Strength Of Lattices Research Articles

Replicating Mg scaffold via 3D printing sacrificial template

The fabrication of hierarchical and porous structures holds significant promise in biomedical science, aerospace, and related fields. Despite advancements in 3D printing technology that have enhanced the capability of complex porous structures, its application in metal fabrication remains challenging. In this paper, we introduce a method involving a 3D printed sacrificial template, created by the material extrusion process, for magnesium (Mg) infiltration. This method facilitates the production of porous Mg scaffolds, with the templates subsequently being water-leached. The morphology, shrinkage rate, compressive strength, and types of lattices of templates were observed and assessed to determine their viability. Further, comprehensive compression tests and cell adhesion experiments were conducted on the Mg scaffolds to evaluate their performance. The results suggest that the templates must possess adequate strength and continuous flow channels for successful Mg infiltration. The scaffolds experienced an average of about 30 % shrinkage from the initial design to the final structure. The porous Mg scaffolds exhibit enhanced compressive strength (47.48 ± 0.84 MPa) at lower porosity (0.52) and demonstrate satisfactory biocompatibility. This research highlights the efficacy and low cost of the template replication method in generating mechanically superior porous Mg scaffolds with customized pore sizes and structures. In future research, this method also holds promise for applications involving newly developed alloys.

Stiffness, strength, anisotropy, and buckling of lattices derived from TPMS and Platonic and Archimedean solids

Lattice metamaterials have gained considerable attention due to their distinctive topological structures and multifunctional properties. In this work, the effect of topology, loading conditions, and relative density on the effective mechanical properties of various novel lattice architectures is investigated numerically and experimentally. Thirteen strut-based lattices derived from triply periodic minimal surfaces (five lattices) as well as Platonic (three lattices) and Archimedean (five lattices) solids are considered for the first time, and their anisotropic mechanical properties, including uniaxial, shear, and bulk moduli and strengths as well as their total stiffness, buckling strengths, Poisson’s ratio, and anisotropy are investigated as a function of a wide range of relative densities (0.1% to 37%). Finite element analysis is employed to capture the full effective behavior of these lattices using periodic boundary conditions. Bifurcation analysis is performed to predict the threshold relative density governing their buckling vs yielding deformation behavior. Selected lattice structures of various relative densities are 3D printed using polymer selective laser sintering additive manufacturing technique and tested under quasi-static uniaxial compression where the experimental and numerical results are compared. The numerical results indicate that the deformation behavior can be altered between stretching and bending dominated mode of deformation as function of loading. Archimedean lattices are shown to outperform a wide range of strut-based lattices. This work opens the doors for more investigations of the multifunctional properties of these novel types of lattices and their engineering applications. Furthermore, the generated comprehensive data are useful in optimizing latticed structures using topology optimization techniques.

Propagation of fundamental gap solitons in the fractional Schrödinger equation with combined linear and nonlinear optical lattices

The propagation of two-dimensional fundamental gap solitons is investigated in the framework of fractional Schrödinger equation with combined linear and nonlinear optical lattices. It is revealed that solitons exist in the first gap and can be stable in a large region. With a phase tilt, the fundamental gap solitons undergo oscillation during the propagation. And the oscillation is enhanced with the increase of the tilt. In addition, propagation of fundamental gap solitons are also studied by longitudinal modulation of Lévy index, nonlinear strength, and period of nonlinear lattices, respectively. With the sudden variation of Lévy index, the fundamental gap solitons undergo oscillation and become unstable, whereas the gradual variation generates the stable soliton. However, both sudden and gradual decreases of nonlinear strength can lead to the distortion of the soliton due to the weak nonlinearity. Interestingly, the small longitudinal modulation of the period of the nonlinear lattice has little effect on the propagation of fundamental gap soliton, while the effect of the large variation of the period of the nonlinear lattice is apparent.

Orthopedic Scaffolds: Evaluation of Structural Strength and Permeability of Fluid Flow via an Open Cell Neovius Structure for Bone Tissue Engineering.

The ability of bone to regenerate itself through mechanobiological responses is its dynamic property. Mechanical cues from a neighboring environment produce the structural strain to promote blood flow and bone marrow mobility that in turn aids the bone regeneration process. Occurrences of these phenomena are crucial for the success of metallic scaffolds implanted in the host bone tissue. Thus, permeability and fluid flow-induced wall shear stress (WSS) are two parameters that directly influence cell bioactivities inside a scaffold and are crucial for effective bone tissue regeneration. Given that the scaffolds shall be implanted in the body, permeability assessment was carried out using non-Newtonian fluid. In this work, the triply periodic minimal surface scaffolds with Neovius architectures were fabricated by using selective laser melting technology. The estimation of fluid flow was carried out using computational fluid dynamics (CFD) analysis with a non-Newtonian blood fluid model. Further, the structural strength of various open cell Neovius lattices was evaluated using a static compression test, and in vitro cell culture using Alamar blue assay was evaluated. Results revealed that the values of intrinsic blood flow permeability of the three-dimensional (3D)-printed open cell porous scaffold with Neovius architecture were of the same order of magnitude as those of human bone, ranging from 0.0025 × 10-9 to 0.0152 × 10-9 m2. The structural elastic modulus and compressive strength of NOCL40, NOCL50, and NOCL60 lattices range from 3.27 to 3.71 GPa and 194 to 205 MPa, respectively. All of the values are comparable to the human bone, thus making these lattices a suitable alternative for orthopedic applications.

Hybrid material usage in TPMS forms fabricated by additive manufacturing, comparison of mechanical strength of lattices produced with AlSi10Mg and 7050

Aluminum-based cellular structures are gaining significant attention across industries due to their lightweight and impressive mechanical properties. With the advent of additive manufacturing (AM), complex periodic cellular structures with varying unit cell forms, sizes, and volume fractions can be fabricated with relative ease. In this study, the mechanical strength of lattice structures fabricated using laser powder bed fusion (LPBF) was investigated, with a focus on the effect of lattice geometry, material type, and outer wall incorporation. Results showed that both material choice and lattice geometry significantly impacted the mechanical properties of the structures. The highest ultimate strength of 400 MPa was observed in the schwartz-p geometry model created with Al 7050 LPBF alloy, with the addition of Zr identified as the key factor in enhancing its strength. The incorporation of an outer wall did not improve the strength of the structures, indicating the importance of material and geometry selection in optimizing mechanical performance. These findings provide valuable insights for the development and advancement of lattice structures in various applications and highlight the potential of additive manufacturing in this field.

Novel laser powder bed fusion Corrax maraging stainless steel lattice with superior specific strength and energy absorption

Laser powder bed fusion (LPBF) is a versatile process for producing lattice structures with complex pore features. In this study, a novel LPBF Corrax maraging stainless steel lattice with superior compressive strength and energy absorption was fabricated and investigated. In samples with a cubic lattice structure and 90 vol% porosity, the specific compressive strength and energy absorption of the LPBF Corrax lattices were as high as 53 kN·m/kg and 13.5 kJ/kg, respectively, which were higher than those of LPBF Ti–6Al–4V by 8% and 67%, respectively. Integrated solution-aging treatments further enhanced the specific compressive strength of Corrax lattice to 73 kN·m/kg and maintained the specific energy absorption. Furthermore, the deformation and fracture behaviors of the Corrax lattice were investigated and are discussed. The findings of this study indicate that LPBF Corrax is a potential material for manufacturing cheap, lightweight components with superior mechanical performances.

Node-reinforced hollow-strut metal lattice materials for higher strength

Intricate hollow-strut metal lattices are novel cellular materials or metamaterials. However, their hollow nodal regions often lead to premature failure under stress. This study reports a design strategy to substantially improve the strength of hollow-strut metal lattices by applying nodal reinforcement. The proposed nodal reinforcement designs increased the yield strength of hollow-strut Ti-6Al-4V cubic lattices by up to 144% and elastic modulus by up to 113% with a modest 21% increase in density compared to the unreinforced lattices. In addition, a 42% increase in peak stress was observed when compared to solid-strut Ti-6Al-4V cubic lattices of similar densities. These properties exceeded the empirical upper limits of the Gibson-Ashby model for cellular metallic materials, thus extending the property envelope. Distinct failure modes were observed for the proposed nodal reinforcement designs. Numerical analysis clarified their role in determining the deformation response.

Improving stiffness and strength of body-centered cubic lattices with an I-shape beam cross-section

The stiffness and strength of body-centered cubic (BCC) lattices are greatly improved by utilizing an I-shape beam cross-section. First, a cross-sectional analysis is performed to demonstrate the improved bending stiffness of the I-shape beams compared with the beams with a circular cross-section. Then, a novel multiscale modeling approach is employed to compute the effective stiffness of the lattices and investigate the stress distribution under a compressive load. The designed lattices are fabricated by selective laser sintering (SLS) and the compression tests are carried out. The results show that the proposed I-shape cross-section significantly improves the stiffness and strength of the BCC lattices. The improvement of the stiffness and strength with different beam slenderness ratios are also investigated. The maximum improvement of the stiffness–weight and strength–weight ratio is 159.13% and 41.42%, respectively. In addition, nonlinear finite element analysis (FEA) is carried out to investigate the mechanisms of improved material properties by different cross-sections. The newly proposed BCC lattices provide a potential alternative to conventional BCC lattices with enhanced stiffness and strength.

3D printing of architectured epoxy-based composite lattices with exceptional strength and toughness

Due to the exceptional mechanical properties, epoxy-based composites have been widely applied as critical aerospace components, semiconductor packaging materials, and multifunctional coatings and adhesives. However, the brittle nature of epoxy resin leads to poor resistance to crack initiation and propagation, significantly hindering their applications as high-performance composites. Herein, we develop an architectured composite lattice with simultaneous high toughness and strength through a 3D printing technique. Strengthening and toughening zones possessing solid and highly ordered lattice structures, respectively, are rationally assembled into a layered structure. The resultant composite lattices deliver significantly improved flexural properties and crack resistance properties, exhibiting 400%, 83% and 36% higher toughness, specific strength, and fracture toughness than their solid counterpart, respectively. The exceptional strength and toughness of the composite lattices come from the synergetic effect of the strengthening and toughening zones, as confirmed by both experimental and theoretical analysis. The current findings provide an effective strategy for the fabrication epoxy-based composites with precisely controlled structures and mechanical performances.

On enhancing mode-dependent failure strength under large deformation: The concept of anti-curvature in honeycomb lattices

Over the last decade, lattice-based artificial materials have demonstrated the possibility of tailoring multifunctional capabilities that are not achievable in traditional materials. While a large set of mechanical properties can be simultaneously modulated by adopting an appropriate network architecture in the conventional periodic lattices, the prospect of enhancing global specific stiffness and failure strength has become rather saturated lately due to intense investigation in this field. Thus there exists a strong rationale for innovative design at a more elementary level in order to break the conventional bounds of specific stiffness and failure strength that can be obtained only by lattice-level geometries. Here we propose a novel concept of anti-curvature in the design of lattice materials, which reveals a dramatic capability in terms of enhancing the elastic failure strength in the nonlinear regime while keeping the relative density unaltered. A semi-analytical bottom-up framework is developed for estimating the onset of failure in honeycomb lattices with the anti-curvature effect in cell walls considering geometric nonlinearity under large deformation. The physically insightful semi-analytical model captures nonlinearity in elastic failure strength of anti-curvature lattices as a function of the degree of curvature and applied stress together with conventional microstructural and intrinsic material properties.

Towards understanding deformation and fracture in cementitious lattice materials: Insights from multiscale experiments and simulations

Tailoring lattice structures is a commonly used method to develop lattice materials with desired mechanical properties. However, for cementitious lattice materials, besides the macroscopic lattice structure, the multi-phase microstructure of cement paste may have substantial impact on the mechanical responses. Therefore, this work proposes a multi-scale numerical modelling method to simulate the deformation and fracture behavior of cementitious lattice materials, such that the influence of cement paste microstructure can be properly captured. On the microscale, the load–displacement response of cement paste is numerically simulated then experimentally validated. In order to rationally investigate the role of cement paste microstructure, the obtained load–displacement response was then formulated to several types of model inputs reflecting different degree of brittleness. These inputs were then used for simulating the mechanical response of macroscale cementitious lattices. By comparing the simulation to experiment, multi-linear behavior (ML) was found to an appropriate method to include the realistic pre-critical cracking and post-peak softening of cement paste in the model. Compared to ideally brittle behavior, using ML as input, the discrepancy between simulated and experimentally tested fracture energy decreases from 37.4% to 12.4%. In addition, the influence of lattice structure on the strength of cementitious lattices was also accurately captured by the proposed model. Randomized cementitious lattice has 21.6% (22.0% from simulation) lower strength than regular lattice. Moreover, the influence of fracture criterion of the proposed model is discussed and elaborated. Owning to the high simulation accuracy, the proposed multi-scale method in this work could be helpful for tailoring the fracture cementitious lattice materials for future studies.

Mechanical Strength of Triply Periodic Minimal Surface Lattices Subjected to Three-Point Bending.

Sandwich panel structures (SPSs) with lattice cores can considerably lower material consumption while simultaneously maintaining adequate mechanical properties. Compared with extruded lattice types, triply periodic minimal surface (TPMS) lattices have light weight but better controllable mechanical properties. In this study, the different types of TPMS lattices inside an SPS were analysed comprehensively. Each SPS comprised two face sheets and a core filled with TPMS lattices. The types of TPMS lattices considered included the Schwarz primitive (SP), Scherk’s surface type 2 (S2), Schoen I-graph-wrapped package (I-WP), and Schoen face-centred cubic rhombic dodecahedron (F-RD). The finite element method was applied to determine the mechanical performance of different TPMS lattices at different relative densities inside the SPS under a three-point bending test, and the results were compared with the values calculated from analytical equations. The results showed a difference of less than 21% between the analytical and numerical results for the deformation. SP had the smallest deformation among the TPMS lattices, and F-RD can withstand the highest allowable load. Different failure modes were proposed to predict potential failure mechanisms. The results indicated that the mechanical performances of the TPMS lattices were mainly influenced by the lattice geometry and relative density.

A novel parameter to tailor the properties of prismatic lattice materials

Lattice materials are extremely efficient in combining high stiffness and strength at low densities. Their architecture is a periodic assembly of bars, which, in most cases, all have the same length and cross-section. This is, however, suboptimal since the level of stress is not the same in all bars. To take these variations into account, we propose to design prismatic lattices with two different bar thicknesses. The ratio of these two thicknesses introduces a new parameter in the design of lattices. Analytical expressions are developed to capture the effect of this new parameter on the elastic modulus, failure mode and compressive strength of hexagonal and triangular lattices. This analytical work is then validated by finite element simulations and experiments performed on polymer lattices fabricated by additive manufacturing. This new parameter offers two advantages in the design of prismatic lattices. First, the thickness ratio can be used to vary the properties of a lattice without changing its relative density. Second, it allows to stiffen and strengthen the lattice along a specific loading direction and therefore, controls the degree of anisotropy. This work opens new possibilities to tailor the mechanical properties of prismatic lattices, and facilitates the creation of new materials by design.

Stereolithography (SLA) 3D printing of carbon fiber-graphene oxide (CF-GO) reinforced polymer lattices

Insufficient mechanical properties of stereolithography (SLA)-printed architected polymer metamaterial limits its wide applications such as in the areas of biomedicine and aerospace. One effective solution is to reinforce the structures with micro- or nano- fibers/particles, but their interfaces are critical for the reinforcement. In this work, a carbon fiber-graphene oxide (CF-GO) polymer composite resin and a mild annealing postprocess have been rationally designed and applied into the manufacturing of oct-truss (OCT) lattices. In situ carbon fiber pulling-out experiment was conducted to exhibit the improve effect of GO on the crosslink of the CF and the polymer matrix interface. We found that the maximum reinforcement was realized when the CF-GO (CF: GO is about 3: 1) content is about 0.8 wt%, followed with annealing. Compared with pure polymer lattices, the compression strength of the CF-GO polymer OCT lattices has been significantly increased from ∼0.22 to ∼2.4 MPa, almost 10 times enhancement. Importantly, the compression strength of the CF-GO polymer OCT lattice (3.08 MPa) further increased by ∼30% after optimized annealing. This work suggests an efficient reinforce strategy for SLA-printed metamaterials, and thus can be valuable for advancing various practical applications of mechanical metamaterials.

Strength and energy absorption characteristics of Ti6Al4V auxetic 3D anti-tetrachiral metamaterials

The strength and energy absorption properties of the auxetic 3D anti-tetrachiral (3ATC) lattice, a member of the newly formalized joint-rotation-dominated cellular topology, were studied for the first time, using analytical modelling, simulations and experiments employing additively manufactured titanium alloy (Ti6Al4V) lattices. A limited ductility failure model was employed in the simulations to accurately account for the enhanced brittleness of 3D printed Ti6Al4V. The 3ATC lattices exhibited 2 distinct relative strength vs. relative density relationships. If the relative density was varied through changes in strut length, the relationship was linear, a result that has, until now, been a distinguishing trait of rigid stretch-dominated lattices, rather than auxetic lattices, which normally experience strut bending. On the other hand, if the relative density was varied through changes in strut width, the relationship was highly nonlinear and does not follow the power law trend that is typical of many cellular solids. The strength of 3ATC lattices can be higher than that of stochastic foams, but were lower than those of stretch-dominated designs. In addition, 3ATC bulk lattices exhibited highly uniform properties across the three different orthogonal loading directions, despite individual unit cells being highly orthotropic. The failure of 3ATC lattices was characterized by a series of bumps in the plateau regime, which corresponded to the sequential failure and compaction of individual unit cell layers in the lattice. The specific energy absorbed during the failure process was found to be linearly related to the failure strength. The mechanical characteristics of the 3ATC lattices are dependent on 3 normalized design parameters: i) strut length, ii) strut width, and iii) eccentricity, offering enhanced flexibility for design optimization over conventional lattice designs. When manufactured with a material of high specific strength like Ti6Al4V, it was shown that 3ATC lattices can be useful as lightweight and high strength auxetic architected metamaterials that provide good energy absorption capabilities.

Structure design influencing the mechanical performance of 3D printing porous ceramics

Different from traditional ceramic materials, three-dimensional (3D) porous ceramics have become a research hotspot in recent years due to combinative of light-weight and high strength. Meanwhile, the 3D printing technique, which can be used to design hierarchical porous structures by combining flexible design and advanced manufacturing procedures, is regarded as a revolutionary and attractive tool for the preparation of 3D porous ceramics. Herein, a novel road is reported for fabricating 3D porous ceramic lattices with excellent mechanical properties by bridging 3D printing and SiC chemical vapor infiltration. The effects of coordination number, rotation angle, hollow structure and sintering temperature on the performance of ceramic lattices were also investigated. As revealed by the results, the cubic lattices possess the highest compressive strength and fracture work, 41.93 MPa and 2126.7 kJ/m2, respectively. Among different hollow lattices, the stability and bearing capacity of triangular structures were superior to that of square and honeycomb structures. The compressive strength of the triangular hollow lattices can reach up to 31.20 MPa. And the fracture work of the 3D porous lattices without rotation can be 7 times that of the lattices with a rotation angle of 30° and 45°. Moreover, as the sintering temperature rises, the compressive strength of 3D porous ceramics gradually increases while the shrinkage tends to be more serious. Additionally, the fracture work of 3D porous ceramics reaches its peak at a sintering temperature of 1400 °C. The approach developed in this work provides a simple, economic, and effective way to fabricate 3D porous ceramics, which leads to promising applications in future functional devices.

The effect of strut size on microstructure and compressive strength of porous Ti6Al4V lattices printed via Direct Ink Writing

Ti6Al4V scaffolds were printed by Direct Ink Writing of a water-based polymeric ink. Different geometries were fabricated in terms of filament size (250 μm, 400 μm and 800 μm) and filament distance (half, same and double the filament size). The designed and actual porosity (total, open and closed), the linear and volumetric shrinkage as well as the microstructure of the scaffolds after sintering were analyzed. The good fitting between designed and actual values of porosity were confirmed both by He-Pycnometry and X-ray micro computed tomography measurements. Results showed that shrinkage decreased with increasing the filament distance over filament size ratio. The microstructure of the scaffolds depended on filament size, showing multiple phases formation for the smallest filament size. The compressive strength behavior was studied experimentally and by computational simulations: the discrepancy between experimental and predicted values of stress-strain compression curves were reflecting the lamellar and acicular phase formation in scaffolds with strut size smaller than 400 μm, whilst they showed a good fitting for scaffolds possessing an equiaxic microstructure.

Maximizing mechanical properties and minimizing support material of PolyJet fabricated 3D lattice structures

Anisotropy of mechanical properties and support material removal are the two main problems when fabricating 3D lattice structures by integrated printing via additive manufacturing (AM) technology. Aiming at these two problems, a snap-fit method is introduced into PolyJet technology to fabricate polymer lattice structures with four typical configurations, namely BCC, BCC-Z, FCC and octet. Printing materials and printing time in this novel method are both reduced by over 80 % compared to the conventional printing method. Uniaxial compression tests indicate that both the strengths and energy absorptions of the four kinds of snap-fitted lattices are increased by over 100 % compared to the integrated counterparts. The effect of strut thickness on compressive responses of the snap-fitted and integrated lattices is investigated. With the decrease of strut thickness, the advantage in the strength of the snap-fitted lattices becomes more obvious compared to the integrated counterparts. Ideal maximum strength models based on yielding, elastic buckling and inelastic buckling are developed and are able to predict the compressive peak strengths of the snap-fitted PolyJet lattices. This study opens up an avenue for the fabrication of large scale 3D printed lattice structures with optimal mechanical properties and without support material removal problem.

Additively manufactured biomedical Ti-Nb-Ta-Zr lattices with tunable Young's modulus: Mechanical property, biocompatibility, and proteomics analysis.

Some β-Ti alloys, such as Ti-Nb-Ta-Zr (TNTZ) alloys, exhibit a low Young's modulus and excellent biocompatibility. These alloys are promising new generation biomedical implant materials. Selective laser melting (SLM) can further enable customer-specific manufacturing of β-Ti alloys to satisfy the ever-increasing need for enhanced biomedical products. In this study, we quantitatively determined the relationships between porosity, yield strength, and Young's modulus of SLM-prepared TNTZ lattices. The study constitutes a critical step toward understanding the behavior of the lattice and eventually enables tuning the Young's modulus to match that of human bones. Fatigue properties were also investigated on as-printed lattices in terms of the stress limit. The biocompatibility study included a routine evaluation of the relative cell growth rate and a proteomics analysis using a common mouse fibroblast cell line, L929. The results indicated that the as-printed TNTZ samples exhibited evidence of protein proliferation of the L929 cells, particularly P06733, and that those proteins are responsible for biological processes and molecular functions. They in turn may have promoted cell regeneration, cell motility, and protein binding, which at least partially explains the good biocompatibility of the as-printed TNTZ at the protein level. The study highlights the promising applications of additively manufactured TNTZ as a bone-replacing material from mechanical and biocompatibility perspectives.

Mechanical performance and fatigue life prediction of lattice structures: Parametric computational approach

Additive manufacturing (AM) highly complex lattice structures with exceptional engineering properties are of special interests for a wide range of engineering applications including biomedical (implant, scaffold), automotive (shock-absorbing, load sensors) and civil engineering (protective layers). This research focuses on developing a numerical framework to predict the mechanical and fatigue properties of lattice structures with various relative densities and architectures. The relationship between geometry parameters and relative density of four lattice structures is investigated. Finite Element Analysis (FEA) is employed to simulate uniaxial compression test so that the elastic modulus and yield strength of lattices are evaluated. Parametric studies on hundred designs for each lattice are conducted to obtain associated design maps. Among the lattice structures investigated, the Simple Cubic (SC) unit cell shows the highest elastic modulus and yield strength at any relative densities, while these properties of Body Centred Cubic (BCC) unit cell is the lowest. Numerical results also reveal the nonuniform distributions of strain & plastic dissipation energy between layers, when multilayer lattice structures are subjected to compression. The fatigue property of lattice structures is also predicted numerically showing the dependence on both relative density and unit cell topology. The normalised fatigue behaviour of SC and Simple Cubic Body Centred Cubic (SC-BCC) are independent of relative density, while Face Centred Cubic (FCC) and BCC are sensitive to its relative density.