both the static and cyclic loading, all the samples showed crack pathways which were not parallel to but made 45° angles with respect to the notch direction. This is due to the fact that in the rhombic dodecahedron unit cell, the weakest struts are located in 45° direction with respect to the notch direction.

Mechanical properties of open-cell rhombic dodecahedron titanium alloy lattice structure manufactured using electron beam melting under dynamic loading

The compressive behavior of Ti-6Al-4V lattice structures with rhombic dodecahedron unit cells is investigated at four different strain rates. Quasi-static compressive experiments are conducted by an electronic universal testing machine with a strain rate of 10−3/s, while Split Hopkinson pressure bar(SHPB) tests are used for achieving higher deformation rates about 1000/s. The loading processes are recorded by a digital and high speed camera respectively for all tests in order to determine the failure modes at different strain rates. The nominal stress-strain relationship is curved afterwards. The results show that the peak stress exhibits certain dependence on the loading rate for the structures with smaller unit cells. The deformation modes are found to be unchanged in quasi-static and SHPB experiments. All specimens are deformed with a shear band along 45°plane firstly. Finite element(FE) model is established based on the specimen with 5mm unit cell size by 3D reconstruction from X-ray tomography to take the surface quality of struts into account. Afterwards, numerical analysis is conducted by LS-DYNA to simulate the specimens impacted at different velocities. The FE results which can be employed to make some useful predictions are partly consistent with the experimental data. Then the crushing behavior of Ti-6Al-4V lattice structure is analyzed by the rigid-power-law hardening(R-PLH) model, and the critical velocities for deformation mode transition are predicted.

Influence of the Unit Cell Geometrical Parameter to the Mechanical Properties of Ti6Al4V Open-Porous Scaffolds Manufactured by Selective Laser Melting

Selective laser melting (SLM) are getting more and more established as reliable methods for producing open-porous scaffolds with accurately controlled pore size, strut size, and porosity. However, the optimal geometrical parameter of the unit cell by SLM remained unclear. In this study, we evaluated the effect of unit geometrical parameters to the mechanical properties of porous scaffolds by finite element analysis method and Mechanical testing method. Six rhombic dodecahedron unit cells were designed with different geometrical parameter and the scaffolds manufactured by SLM using Ti6Al4V. The compression testing results show that the specimens with the same pore size, the elastic modulus and the strength are increased with increasing strut size and the specimens with the same strut size, the elastic modulus and the strength are decreased with increasing strut size. The porosity can be calculated by pore size and strut size. The compression strength of the porous scaffolds is 114MPa~258MPa and the quasi-elastic gradient is 3.18Gpa~8.64Gpa, which are similar to human bone. The simulation values are different from the experiment values but the variation tendency is in accordance.

Computational prediction of the fatigue behavior of additively manufactured porous metallic biomaterials

The mechanical behavior of additively manufactured porous biomaterials has recently received increasing attention. While there is a relatively large body of data available on the static mechanical properties of such biomaterials, their fatigue behavior is not yet well-understood. That is partly because systematic study of the fatigue behavior of these porous biomaterials is time-consuming and expensive due to the large number of involved factors. In the current study, we propose a computational approach based on finite element method that could be used to predict the fatigue behavior of porous biomaterials given their type of repeating unit cell, dimensions of the unit cell, and S–N curve of the parent material. We applied the proposed approach to predict the fatigue behavior of porous titanium alloy (Ti–6Al–4V) biomaterials manufactured using selective laser melting based on the rhombic dodecahedron unit cell and compared our computational results with experimental observations from one of our recent studies. The evolution of the displacement, elastic modulus, and number of failed struts vs. the number of loading cycle followed a two-stage pattern. In the first stage, there was a relatively slow rate of change in the above-mentioned variables, while they changed very rapidly in the second stage. That compares to the behavior observed in our experimental study. The computationally predicted S–N curve well matched the experimental observations for stress levels not exceeding 60% of the yield stress of the porous structures. For higher stress levels, the presented approach substantially underestimated the fatigue life of the porous structures. The effects of the irregularities caused by the additive manufacturing process on the fatigue behavior of the porous structures were also studied. It was found that those irregularities substantially decrease the fatigue life particularly for lower stress levels.

Relationship between unit cell type and porosity and the fatigue behavior of selective laser melted meta-biomaterials

Meta-materials are structures when their small-scale properties are considered, but behave as materials when their homogenized macroscopic properties are studied. There is an intimate relationship between the design of the small-scale structure and the homogenized properties of such materials. In this article, we studied that relationship for meta-biomaterials that are aimed for biomedical applications, otherwise known as meta-biomaterials. Selective laser melted porous titanium (Ti6Al4V ELI) structures were manufactured based on three different types of repeating unit cells, namely cube, diamond, and truncated cuboctahedron, and with different porosities. The morphological features, static mechanical properties, and fatigue behavior of the porous biomaterials were studied with a focus on their fatigue behavior. It was observed that, in addition to static mechanical properties, the fatigue properties of the porous biomaterials are highly dependent on the type of unit cell as well as on porosity. None of the porous structures based on the cube unit cell failed after 106 loading cycles even when the applied stress reached 80% of their yield strengths. For both other unit cells, higher porosities resulted in shorter fatigue lives for the same level of applied stress. When normalized with respect to their yield stresses, the S-N data points of structures with different porosities very well (R2>0.8) conformed to one single power law specific to the type of the unit cell. For the same level of normalized applied stress, the truncated cuboctahedron unit cell resulted in a longer fatigue life as compared to the diamond unit cell. In a similar comparison, the fatigue lives of the porous structures based on both truncated cuboctahedron and diamond unit cells were longer than that of the porous structures based on the rhombic dodecahedron unit cell (determined in a previous study). The data presented in this study could serve as a basis for design of porous biomaterials as well as for corroboration of relevant analytical and computational models.

Flexural properties of Ti6Al4V rhombic dodecahedron open cellular structures fabricated with electron beam melting

Open cellular structures fabricated in Ti6Al4V using the electron beam melting (EBM) process have been proposed for tissue scaffolds and low stiffness implants that approximate the properties of bone. The properties of these structures, regardless of cell geometry, have often been determined through compressive testing, and very few of these studies have investigated the flexural properties. For certain types of implants that are designed to fill very large segmental defects in appendicular bones, such as those used in limb sparing, compression testing does not provide the necessary insight into the complex loading states typical of bending. In this study, EBM-fabricated Ti6Al4V prismatic bars, populated with rhombic dodecahedron unit cells of various sizes and relative densities, were subjected to four-point flexure tests. While the results generally follow the power scaling models of Gibson and Ashby, the use of these models as a design tool is limited by machine resolution, particularly when producing structures with small pore sizes required for bone ingrowth.