Exploring the optimal mechanical properties of triply periodic minimal surface structures for biomedical applications: A Numerical analysis

Currently, cutting-edge Additive Manufacturing techniques, such as Selective Laser Melting (SLM) and Electron Beam Melting (EBM), offer manufacturers a valuable avenue, especially in biomedical devices. These techniques produce intricate porous structures that draw inspiration from nature, boast biocompatibility, and effectively counter the adverse issues tied to solid implants, including stress shielding, cortical hypertrophy, and micromotions. Within the domain of such porous structures, Triply Periodic Minimal Surface (TPMS) configurations, specifically the Gyroid, Diamond, and Primitive designs, exhibit exceptional performance due to their bioinspired forms and remarkable mechanical and fatigue properties, outshining other porous counterparts. Consequently, they emerge as strong contenders for biomedical implants. However, assessing the mechanical properties and manufacturability of TPMS structures within the appropriate ranges of pore size, unit cell size, and porosity tailored for biomedical applications remains paramount. This study aims to scrutinize the mechanical behavior of Gyroid, Diamond, and Primitive structures in solid and sheet network iterations within the morphological parameter ranges suitable for tasks like cell seeding, vascularization, and osseointegration. A comparison with the mechanical characteristics of host bones is also undertaken. The methodology revolves around Finite Element Method (FEM) analysis. The six structures are originally modeled with unit cell sizes of 1, 1.5, 2, and 2.5 mm, and porosity levels ranging from 50% to 85%. Subsequently, mechanical properties, such as elasticity modulus and yield strength, are quantified through numerical analysis. The results underscore that implementing TPMS designs enables unit cell sizes between 1 and 2.5 mm, facilitating pore sizes within the suitable range of approximately 300-1500 μm for biomedical implants. Elasticity modulus spans from 1.5 to 33.8 GPa, while yield strength ranges around 20-304.5 MPa across the 50%-85% porosity spectrum. Generally, altering the unit cell size exhibits minimal impact on mechanical properties within the range above; however, it's noteworthy that smaller porosities correspond to heightened defects in additively manufactured structures. Thus, for an acceptable pore size range of 500-1000 μm and a minimum wall thickness of 150 μm, a prudent choice would involve adopting a 2.5 mm unit cell size.

Mechanobiological optimization of scaffolds for bone tissue engineering

Synthetic bone graft scaffolds aim to generate new bone tissue and alleviate the limitations of autografts and allografts. To meet that aim, it is essential to have a design approach able to generate scaffold architectures that will promote bone formation. Here, we present a topology-varying design optimization method, the "mixed-topology" approach, that generates new designs from a set of starting structures. This approach was used with objective functions focusing on improving the scaffold's local mechanical microenvironments to mechanobiologically promote bone formation within the scaffold and constraints to ensure manufacturability and achieve desired macroscale properties. The results demonstrate that this approach can successfully generate scaffold designs with improved microenvironments, taking into account different combinations of relevant stimuli and constraints.

Optimization of functionally graded solid-network TPMS meta-biomaterials

The current study enhances the performance of solid-network triply periodic minimal surface (TPMS) cellular materials through using cell size grading along with the Taguchi method. Cell size grading is a novel technique used to control the size of pores and the surface area without changing the relative density. In this context, experimental compression testing was conducted on six distinct geometries of cell size graded TPMS structures (Diamond, Fischer-Koch S, Gyroid, IWP, Primitive, and Schoen-F-RD) manufactured with dental resin using a masked stereolithography (MSLA) printer. The findings indicated that mean total energy absorption was greater for smaller initial cell sizes (4 and 6 mm) compared to larger sizes (12 mm). Consistent patterns were also observed with respect to final cell sizes. Upon examination of the stress-strain relationships between D and I-WP, it is evident that D exhibits a higher initial peak stress point. However, subsequent to a significant decline, it exhibits a tremendous degree of volatility before recovering. Conversely, I-WP demonstrated greater stability throughout the experiments, with a notably greater maximum stress effect. A significant influence was observed from the initial cell size on stress, with larger sizes leading to a reduction in absorbed energy. The acquired results serve as an essential basis for the identification of optimized designs that may be implemented to enhance the structures' durability.

Multi-parameter design of triply periodic minimal surface scaffolds: from geometry optimization to biomechanical simulation

This study introduces a multi-parameter design methodology to create triply periodic minimal surface (TPMS) scaffolds with predefined geometric characteristics. The level-set constant and unit cell lengths are systematically correlated with targeted porosity and minimum pore sizes. Network and sheet scaffolds featuring diamond, gyroid, and primitive level-set structures are generated. Three radially graded schemes are applied to each of the six scaffold type, accommodating radial variations in porosity and pore sizes. Computer simulations are conducted to assess the biomechanical performance of 18 scaffold models. Results disclose that diamond and gyroid scaffolds exhibit more expansive design ranges than primitive counterparts. While primitive scaffolds display the highest Young's modulus and permeability, their lower yield strength and mesenchymal stem cell (MSC) adhesion render them unsuitable for bone scaffolds. Gyroid scaffolds demonstrate superior mechanical and permeability performances, albeit with slightly lower MSC adhesion than diamond scaffolds. Sheet scaffolds, characterized by more uniform material distribution, exhibit superior mechanical performance in various directions, despite slightly lower permeability. The higher specific surface area of sheet scaffolds contributes to elevated MSC adhesion. The stimulus factor analysis also revealed the superior differentiation potential of sheet scaffolds over network ones. The diamond sheet type demonstrated the optimal differentiation. Introducing radial gradations enhances axial mechanical performance at the expense of radial mechanical performance. Radially decreasing porosity displays the highest permeability, MSC adhesion, and differentiation capability, aligning with the structural characteristics of human bones. This study underscores the crucial need to balance diverse biomechanical properties of TPMS scaffolds for bone tissue engineering.

Biomimetic Structure Hydrogel Loaded with Long-Term Storage Platelet-Rich Plasma in Diabetic Wound Repair

Exploring the preparation of multifunctional hydrogels from a bionic perspective is an appealing strategy. Here, a multifunctional hydrogel dressing inspired by the characteristics of porous extracellular matrix produced during Acomys wound healing is prepared. These dressings are printed by digital light processing printing of hydrogels composed of gelatin methacrylate, hyaluronic acid methacrylate, and pretreated platelet-rich plasma (PRP) to shape out triply periodic minimal surface structures, which are freeze-dried for long-term storage. These dressings mimic the porous extracellular matrix of Acomys, while the freeze-drying technique effectively extends the storage duration of PRP viability. Through in vivo and in vitro experiments, the biomimetic dressings developed in this study modulate cell behavior and facilitate wound healing. Consequently, this research offers a novel approach for the advancement of regenerative wound dressings.

Comparative Study of the Effective Properties of 0-3 and Gyroid Triply Periodic Minimal Surface Cement-Piezocomposites

In the present numerical simulation work, effective elastic and piezoelectric properties are calculated and a comparative study is conducted on a cement matrix-based piezocomposite with 0-3 and gyroid triply periodic minimal surface (TPMS) inclusions. The present study compares the effective properties of different piezoelectric materials having two different types of connectivity of the inclusions namely, 0-3 inclusions where the inclusions are physically separated from each other and are embedded within the matrix and the second one is TPMS inclusions having interpenetrating phase type connectivity. Effective properties are calculated for four different materials at five different volume fractions namely, 10%, 15%, 20%, 25%, and 30% volume fractions of inclusion by volume. In terms of effective properties and direct piezoelectric effect, TPMS piezocomposite is found to perform better compared to 0-3 piezocomposite. Lead-free piezoelectric material 0.5Ba(Ca0.8Zr0.2)O3 - 0.5(Ba0.7Ca0.3)TiO3 demonstrates better performance compared to all other material inclusions studied. The present study attempts to highlight improved piezoelectric effective properties of lead-free material-based piezocomposites with TPMS inclusions.

Surface Morphology, Compressive Behavior, and Energy Absorption of Graded Triply Periodic Minimal Surface 316L Steel Cellular Structures Fabricated by Laser Powder Bed Fusion

Laser powder bed fusion (LPBF) is an emerging technique for the fabrication of triply periodic minimal surface (TPMS) structures in metals. In this work, different TPMS structures such as Diamond, Gyroid, Primitive, Neovius, and Fisher-Koch S with graded relative densities are fabricated from 316L steel using LPBF. The graded TPMS samples are subjected to sandblasting to improve the surface finish before mechanical testing. Quasi-static compression tests are performed to study the deformation behavior and energy absorption capacity of TPMS structures. The results reveal superior stiffness and energy absorption capabilities for the graded TPMS samples compared to the uniform TPMS structures. The Fisher-Koch S and Primitive samples show higher strength whereas the Fisher-Koch S and Neovius samples exhibit higher elastic modulus. The Neovius type structure shows the highest energy absorption up to 50% strain among all the TPMS structures. The Gibson-Ashby coefficients are calculated for the TPMS structures, and it is found that the C₂ values are in the range suggested by Gibson and Ashby while C₁ values differ from the proposed range.

Imperfections Formation in Thin Layers of NiTi Triply Periodic Minimal Surface Lattices Fabricated Using Laser Powder Bed Fusion

In this paper, thin layers of NiTi shape memory alloy (SMA) triply periodic minimal surface lattices (TPMS) are fabricated using laser powder bed fusion (LPBF), considering different laser scanning strategies and relative densities. The obtained architected samples are studied using experimental methods to characterize their microstructural features, including the formation of cracks and balling imperfections. It is observed that balling is not only affected by the parameters of the fabrication process but also by structural characteristics, including the effective densities of the fabricated samples. In particular, it is reported here that higher densities of the TPMS geometries considered are generally associated with increased dimensions of balling imperfections. Moreover, scanning strategies at 45° angle with respect to the principal axes of the samples resulted in increased balling.

On the Effect of Lattice Topology on Mechanical Properties of SLS Additively Manufactured Sheet-, Ligament-, and Strut-Based Polymeric Metamaterials

Cellular lattices with architectural intricacy or metamaterials have gained a substantial amount of attention in the past decade due to the recent advances in additive manufacturing methods. The lattice topology controls its physical and mechanical properties; therefore, the main challenge is selecting the appropriate lattice topology for a desired function and application. In this work, we comprehensively study the topology–property relationship of three classes of polymer metamaterials based on triply periodic minimal surfaces (TPMS) of sheet/shell and ligament types, and other types of well-known strut-based lattices. The study uses a holistic approach of designing, additive manufacturing, microstructural characterization, and compressive uniaxial mechanical testing of these polymer lattices that are 3D-printed using the laser powder bed fusion technique known as selective laser sintering (SLS). In total, 55 lattices with different topologies and relative densities were 3D-printed and tested. Printing quality was assessed using scanning electron microscopy and micro-computed tomography. The extracted mechanical properties of elastic modulus, yield strength, plateau strength, and energy absorption are thoroughly compared between the different lattice architectures. The results show that all the investigated ligament-based TPMS polymer lattices exhibit bending-dominated elastic and plastic behavior, indicating that they are suitable candidates for energy absorbing applications. The sheet-based TPMS polymer lattices, similarly to the well-known Octet-Truss lattice, exhibited an elastic stretching-dominated mode of deformation and proved to have exceptional stiffness as compared to all other topologies, especially at low relative densities. However, the sheet-based TPMS polymer lattices exhibited a bending-dominated plastic behavior which is mainly driven by manufacturing defects. Overall, however, sheet-based TPMS polymer lattices exhibited the best mechanical properties, followed by strut-based lattices and finally by ligament-based TPMS lattices. Finally, it is depicted that at high relative densities, the mechanical properties of lattices of various architectures tend to converge, which implies that the topological effect is more significant at low relative densities. Generally, this study provides important insights about the selection of polymer mechanical metamaterials for various applications, and shows the superiority of TPMS-based polymer metamaterials as compared to several other classes of polymer mechanical metamaterials.

Performance Improvement of Glass Microfiber Based Thermal Transpiration Pump Using TPMS

The Knudsen pump, known as a thermal transpiration membrane, is an air inducer that has been mostly studied for small-scale power generation devices. It is a porous medium that does not require any mechanically moving component, but rather uses the temperature gradient across two surfaces of the membrane to induce air from the colder side to the hotter side. If the temperature on the colder side of the membrane is reduced by a thermal guard, the pumping performance of the membrane seems to be improved. Therefore, the membrane integrating with TPMS structures as thermal guards for both experiment and simulation were conducted in this study. The results of flow rate and temperature distribution on the membrane surface were compared. Three characteristic parameters of the membrane, i.e., area factor, pore radius and permeability, were found and can be used in an equation to estimate the air flow rate through the membrane. Diamond was found to be the highest flow improvement while Primitive was the lowest flow improvement. The simulation results with varying %RD also supported that the contact area between the TPMS structure and the membrane inlet surface made Diamond conduct more heat out from the membrane surface than other TPMS structures.

Scientometric Review for Research Patterns on Additive Manufacturing of Lattice Structures

Over the past 15 years, interest in additive manufacturing (AM) on lattice structures has significantly increased in producing 3D/4D objects. The purpose of this study is to gain a thorough grasp of the research pattern and the condition of the field's research today as well as identify obstacles towards future research. To accomplish the purpose, this work undertakes a scientometric analysis of the international research conducted on additive manufacturing for lattice structure materials published from 2002 to 2022. A total of 1290 journal articles from the Web of Science (WoS) database and 1766 journal articles from the Scopus database were found using a search system. This paper applied scientometric science, which is based on bibliometric analysis. The data were subjected to a scientometric study, which looked at the number of publications, authorship, regions by countries, keyword co-occurrence, literature coupling, and scientometric mapping. VOSviewer was used to establish research patterns, visualize maps, and identify transcendental issues. Thus, the quantitative determination of the primary research framework, papers, and themes of this research field was possible. In order to shed light on current developments in additive manufacturing for lattice structures, an extensive systematic study is provided. The scientometric analysis revealed a strong bias towards researching AM on lattice structures but little concentration on technologies that emerge from it. It also outlined its unmet research needs, which can benefit both the industry and academia. This review makes a prediction for the future, with contributions by educating researchers, manufacturers, and other experts on the current state of AM for lattice structures.

High-Throughput Optimal Design of Spacers Using Triply Periodic Minimal Surfaces in BWRO

The development of advanced feed spacers under different working conditions can enhance the performance of the reverse osmosis (RO) desalination process. The 3D-printed experimental results on triply periodic minimal surfaces (TPMS) -based spacers in previous literature indicate that the spacers have higher permeation flux of water compared to those of the common commercial spacers. In this paper, a hybrid modeling approach is developed and applied to predict and evaluate the performance of TPMS-based spacers. The effect of feed channels’ height and porosity on the performance of spacers in brackish water RO (BWRO) process is studied by using a high-throughput approach. The predicted pressure drop by new simulations using the TPMS-based spacers (≈0.09–0.27 bar) from inlet to outlet in a typical two-stage BWRO system is reduced by more than 89% than that of using the commercial spacer (≈2.57 bar). Using the designed advanced spacers, the average permeation flux of water increases more than 8.6% compared to that of the commercial one. With the increase in feed channel height and porosity, the performance of spacers is gradually improved. TPMS-based spacers have significant industrial application prospects.

Programmed Plastic Deformation in Mathematically-Designed Architected Cellular Materials

The ability to control the exhibited plastic deformation behavior of cellular materials under certain loading conditions can be harnessed to design more reliable and structurally efficient damage-tolerant materials for crashworthiness and protective equipment applications. In this work, a mathematically-based design approach is proposed to program the deformation behavior of cellular materials with minimal surface-based topologies and ductile constituent material by employing the concept of functional grading to control the local relative density of unit cells. To demonstrate the applicability of this design tactic, two examples are presented. Rhombic, and double arrow deformation profiles were programmed as the desired deformation patterns. Grayscale images were used to map the relative density distribution of the cellular material. 316L stainless steel metallic samples were fabricated using the powder bed fusion additive manufacturing technique. Results of compressive tests showed that the designed materials followed the desired programmed deformation behavior. Results of mechanical testing also showed that samples with programmed deformation exhibited higher plateau stress and toughness values as compared to their uniform counterparts while no effect on Young’s modulus was observed. Plateau stress values increased by 8.6% and 13.4% and toughness values increased by 5.6% and 11.2% for the graded-rhombic and graded-arrow patterns, respectively. Results of numerical simulations predicted the exact deformation behavior that was programmed in the samples and that were obtained experimentally.

Application of Ceramic Lattice Structures to Design Compact, High Temperature Heat Exchangers: Material and Architecture Selection

In this work, we report the design of ceramic lattices produced via additive manufacturing (AM) used to improve the overall performances of compact, high temperature heat exchangers (HXs). The lattice architecture was designed using a Kelvin cell, which provided the best compromise among effective thermal conductivity, specific surface area, dispersion coefficient and pressure loss, compared to other cell geometries. A material selection was performed considering the specific composition of the fluids and the operating temperatures of the HX, and Silicon Carbide (SiC) was identified as promising materials for the application. The 3D printing of a polymeric template combined with the replica method was chosen as the best manufacturing approach to produce SiC lattices. The heat transfer behaviour of various lattice configurations, based on the Kelvin cell, was determined through computational fluid dynamics (CFD). The results are used to discuss the application of such structures to compact high temperature HXs.