Infill Optimization for Additive Manufacturing-Approaching Bone-Like Porous Structures

Explicit Topology Optimization of Voronoi Foams

Topology optimization can maximally leverage the high DOFs and mechanical potentiality of porous foams but faces challenges in adapting to free-form outer shapes, maintaining full connectivity between adjacent foam cells, and achieving high simulation accuracy. Utilizing the concept of Voronoi tessellation may help overcome the challenges owing to its distinguished properties on highly flexible topology, natural edge connectivity, and easy shape conforming. However, a variational optimization of the so-called Voronoi foams has not yet been fully explored. In addressing the issue, a concept of explicit topology optimization of open-cell Voronoi foams is proposed that can efficiently and reliably guide the foam's topology and geometry variations under critical physical and geometric requirements. Taking the site (or seed) positions and beam radii as the DOFs, we explore the differentiability of the open-cell Voronoi foams w.r.t. its seed locations, and propose a highly efficient local finite difference method to estimate the derivatives. During the gradient-based optimization, the foam topology can change freely, and some seeds may even be pushed out of shape, which greatly alleviates the challenges of prescribing a fixed underlying grid. The foam's mechanical property is also computed with a much-improved efficiency by an order of magnitude, in comparison with benchmark FEM, via a new material-aware numerical coarsening method on its highly heterogeneous density field counterpart. We show the improved performance of our Voronoi foam in comparison with classical topology optimization approaches and demonstrate its advantages in various settings.

Generating Virtual Bone Scans for the Purpose of Investigating the Effects of Cortical Microstructure

Evaluating the contribution of microstructure to overall bone strength is tricky since it is difficult to control changes to pore structure in human or animal samples. We developed an open-source program that can generate three-dimensional (3D) models of micron-scale cortical bone. These models can be highly customized with a wide array of variable input parameters to allow for generation of samples similar to micro-computed topography scans of cortical bone or with specific geometric features. The program can generate samples with specific desired porosities and minor deviations in pore diameter from human samples: 1.67% (±4.90) using literature values, and 1.36% (±2.39) with optimized values. When coupled with finite element analysis, this open-source program could be a useful tool for evaluating stress distributions caused by microstructural changes.

Effects of Infill Patterns on the Mechanical and Tribological Behaviour of 3D-Printed Polylactic Acid/Bamboo Biocomposites for Structural Applications

Composite materials are gaining attention owing to their exemplary characteristics and, if the materials are eco-friendly, they attract much more. One such composite of poly lactic acid (PLA) combined with bamboo fiber in the ratio of 80:20 is selected for this study. The composites are manufactured using additive manufacturing, or the 3D-printing technique. In this article, a novel approach of infilling a honeycomb with around 12 infill patterns has been made, and all the 3D-printed specimens were tested for their mechanical and tribological properties. The 3D-printed composites were characterized using Fourier Transform InfraRed spectroscopy (FTIR) and X-Ray Diffraction (XRD) to evaluate their chemical composition and crystallite size (CS), respectively. Based on the results, the cross infill pattern outperforms irregular geometries like the Gyroid in terms of impact strength owing to its efficient stress distribution and superior interlayer bonding. By utilizing bidirectional reinforcement and distributing loads uniformly, the grid infill was able to attain the Shore D maximum hardness due to its strong 3D lattice structure; the Octet infill is very resistant to wear, which improves energy absorption and decreases material loss. Such honeycomb-filled 3D-printed composites can act as high-mechanical-strength components and find their applications in aerospace applications like drones and their allied structures.

A New Slicer-Based Method to Generate Infill Inspired by Sandwich-Patterns for Reduced Material Consumption

This work presents a novel infill method for additive manufacturing, specifically designed to optimize material use and enhance stiffness in fused filament fabrication (FFF) parts through a geometry-aware, corrugated design inspired by sandwich structures. Unlike standard infill patterns, which typically employ uniform, space-filling grids that often disregard load-specific requirements, this method generates a cavity inside the component to be printed and fill the space between inner and outer contours with continuous, adaptable extrusion paths. This design enables consistent support and improved load distribution, making it particularly effective for parts under bending stresses, as it enhances structural resilience without requiring additional material. Simulations performed on a 10 cm3 test part using this method showed potential reductions in material consumption by up to 77% and a decrease in print time by 78%, while maintaining stiffness comparable to parts using conventional 100% grid infill. Additionally, simulations demonstrated that the new corrugated infill pattern provides near-isotropic stiffness, addressing the anisotropic limitations often seen in traditional infill designs that are sensitive to load orientation. This geometry-aware infill strategy thus contributes to balanced stiffness across complex geometries, enhancing reliability under mechanical loads. By integrating directly with slicer software, this approach simplifies advanced stiffness optimization without the necessity of finite element analysis-based topology optimization.

Anatomically and mechanically conforming patient-specific spinal fusion cages designed by full-scale topology optimization

Cage subsidence after instrumented lumbar spinal fusion surgery remains a significant cause of treatment failure, specifically for posterior or transforaminal lumbar interbody fusion. Recent advancements in computational techniques and additive manufacturing, have enabled the development of patient-specific implants and implant optimization to specific functional targets. This study aimed to introduce a novel full-scale topology optimization formulation that takes the structural response of the adjacent bone structures into account in the optimization process. The formulation includes maximum and minimum principal strain constraints that lower strain concentrations in the adjacent vertebrae. This optimization approach resulted in anatomically and mechanically conforming spinal fusion cages. Subsidence risk was quantified in a commercial finite element solver for off-the-shelf, anatomically conforming and the optimized cages, in two representative patients. We demonstrated that the anatomically and mechanically conforming cages reduced subsidence risk by 91% compared to an off-the-shelf implant with the same footprint for a patient with normal bone quality and 54% for a patient with osteopenia. Prototypes of the optimized cage were additively manufactured and mechanically tested to evaluate the manufacturability and integrity of the design and to validate the finite element model.

In silico medical device testing of anatomically and mechanically conforming patient-specific spinal fusion cages designed by full-scale topology optimisation

A full-scale topology optimisation formulation has been developed to automate the design of cages used in instrumented transforaminal lumbar interbody fusion. The method incorporates the mechanical response of the adjacent bone structures in the optimisation process, yielding patient-specific spinal fusion cages that both anatomically and mechanically conform to the patient, effectively mitigating subsidence risk compared to generic, off-the-shelf cages and patient-specific devices. In this study, in silico medical device testing on a cohort of seven patients was performed to investigate the effectiveness of the anatomically and mechanically conforming devices using titanium and PEEK implant materials. A median reduction in the subsidence risk by 89% for titanium and 94% for PEEK implant materials was demonstrated compared to an off-the-shelf implant. A median reduction of 75% was achieved for a PEEK implant material compared to an anatomically conforming implant. A credibility assessment of the computational model used to predict the subsidence risk was provided according to the ASME V&V40-2018 standard.

Topology Optimization Via Spatially-Varying TPMS

Structural design with multi-family triply periodic minimal surfaces (TPMS) is a meaningful work that can combine the advantages of different types of TPMS. However, very few methods consider the influence of the blending of different TPMS on structural performance, and the manufacturability of final structure. Therefore, this work proposes a method to design manufacturable microstructures with topology optimization (TO) based on spatially-varying TPMS. In our method, different types of TPMS are simultaneously considered in the optimization to maximize the performance of designed microstructure. The geometric and mechanical properties of the unit cells generated with TPMS, that is minimal surface lattice cell (MSLC), are analyzed to obtain the performance of different types of TPMS. In the designed microstructure, MSLCs of different types are smoothly blended with an interpolation method. To analyze the influence of deformed MSLCs on the performance of the final structure, the blending blocks are introduced to describe the connection cases between different types of MSLCs. The mechanical properties of deformed MSLCs are analyzed and applied in TO process to reduce the influence of deformed MSLCs on the performance of final structure. The infill resolution of MSLC within a given design domain is determined according to the minimal printable wall thickness of MSLC and structural stiffness. Both numerical and physical experimental results demonstrate the effectiveness of the proposed method.

A Systematic Review on the Generation of Organic Structures through Additive Manufacturing Techniques

Additive manufacturing (AM) has emerged as a transformative technology in the fabrication of intricate structures, offering unparalleled adaptability in crafting complex geometries. Particularly noteworthy is its burgeoning significance within the realm of medical prosthetics, owing to its capacity to seamlessly replicate anatomical forms utilizing biocompatible materials. Notably, the fabrication of porous architectures stands as a cornerstone in orthopaedic prosthetic development and bone tissue engineering. Porous constructs crafted via AM exhibit meticulously adjustable pore dimensions, shapes, and porosity levels, thus rendering AM indispensable in their production. This systematic review ventures to furnish a comprehensive examination of extant research endeavours centred on the generation of porous scaffolds through additive manufacturing modalities. Its primary aim is to delineate variances among distinct techniques, materials, and structural typologies employed, with the overarching objective of scrutinizing the cutting-edge methodologies in engineering self-supported stochastic printable porous frameworks via AM, specifically for bone scaffold fabrication. Findings show that most of the structures analysed correspond to lattice structures. However, there is a strong tendency to use organic structures generated by mathematical models and printed using powder bed fusion techniques. However, no work has been found that proposes a self-supporting design for organic structures.

A Parametric Design Method for Engraving Patterns on Thin Shells

Designing thin-shell structures that are diverse, lightweight, and physically viable is a challenging task for traditional heuristic methods. To address this challenge, we present a novel parametric design framework for engraving regular, irregular, and customized patterns on thin-shell structures. Our method optimizes pattern parameters such as size and orientation, to ensure structural stiffness while minimizing material consumption. Our method is unique in that it works directly with shapes and patterns represented by functions, and can engrave patterns through simple function operations. By eliminating the need for remeshing in traditional FEM methods, our method is more computationally efficient in optimizing mechanical properties and can significantly increase the diversity of shell structure design. Quantitative evaluation confirms the convergence of the proposed method. We conduct experiments on regular, irregular, and customized patterns and present 3D printed results to demonstrate the effectiveness of our approach.

Multiscale topology optimization of pelvic bone for combined walking and running gait cycles

We propose a multiscale topology optimization procedure of pelvic bone using weighted compliance minimization. In macroscale optimization, a level set-based method is used, which gives a binary structure. In microscale optimization, cubic lattice-based homogenization is done while keeping the global geometry fixed. For the macroscale, a volume constraint equal to the volume of the pelvic bone is imposed, whereas, for the microscale, a mass constraint equal to the mass of the pelvic bone is imposed. The optimal geometries are compared with pelvic bone using different metrics and show good similarity with the same. Designed geometries are additively manufactured and experimentally tested for stiffness.

Method of computational design for additive manufacturing of hip endoprosthesis based on basic-cell concept

Endoprosthetic hip replacement is the conventional way to treat osteoarthritis or a fracture of a dysfunctional joint. Different manufacturing methods are employed to create reliable patient-specific devices with long-term performance and biocompatibility. Recently, additive manufacturing has become a promising technique for the fabrication of medical devices, because it allows to produce complex samples with various structures of pores. Moreover, the limitations of traditional fabrication methods can be avoided. It is known that a well-designed porous structure provides a better proliferation of cells, leading to improved bone remodeling. Additionally, porosity can be used to adjust the mechanical properties of designed structures. This makes the design and choice of the structure's basic cell a crucial task. This study focuses on a novel computational method, based on the basic-cell concept to design a hip endoprosthesis with an unregularly complex structure. A cube with spheroid pores was utilized as a basic cell, with each cell having its own porosity and mechanical properties. A novelty of the suggested method is in its combination of the topology optimization method and the structural design algorithm. Bending and compression cases were analyzed for a cylinder structure and two hip implants. The ability of basic-cell geometry to influence the structure's stress-strain state was shown. The relative change in the volume of the original structure and the designed cylinder structure was 6.8%. Computational assessments of a stress-strain state using the proposed method and direct modeling were carried out. The volumes of the two types of implants decreased by 9% and 11%, respectively. The maximum von Mises stress was 600 MPa in the initial design. After the algorithm application, it increased to 630 MPa for the first type of implant, while it is not changing in the second type of implant. At the same time, the load-bearing capacity of the hip endoprostheses was retained. The internal structure of the optimized implants was significantly different from the traditional designs, but better structural integrity is likely to be achieved with less material. Additionally, this method leads to time reduction both for the initial design and its variations. Moreover, it enables to produce medical implants with specific functional structures with an additive manufacturing method avoiding the constraints of traditional technologies.

Machine learning-enabled constrained multi-objective design of architected materials

Architected materials that consist of multiple subelements arranged in particular orders can demonstrate a much broader range of properties than their constituent materials. However, the rational design of these materials generally relies on experts' prior knowledge and requires painstaking effort. Here, we present a data-efficient method for the high-dimensional multi-property optimization of 3D-printed architected materials utilizing a machine learning (ML) cycle consisting of the finite element method (FEM) and 3D neural networks. Specifically, we apply our method to orthopedic implant design. Compared to uniform designs, our experience-free method designs microscale heterogeneous architectures with a biocompatible elastic modulus and higher strength. Furthermore, inspired by the knowledge learned from the neural networks, we develop machine-human synergy, adapting the ML-designed architecture to fix a macroscale, irregularly shaped animal bone defect. Such adaptation exhibits 20% higher experimental load-bearing capacity than the uniform design. Thus, our method provides a data-efficient paradigm for the fast and intelligent design of architected materials with tailored mechanical, physical, and chemical properties.

Conceptual design of compliant bone scaffolds by full-scale topology optimization

A promising new treatment for large and complex bone defects is to implant specifically designed and additively manufactured synthetic bone scaffolds. Optimizing the scaffold design can potentially improve bone in-growth and prevent under- and over-loading of the adjacent tissue. This study aims to optimize synthetic bone scaffolds over multiple-length scales using the full-scale topology optimization approach, and to assess the effectiveness of this approach as an alternative to the currently used mono- and multi-scale optimization approaches for orthopaedic applications. We present a topology optimization formulation, which is matching the scaffold's mechanical properties to the surrounding tissue in compression. The scaffold's porous structure is tuneable to achieve the desired morphological properties to enhance bone in-growth. The proposed approach is demonstrated in-silico, using PEEK, cortical bone and titanium material properties in a 2D parameter study and on 3D designs. Full-scale topology optimization indicates a design improvement of 81% compared to the multi-scale approach. Furthermore, 3D designs for PEEK and titanium are additively manufactured to test the applicability of the method. With further development, the full-scale topology optimization approach is anticipated to offer a more effective alternative for optimizing orthopaedic structures compared to the currently used multi-scale methods.

Application of Functionally Graded Shell Lattice as Infill in Additive Manufacturing

The significance of lightweight designs has become increasingly paramount due to the growing demand for sustainability. Consequently, this study aims to demonstrate the potential of utilising a functionally graded lattice as an infill structure in designing an additively manufactured bicycle crank arm to achieve construction lightness. The authors seek to determine whether functionally graded lattice structures can be effectively implemented and explore their potential real-world applications. Two aspects determine their realisations: the lack of adequate design and analysis methods and the limitations of existing additive manufacturing technology. To this end, the authors employed a relatively simple crank arm and design exploration methods for structural analysis. This approach facilitated the efficient identification of the optimal solution. A prototype was subsequently developed using fused filament fabrication for metals, enabling the production of a crank arm with the optimised infill. As a result, the authors developed a lightweight and manufacturable crank arm showing a new design and analysis method implementable in similar additively manufactured elements. The percentage increase of a stiffness-to-mass ratio of 109.6% was achieved compared to the initial design. The findings suggest that the functionally graded infill based on the lattice shell improves structural lightness and can be manufactured.

A Support-Free Infill Structure Based on Layer Construction for 3D Printing

The design of the light-weight infill structure is a hot research topic in additive manufacturing. In recent years, various infill structures have been proposed to reduce the amount of printing material. However, 3D models filled with them may have very different structural performances under different loading conditions. In addition, most of them are not self-supporting. To mitigate these issues, a novel light-weight infill structure based on the layer construction is proposed in this article. The layers of the proposed infill structure continuously and periodically transform between triangles and hexagons. The geometries of two adjacent layers are controlled to be self-supporting for different 3D printing technologies. The machine code (Gcode) of the filled 3D model is generated in the construction of the infill structure for 3D printers. That means 3D models filled with the proposed infill structure do not need an extra slicing process before printing, which is time consuming in some cases. Structural simulations and physical experiments demonstrate that our infill structure has comparable structural performance under different loading conditions. Furthermore, the relationship between the structural stiffness and the parameters of the infill structure is investigated, which will be helpful for non-professional users.

Additively manufactured metallic biomaterials

Metal additive manufacturing (AM) has led to an evolution in the design and fabrication of hard tissue substitutes, enabling personalized implants to address each patient's specific needs. In addition, internal pore architectures integrated within additively manufactured scaffolds, have provided an opportunity to further develop and engineer functional implants for better tissue integration, and long-term durability. In this review, the latest advances in different aspects of the design and manufacturing of additively manufactured metallic biomaterials are highlighted. After introducing metal AM processes, biocompatible metals adapted for integration with AM machines are presented. Then, we elaborate on the tools and approaches undertaken for the design of porous scaffold with engineered internal architecture including, topology optimization techniques, as well as unit cell patterns based on lattice networks, and triply periodic minimal surface. Here, the new possibilities brought by the functionally gradient porous structures to meet the conflicting scaffold design requirements are thoroughly discussed. Subsequently, the design constraints and physical characteristics of the additively manufactured constructs are reviewed in terms of input parameters such as design features and AM processing parameters. We assess the proposed applications of additively manufactured implants for regeneration of different tissue types and the efforts made towards their clinical translation. Finally, we conclude the review with the emerging directions and perspectives for further development of AM in the medical industry.

Additive Manufacturing of Biomaterials-Design Principles and Their Implementation

Additive manufacturing (AM, also known as 3D printing) is an advanced manufacturing technique that has enabled progress in the design and fabrication of customised or patient-specific (meta-)biomaterials and biomedical devices (e.g., implants, prosthetics, and orthotics) with complex internal microstructures and tuneable properties. In the past few decades, several design guidelines have been proposed for creating porous lattice structures, particularly for biomedical applications. Meanwhile, the capabilities of AM to fabricate a wide range of biomaterials, including metals and their alloys, polymers, and ceramics, have been exploited, offering unprecedented benefits to medical professionals and patients alike. In this review article, we provide an overview of the design principles that have been developed and used for the AM of biomaterials as well as those dealing with three major categories of biomaterials, i.e., metals (and their alloys), polymers, and ceramics. The design strategies can be categorised as: library-based design, topology optimisation, bio-inspired design, and meta-biomaterials. Recent developments related to the biomedical applications and fabrication methods of AM aimed at enhancing the quality of final 3D-printed biomaterials and improving their physical, mechanical, and biological characteristics are also highlighted. Finally, examples of 3D-printed biomaterials with tuned properties and functionalities are presented.

Investigation of Tensile Properties of Different Infill Pattern Structures of 3D-Printed PLA Polymers: Analysis and Validation Using Finite Element Analysis in ANSYS

The advancement of 3D-printing technology has ushered in a new era in the production of machine components, building materials, prototypes, and so on. In 3D-printing techniques, the infill reduces the amount of material used, thereby reducing the printing time and sustaining the aesthetics of the products. Infill patterns play a significant role in the property of the material. In this research, the mechanical properties of specimens are investigated for gyroid, rhombile, circular, truncated octahedron, and honeycomb infill structures (hexagonal). Additionally, the tensile properties of PLA 3D-printed objects concerning their infill pattern are demonstrated. The specimens were prepared with various infill patterns to determine the tensile properties. The fracture of the specimen was simulated and the maximum yield strengths for different infill structures and infill densities were determined. The results show the hexagonal pattern of infill holds remarkable mechanical properties compared with the other infill structures. Through the variation of infill density, the desired tensile strength of PLA can be obtained based on the applications and the optimal weight of the printed parts.

Efficient Representation and Optimization for TPMS-Based Porous Structures

In this approach, we present an efficient topology and geometry optimization of triply periodic minimal surfaces (TPMS) based porous shell structures, which can be represented, analyzed, optimized and stored directly using functions. The proposed framework is directly executed on functions instead of remeshing (tetrahedral/hexahedral), and this framework substantially improves the controllability and efficiency. Specifically, a valid TPMS-based porous shell structure is first constructed by function expressions. The porous shell permits continuous and smooth changes of geometry (shell thickness) and topology (porous period). The porous structures also inherit several of the advantageous properties of TPMS, such as smoothness, full connectivity (no closed hollows), and high controllability. Then, the problem of filling an object's interior region with porous shell can be formulated into a constraint optimization problem with two control parameter functions. Finally, an efficient topology and geometry optimization scheme is presented to obtain optimized scale-varying porous shell structures. In contrast to traditional heuristic methods for TPMS, our work directly optimize both the topology and geometry of TPMS-based structures. Various experiments have shown that our proposed porous structures have obvious advantages in terms of efficiency and effectiveness.

Multi-functional topology optimization of Victoria cruziana veins

The growth and development of biological tissues and organs strongly depend on the requirements of their multiple functions. Plant veins yield efficient nutrient transport and withstand various external loads. Victoria cruziana, a tropical species of the Nymphaeaceae family of water lilies, has evolved a network of three-dimensional and rugged veins, which yields a superior load-bearing capacity. However, it remains elusive how biological and mechanical factors affect their unique vein layout. In this paper, we propose a multi-functional and large-scale topology optimization method to investigate the morphomechanics of Victoria cruziana veins, which optimizes both the structural stiffness and nutrient transport efficiency. Our results suggest that increasing the branching order of radial veins improves the efficiency of nutrient delivery, and the gradient variation of circumferential vein sizes significantly contributes to the stiffness of the leaf. In the present method, we also consider the optimization of the wall thickness and the maximum layout distance of circumferential veins. Furthermore, biomimetic leaves are fabricated by using the three-dimensional printing technique to verify our theoretical findings. This work not only gains insights into the morphomechanics of Victoria cruziana veins, but also helps the design of, for example, rib-reinforced shells, slabs and dome skeletons.

Concurrent Topological Structure and Cross-Infill Angle Optimization for Material Extrusion Polymer Additive Manufacturing with Microstructure Modeling

This paper contributes a concurrent topological structure and cross-infill angle optimization method for material extrusion type additive manufacturing (AM). This method features in modeling the process-induced material anisotropy through microscopic geometric modeling obtained by scanning electron micrographs. Numerical homogenization is performed to evaluate the equivalent effective properties of the 100-percentage cross-infilled local microstructures, and by introducing fitting functions, the relationship between equivalent effective material properties and varying cross-infill angles is empirically constructed. Then, optimization problems involving cross-infill angles as design variables are formulated, including concurrent optimization formulation. Numerical and experimental studies are conducted to illustrate the effectiveness of the proposed method. Both the numerical and experimental results demonstrate that the structural stiffness obtained by our proposed method has evidently improved.

An Aggregation-Free Local Volume Fraction Formulation for Topological Design of Porous Structure

Cellular structure can possess superior mechanical properties and low density simultaneously. Additive manufacturing has experienced substantial progress in the past decades, which promotes the popularity of such bone-like structure. This paper proposes a methodology on the topological design of porous structure. For the typical technologies such as the p-norm aggregation and implicit porosity control, the violation of the maximum local volume constraint is inevitable. To this end, the primary optimization problem with bounds of local volume constraints is transformed into unconstrained programming by setting up a sequence of minimization sub-problems in terms of the augmented Lagrangian method. The approximation and algorithm using the concept of moving asymptotes is employed as the optimizer. Several numerical tests are provided to illustrate the effectiveness of the proposed approach in comparison with existing approaches. The effects of the global and local volume percentage, influence radius and mesh discretization on the final designs are investigated. In comparison to existing methods, the proposed method is capable of accurately limiting the upper bound of global and local volume fractions, which opens up new possibilities for additive manufacturing.

Optimization of structural parameters on hollow spherical cells manufactured by Fused Deposition Modeling (FDM) using Taguchi method

There is a growing need for 3D printing of polymer structures in a cost-effective way and green. This study presents an experimental approach to investigate structural parameters effects on mechanical properties of polylactic acid (PLA) hollow-sphere structures manufactured with fused deposition modeling (FDM). The mechanical behavior characteristics of square_hexagonal stacking, closed_open porosity and parallel_perpendicular compression direction compared to the direction of manufacture under quasi-static uniaxial compression are examined using Taguchi method. The S/N ratio analysis and the Analysis of Variance (ANOVA) were used to find the optimal parameters that improve the mechanical properties (Young modulus, yield strength) and to provide a significant ranking of the different parameters analyzed in this paper. It was found that the optimum level and significance of each process parameter vary for “hexagonal cells,” “open porosity” and “parallel direction.” The optimal values of the results give a Young modulus E of 90.12 MPa and a yield strength [Formula: see text] of 3 MPa. Furthermore, the experimental results further reveal that the porous structure with the loading direction that is parallel to the direction of manufacture, has a higher strength and a progressive collapse of the cells to those with a perpendicular direction.

Integrating Geometric Data into Topology Optimization via Neural Style Transfer

This research proposes a novel topology optimization method using neural style transfer to simultaneously optimize both structural performance for a given loading condition and geometric similarity for a reference design. For the neural style transfer, the convolutional layers of a pre-trained neural network extract and quantify characteristic features from the reference and input designs for optimization. The optimization analysis is evaluated as a single weighted objective function with the ability for the user to control the influence of the neural style transfer with the structural performance. As seen in architecture and consumer-facing products, the visual appeal of a design contributes to its overall value along with mechanical performance metrics. Using this method, a designer allows the tool to find the ideal compromise of these metrics. Three case studies are included to demonstrate the capabilities of this method with various loading conditions and reference designs. The structural performances of the novel designs are within 10% of the baseline without geometric reference, and the designs incorporate features in the given reference such as member size or meshed features. The performance of the proposed optimizer is compared against other optimizers without the geometric similarity constraint.

Interactive Focus+Context Rendering for Hexahedral Mesh Inspection

The visual inspection of a hexahedral mesh with respect to element quality is difficult due to clutter and occlusions that are produced when rendering all element faces or their edges simultaneously. Current approaches overcome this problem by using focus on specific elements that are then rendered opaque, and carving away all elements occluding their view. In this work, we make use of advanced GPU shader functionality to generate a focus+context rendering that highlights the elements in a selected region and simultaneously conveys the global mesh structure and deformation field. To achieve this, we propose a gradual transition from edge-based focus rendering to volumetric context rendering, by combining fragment shader-based edge and face rendering with per-pixel fragment lists. A fragment shader smoothly transitions between wireframe and face-based rendering, including focus-dependent rendering style and depth-dependent edge thickness and halos, and per-pixel fragment lists are used to blend fragments in correct visibility order. To maintain the global mesh structure in the context regions, we propose a new method to construct a sheet-based level-of-detail hierarchy and smoothly blend it with volumetric information. The user guides the exploration process by moving a lens-like hotspot. Since all operations are performed on the GPU, interactive frame rates are achieved even for large meshes.

Dual Graded Lattice Structures: Generation Framework and Mechanical Properties Characterization

Additive manufacturing (AM) enables the production of complex structured parts with tailored properties. Instead of manufacturing parts as fully solid, they can be infilled with lattice structures to optimize mechanical, thermal, and other functional properties. A lattice structure is formed by the repetition of a particular unit cell based on a defined pattern. The unit cell's geometry, relative density, and size dictate the lattice structure's properties. Where certain domains of the part require denser infill compared to other domains, the functionally graded lattice structure allows for further part optimization. This manuscript consists of two main sections. In the first section, we discussed the dual graded lattice structure (DGLS) generation framework. This framework can grade both the size and the relative density or porosity of standard and custom unit cells simultaneously as a function of the structure spatial coordinates. Popular benchmark parts from different fields were used to test the framework's efficiency against different unit cell types and grading equations. In the second part, we investigated the effect of lattice structure dual grading on mechanical properties. It was found that combining both relative density and size grading fine-tunes the compressive strength, modulus of elasticity, absorbed energy, and fracture behavior of the lattice structure.

The Micro Topology and Statistical Analysis of the Forces of Walking and Failure of an ITAP in a Femur

This paper studies the forces acting upon the Intraosseous Transcutaneous Amputation Prosthesis, ITAP, that has been designed for use in a quarter amputated femur. To design in a failure feature, utilising a safety notch, which would stop excessive stress, σ, permeating the bone causing damage to the user. To achieve this, the topology of the ITAP was studied using MATLAB and ANSYS models with a wide range of component volumes. The topology analysis identified critical materials and local maximum stresses when modelling the applied loads. This together with additive layer manufacture allows for bespoke prosthetics that can improve patient outcomes. Further research is needed to design a fully functional, failure feature that is operational when extreme loads are applied from any direction. Physical testing is needed for validation of this study. Further research is also recommended on the design so that the σ within the ITAP is less than the yield stress, σ_s, of bone when other loads are applied from running and other activities.

Design Optimization and Manufacturing of Bio-fixed tibial implants using 3D printing technology

To obtain high performance (matching, mechanical properties, and biocompatibility) of personalized biomechanical fixation-type tibial implants, three-dimensional reconstruction was performed using a combination of reverse and positive methods. The implant design was optimized using a topological optimization method, the shape-optimized B-unit structure was filled, and the performance was evaluated for implants prepared by direct forming technology of Selective Laser Melting (3D Printing). The results show obviously reduced weight of the tibial implant, increased stress and displacement, yet with a more uniform distribution. The mechanical properties of the tibial implant were lower than those of the B-units, the weight was lighter, and the stress distribution was more uniform. The surface of the tibial implants prepared by SLM appeared clean and bright, the metal texture was good, the structure between the porous struts was clear, the surface had low powder adhesion, the lap joint was good, and no obvious warping deformation or forming defects were observed. The results of this study provide a foundation for the direct application of high performance personalized biofixation implants.

Design and Optimization of Conforming Lattice Structures

Inspired by natural cellular materials such as trabecular bone, lattice structures have been developed as a new type of lightweight material. In this paper we present a novel method to design lattice structures that conform with both the principal stress directions and the boundary of the optimized shape. Our method consists of two major steps: the first optimizes concurrently the shape (including its topology) and the distribution of orthotropic lattice materials inside the shape to maximize stiffness under application-specific external loads; the second takes the optimized configuration (i.e., locally-defined orientation, porosity, and anisotropy) of lattice materials from the previous step, and extracts a globally consistent lattice structure by field-aligned parameterization. Our approach is robust and works for both 2D planar and 3D volumetric domains. Numerical results and physical verifications demonstrate remarkable structural properties of conforming lattice structures generated by our method.

Enabling intensification of multiphase chemical processes with additive manufacturing

Fixed bed supports of various materials (metal, ceramic, polymer) and geometries are used to enhance the performance of many unit operations in chemical processes. Consider first metal and ceramic monolith support structures, which are typically extruded. Extruded monoliths contain regular, parallel channels enabling high throughput because of the low pressure drop accompanying high flow rate. However, extruded channels have a low surface-area-to-volume ratio resulting in low contact between the fluid phase and the support. Additive manufacturing, also referred to as three dimensional printing (3DP), can be used to overcome these disadvantages by offering precise control over key design parameters of the fixed bed including material-of-construction and total bed surface area, as well as accommodating system integration features compatible with continuous flow chemistry. These design parameters together with optimized extrinsic process conditions can be tuned to prepare customizable separation and reaction systems based on objectives for chemical process and/or the desired product. We discuss key elements of leveraging the flexibility of additive manufacturing to intensification with a focus on applications in continuous flow processes and disperse, multiphase systems enabling a range of scalable chemistry spanning discovery to manufacturing operations.

Strong 3D Printing by TPMS Injection

3D printed objects are rapidly becoming prevalent in science, technology and daily life. An important question is how to obtain strong and durable 3D models using standard printing techniques. This question is often translated to computing smartly designed interior structures that provide strong support and yield resistant 3D models. In this paper we suggest a combination between 3D printing and material injection to achieve strong 3D printed objects. We utilize triply periodic minimal surfaces (TPMS) to define novel interior support structures. TPMS are closed form and can be computed in a simple and straightforward manner. Since TPMS are smooth and connected, we utilize them to define channels that adequately distribute injected materials in the shape interior. To account for weak regions, TPMS channels are locally optimized according to the shape stress field. After the object is printed, we simply inject the TPMS channels with materials that solidify and yield a strong inner structure that supports the shape. Our method allows injecting a wide range of materials in an object interior in a fast and easy manner. Results demonstrate the efficiency of strong printing by combining 3D printing and injection together.

Design and Optimization of Lattice Structures: A Review

Cellular structures consist of foams, honeycombs, and lattices. Lattices have many outstanding properties over foams and honeycombs, such as lightweight, high strength, absorbing energy, and reducing vibration, which has been extensively studied and concerned. Because of excellent properties, lattice structures have been widely used in aviation, bio-engineering, automation, and other industrial fields. In particular, the application of additive manufacturing (AM) technology used for fabricating lattice structures has pushed the development of designing lattice structures to a new stage and made a breakthrough progress. By searching a large number of research literature, the primary work of this paper reviews the lattice structures. First, based on the introductions about lattices of literature, the definition and classification of lattice structures are concluded. Lattice structures are divided into two general categories in this paper: uniform and non-uniform. Second, the performance and application of lattice structures are introduced in detail. In addition, the fabricating methods of lattice structures, i.e., traditional processing and additive manufacturing, are evaluated. Third, for uniform lattice structures, the main concern during design is to develop highly functional unit cells, which in this paper is summarized as three different methods, i.e., geometric unit cell based, mathematical algorithm generated, and topology optimization. Forth, non-uniform lattice structures are reviewed from two aspects of gradient and topology optimization. These methods include Voronoi-tessellation, size gradient method (SGM), size matching and scaling (SMS), and homogenization, optimization, and construction (HOC). Finally, the future development of lattice structures is prospected from different aspects.

Digital biofabrication to realize the potentials of plant roots for product design

Technological and economic opportunities, alongside the apparent ecological benefits, point to biodesign as a new industrial paradigm for the fabrication of products in the twenty-first century. The presented work studies plant roots as a biodesign material in the fabrication of self-supported 3D structures, where the biologically and digitally designed materials provide each other with structural stability. Taking a material-driven design approach, we present our systematic tinkering activities with plant roots to better understand and anticipate their responsive behaviour. These helped us to identify the key design parameters and advance the unique potential of plant roots to bind discrete porous structures. We illustrate this binding potential of plant roots with a hybrid 3D object, for which plant roots connect 600 computationally designed, optimized, and fabricated bioplastic beads into a low stool.

Multilevel Design for the Interior of 3D Fabrications

This article presents a multilevel design for infill patterns. The method partitions an input model into subareas and each subarea are applied with different scales of infill patterns. The number of subareas can be decided by users. For each subarea, there are different values of the scaling parameter that determines the number of columns and rows of pattern elements, which is useful to change the weight and strength of a certain area by user demands. Subareas can be symmetric or asymmetric to each other depending on the geometry of a 3D model and the application requirements. In each subarea, there are generated symmetric patterns. The proposed method is also applicable to combining different patterns. The aim of our work is to create lightweight 3D fabrications with lighter interior structures to minimize printing materials and supplementary to strengthen thin parts of objects. Our approach allows for the composition of sparse and dense distributions of patterns of interior 3D fabrications in an efficient way so users can fabricate their own 3D designs.

New aspects of the trabecular bone remodeling regulatory model resulting from the shape optimization studies

The trabecular bone can adapt its form to mechanical loads and form structures that are both lightweight and very stiff. In this sense, it is a problem similar to structural optimization, especially topology optimization. The natural phenomenon leading to mechanical optimization of the bone structures is called trabecular bone remodeling. The main assumption and the benchmark for the numerical models of the phenomenon is the observation that the strain energy density on the structural surface is constant. This constant value corresponds to the homeostatic strain energy density, the state of bone tissue with a perfect balance of the loss, and gain of the bone mass. We assumed that the trabecular bone can form an optimal structure. The idea behind the investigation is to carry out studies on the ground of mechanics and to interpret clinical observations in the context of the results obtained from the optimization studies. In this way, clinical observations have been confirmed by strict arguments based on mechanics, leading to the unequivocal conclusion that equalization of the strain energy density on the trabecular bone surface allows minimizing the strain energy in the whole structure of the bone. This proves the veracity of the assumption that the remodeling process leads to the formation of the structure with the highest stiffness. In addition, this article elaborates on two new aspects of the remodeling phenomenon resulting directly from the considerations in the field of shape optimization important for numerical simulation. The first one concerns the influence of surface curvature on the remodeling process. The second one concerns the role of the bone surface where different loads are analyzed. Both aspects show the need of actual trabecular bone geometry model for the simulation of the trabecular bone remodeling phenomenon.

Personalized Design of Functional Gradient Bone Tissue Engineering Scaffold

The porous structure of the natural bone not only has the characteristics of lightweight and high strength, but also is conducive to the growth of cells and tissues due to interconnected pores. In this paper, a novel gradient-controlled parametric modeling technology is presented to design bone tissue engineering (BTE) scaffold. First of all, the method functionalizes the pore distribution in the bone tissue, and reconstructs the pore distribution of the bone tissue in combination with the pathological analysis of the bone defect area of the individual patient. Then, based on the reconstructed pore distribution, the Voronoi segmentation algorithm and the contour interface optimization method are used to reconstruct the whole model of the bone tissue. Finally, the mechanical properties of the scaffold are studied by the finite element analysis (FEA) of different density gradient scaffolds. The results show that the method is highly feasible. BTE scaffold can be designed by irregular design methods and adjustment of pore distribution parameters, which is similar with natural bone in structural characteristics and biomechanical properties.

Parametric Modeling of Biomimetic Cortical Bone Microstructure for Additive Manufacturing

In this work we present a novel algorithm for generating in-silico biomimetic models of a cortical bone microstructure towards manufacturing biomimetic bone via additive manufacturing. The software provides a tool for physicians or biomedical engineers to develop models of cortical bone that include the inherent complexity of the microstructure. The correspondence of the produced virtual prototypes with natural bone tissue was assessed experimentally employing Digital Light Processing (DLP) of a thermoset polymer resin to recreate healthy and osteoporotic bone tissue microstructure. The proposed tool was successfully implemented to develop cortical bone structure based on osteon density, cement line thickness, and the Haversian and Volkmann channels to produce a user-designated bone porosity that matches within values reported from literature for these types of tissues. Characterization of the specimens using a Scanning Electron Microscopy with Focused Ion Beam (SEM/FIB) and Computer Tomography (CT) revealed that the manufacturability of intricated virtual prototype is possible for scaled-up versions of the tissue. Modeling based on the density, inclination and size range of the osteon and Haversian and Volkmann´s canals granted the development of a dynamic in-silico porosity (13.37⁻21.49%) that matches with models of healthy and osteoporotic bone. Correspondence of the designed porosity with the manufactured assessment (5.79⁻16.16%) shows that the introduced methodology is a step towards the development of more refined and lifelike porous structures such as cortical bone. Further research is required for validation of the proposed methodology model of the real bone tissue and as a patient-specific customization tool of synthetic bone.

Mechanical performance of additively manufactured meta-biomaterials

Additive manufacturing (AM) (=3D printing) and rational design techniques have enabled development of meta-biomaterials with unprecedented combinations of mechanical, mass transport, and biological properties. Such meta-biomaterials are usually topologically ordered and are designed by repeating a number of regular unit cells in different directions to create a lattice structure. Establishing accurate topology-property relationships is of critical importance for these materials. In this paper, we specifically focus on AM metallic meta-biomaterials aimed for application as bone substitutes and orthopaedic implants and review the currently available evidence regarding their mechanical performance under quasi-static and cyclic loading conditions. The topology-property relationships are reviewed for regular beam-based lattice structures, sheet-based lattice structures including those based on triply periodic minimal surface, and graded designs. The predictive models used for establishing the topology-property relationships including analytical and computational models are covered as well. Moreover, we present an overview of the effects of the AM processes, material type, tissue regeneration, biodegradation, surface bio-functionalization, post-manufacturing (heat) treatments, and loading profiles on the quasi-static mechanical properties and fatigue behavior of AM meta-biomaterials. AM meta-biomaterials exhibiting unusual mechanical properties such as negative Poisson's ratios (auxetic meta-biomaterials), shape memory behavior, and superelasitcity as well as the potential applications of such unusual behaviors (e.g. deployable implants) are presented too. The paper concludes with some suggestions for future research. STATEMENT OF SIGNIFICANCE: Additive manufacturing enables fabrication of meta-biomaterials with rare combinations of topological, mechanical, and mass transport properties. Given that the micro-scale topological design determines the macro-scale properties of meta-biomaterials, establishing topology-property relationships is the central research question when rationally designing meta-biomaterials. The interest in understanding the relationship between the topological design and material type on the one hand and the mechanical properties and fatigue behavior of meta-biomaterials on the other hand is currently booming. This paper presents and critically evaluates the most important trends and findings in this area with a special focus on the metallic biomaterials used for skeletal applications to enable researchers better understand the current state-of-the-art and to guide the design of future research projects.

Additively manufactured porous metallic biomaterials

Additively manufactured (AM, =3D printed) porous metallic biomaterials with topologically ordered unit cells have created a lot of excitement and are currently receiving a lot of attention given their great potential for improving bone tissue regeneration and preventing implant-associated infections.

A review of the design methods of complex topology structures for 3D printing

As a matter of fact, most natural structures are complex topology structures with intricate holes or irregular surface morphology. These structures can be used as lightweight infill, porous scaffold, energy absorber or micro-reactor. With the rapid advancement of 3D printing, the complex topology structures can now be efficiently and accurately fabricated by stacking layered materials. The novel manufacturing technology and application background put forward new demands and challenges to the current design methodologies of complex topology structures. In this paper, a brief review on the development of recent complex topology structure design methods was provided; meanwhile, the limitations of existing methods and future work are also discussed in the end.