Additive Manufactured Lattice Structures Research Articles

Predicting fatigue life of additively manufactured lattice structures using the image-based Finite Cell Method and average strain energy density

A well-known Achilles' heel of laser powder bed fusion (L-PBF) additive manufactured lattice structures is the difficulty in predicting fatigue properties. The presence of manufacturing-induced defects significantly affects the fatigue resistance of the porous component and must be accurately captured by predictive models. To tackle this challenge, the as-built geometry of the lattice needs to be modeled, which introduces another challenge on the computational front. For the first time, a model based on the computer tomography (μ-CT) reconstruction of the as-built lattice geometry is simulated with the efficient finite cell method and combined with the average strain energy density (ASED) to obtain accurate fatigue predictions. This work presents a workflow for determining the fatigue resistance of lattice metamaterial, followed by a case study for method validation. The validation shows a good agreement between the predicted fatigue life and the experimental results.

Machine learning approaches for predicting mechanical properties in additive manufactured lattice structures

This study examines the mechanical performance of various lattice structures, highlighting the roles of geometric configurations, material properties, and processing conditions. Through advance feature importance analysis and correlation heatmaps, key determinants of mechanical behaviour such as lattice volume, surface roughness, micro-Vickers hardness, and lattice dimensions are identified. The findings reveal that lattice volume and surface roughness are the most significant predictors of displacement, accounting for 24.29 % and 23.71 % of the predictive power, respectively. An inverse relationship between micro-Vickers hardness and displacement emphasizes the need for material hardness optimization in design processes. Scatterplot analyses show complex interactions between surface roughness and micro-Vickers hardness across different conditions. Gyroid and BCC lattices exhibit inverse linear trends, while honeycomb and diamond display distinct linear and horizontal patterns, respectively. These complexities necessitate advanced analytical techniques like machine learning to capture and predict the mechanical behaviours of lattice structures effectively. Machine learning’s ability to handle high-dimensional data and identify non-linear relationships is crucial for accurate predictive models. The study also assesses the impact of post-processing conditions, indicating that stress relief and heat treatment enhances structural integrity and optimizes the material microstructure. This research provides a framework for designing and optimizing lattice structures, guiding informed decisions to meet performance standards.

Twist design of lattice structure fabricated by powder bed fusion to adjust the energy absorption behavior

Additive manufactured lattice structures offer great potential for impact resistance applications. They exhibit excellent energy absorption characteristics during the elasto-plastic deformation process, providing protection to internal devices. However, the mechanical response of lattice structures undergoes substantial variations during the deformation process, thereby imposing limitations on their energy absorption behavior. This study introduces a novel twist design to modify the energy absorption behavior of rectangular and hollow cylindrical lattice structures. Powder bed fusion was used to fabricate the twisted lattice structures. The study employed a combination of compressive simulations and experimental investigations to systematically explore the impact of the twist angle on the peak crushing force, energy absorption, and crash load efficiency of the structures. Adjusting the twist angle results in a reduction of the peak crushing force and a transition towards a stable loading profile during the deformation process. Moreover, the crash load efficiency is also reduced. The twist design concept presented in this paper provides insight into designing and optimizing lattice structures for energy absorption applications.

Stress-driven generative design and numerical assessment of customized additive manufactured lattice structures

The rise of additive manufacturing (AM) has positioned lattice infilling as a pivotal strategy for creating lightweight, customized engineering components. This study presents a generative method that enables the conformal design and stiffness prediction of complex gradient strut-node lattice structures. A stress-driven Multi-Agent System (MAS) is introduced for the parametric optimization of lattice material distribution, incorporating geometric limitations, stress factors, and AM constraints. A beam element model simplifies the numerical analysis of the structure linear stiffness. By applying the Response Surface Method (RSM), a numerical model is established, not only conducting a quantitative analysis on the sensitivity of MAS design variables but predicting mechanical performance. This method is validated by designing a supporting component, demonstrating that the optimized lattice design can achieve a linear stiffness 1.4 times greater than that of conventional uniform lattice infills for the same mass. This research provides a comprehensive framework for the efficient design and analysis of irregular lattice structures at a macroscopic scale.

Novel optimal design-making model of additive manufactured lattice structures based on mechanical physical model

Biostructure-inspired design methods play an important role in improving the mechanical properties of lattice structures with the same volume fraction. However, the current biostructure-inspired design methods mostly stay in the imitation of physical form/structure, and the natural evolution mechanism of biological structure is not clear in the optimization strategy of lattice structure. Combined with the fact that the zero-value average curvature of the minimal surface follows the Principle of Least Action (PLA), a new mechanical design strategy is proposed in this paper. Firstly, the mechanical model of BCC is solved. Furthermore, the physical model descripting the mechanical properties of lattice structures is solved equivalently, which shows that the regulation of mechanical properties of lattice structures can be more intuitively understood as the extreme motion for the pellet under various influencing factors. Moreover, the new design strategy for the mechanical properties of lattice structures is solved based on PLA. Finally, serials of BCC lattice structures are gained through node radius optimization. Then, the curvature characteristics and mechanical properties of optimized BCC structure are explored by means of simulation and experiment. The results show that the proposed design strategy has obvious effect in improving mechanical properties and provides a theoretical basis and technical route for the development of multiphysics applications of lattice structures.

Design Strategies towards the Optimization of 3D Additive Manufactured Lattice Structures

Additive manufacturing (AM) techniques are based on the process of joining materials, layer upon layer, differently from subtractive manufacturing methods. The design for AM allows for the creation of complex shapes as well as for the improvement of the performance of critical components in several fields, spanning from aerospace and automotive to biomedical applications. On the other hand, unlike man-made high load-bearing capacity devices, which are usually dense solids, nature uses mesoscopic or microscopic cellular structures as a fundamental support for the design. The increasing applications of AM in industrial production have led to product reimagination from a novel standpoint, enabling the fabrication of advanced lattice structures using polymer-based materials. Over the past few years, many efforts have been made to develop strategies for finding the design which is best suited to the requirements. In the current research, specific design scenarios were explored, the aim being to develop novel lattice structures for energy absorption, using an AM technique (i.e., fused deposition modelling) and a modified Acrylonitrile Styrene Acrylate (ASA)-based material. The fabricated structures were preliminarily analysed by means of compression tests.

A Hybrid Data-Driven Metaheuristic Framework to Optimize Strain of Lattice Structures Proceeded by Additive Manufacturing.

This research is centered on optimizing the mechanical properties of additively manufactured (AM) lattice structures via strain optimization by controlling different design and process parameters such as stress, unit cell size, total height, width, and relative density. In this regard, numerous topologies, including sea urchin (open cell) structure, honeycomb, and Kelvin structures simple, round, and crossbar (2 × 2), were considered that were fabricated using different materials such as plastics (PLA, PA12), metal (316L stainless steel), and polymer (thiol-ene) via numerous AM technologies, including stereolithography (SLA), multijet fusion (MJF), fused deposition modeling (FDM), direct metal laser sintering (DMLS), and selective laser melting (SLM). The developed deep-learning-driven genetic metaheuristic algorithm was able to achieve a particular strain value for a considered topology of the lattice structure by controlling the considered input parameters. For instance, in order to achieve a strain value of 2.8 × 10-6 mm/mm for the sea urchin structure, the developed model suggests the optimal stress (11.9 MPa), unit cell size (11.4 mm), total height (42.5 mm), breadth (8.7 mm), width (17.29 mm), and relative density (6.67%). Similarly, these parameters were controlled to optimize the strain for other investigated lattice structures. This framework can be helpful in designing various AM lattice structures of desired mechanical qualities.

Multi-Objective Parametric Shape Optimisation of Body-Centred Cubic Lattice Structures for Additive Manufacturing

There has been significant interest in additively manufactured lattice structures in recent years due to their enhanced mechanical and multi-physics properties, making them suitable candidates for various applications. This study presents a multi-parameter implicit equation model for designing body-centred cubic (BCC) lattice structures. The model is used in conjunction with a multi-objective genetic algorithm (MOGA) approach to maximise the stiffness of the BCC lattice structure while minimising von-Mises stress within the structure under a specific loading condition. The selected design from the MOGA at a specific lattice density is compared with the classical BCC lattice structure and the designs generated by a single-objective genetic algorithm, which focuses on maximising stiffness or minimising von-Mises stress alone. By conducting a finite element analysis on the optimised samples and performing mechanical testing on the corresponding 3D-printed specimens, it was observed that the optimised lattice structures exhibited a substantial improvement in mechanical performance compared to the classical BCC model. The suitability of multi-objective and single-objective optimisation approaches for designing lattice structures was further investigated by comparing the corresponding designs in terms of their stiffness and maximum von-Mises stress values. The results from the numerical analysis and experimental testing demonstrate the significance of the application of an appropriate optimisation strategy for designing lattice structures for additive manufacturing.

G-Puzzle: Infilling 3D Models With Reinforced G-Lattices

Abstract G-Lattices (proposed by Armanfar and Gunpinar) are a group of novel periodic and strut-based lattice structures for additive manufacturing. It has been demonstrated that these structures have superior mechanical properties under compression compared to conventional lattice structures. This paper introduces an extension of G-Lattices (i.e., reinforced G-Lattices) that also have better mechanical performance under inclined (compression) loading conditions. For different inclined loads, separate reinforced G-Lattices are first optimized, and a G-Lattice library is formed. For a part under loading, displacement vectors in each unit cell (cubic domains within the inner region of the part) are then extracted. Based on these vectors, (pre-optimized) reinforced G-Lattices are selected from the G-Lattice library and utilized (as infills) in the unit cells. This process is called G-Puzzling. As a proof of concept, parts under three different inclined loading conditions are infilled using reinforced G-Lattices and investigated based on stiffness-over-volume ratios. According to these experiments, the resulting parts, on average, exhibit more than 30% better mechanical performance compared to FBCCZ (a conventional lattice structure).

Topology optimization of fibre reinforced polymer lattice structures for additive manufacturing

The material anisotropy induced by the related additive manufacturing (AM) extrusion process and the geometric errors introduced into the unit lattices by the stair-stepping artifacts were coupled in the topology optimization model to ensure the accuracy and reliability of the optimal design for the fibre reinforced polymer lattice structures. The material properties of the 3D printed carbon fibre reinforced polymers (CFRP) were firstly systematically investigated by extensive tensile tests aided by the digital image correlation (DIC) system, through which the microscale material anisotropy was clarified. Moreover, the accurate orthotropic material models were introduced into the as-fabricated mesoscale unit lattices with geometric errors to obtain the effective mechanical properties. Finally, mechanical performance of the macroscale structures was optimized by the integration of the ideal and as-fabricated unit lattices with the homogenization-based topology optimization method. The AM process-induced material anisotropy and geometric errors result in significant deviations of the mechanical property of the topologically optimized macrostructures and more accurate topology optimization results can be achieved considering the microscale material anisotropy and the geometric error in the mesoscale unit lattice. The results obtained in this investigation indicate that it is essential to comprehensively consider the AM process-induced microscale material anisotropy and mesoscale geometric errors in the topology optimization of fibre reinforced polymer lattice structures to improve the accuracy and reliability of the optimal design.

Mechanical Characterisation and Simulation of the Tensile Behaviour of Polymeric Additively Manufactured Lattice Structures

BackgroundThe mechanical properties of lattice structures have been primarily investigated using uniaxial compression loads. Particularly for polymers, tensile properties are rarely considered because of the difficulties of defining a suitable specimen design in which the fracture occurs within the gauge length.ObjectiveThis work proposes a novel formulation to obtain a specimen for the tensile test with a gradation of the lattice density at the interface with the bulk portion, which realises a uniform stress distribution. The aim is to combine a localisation of the fracture in the gauge length with a specimen geometry accomplishing the EN ISO 527 standard and analyse the correlation between the mechanical performance and the defects induced by the process on such thin structures.MethodsThe formulation is experimentally and numerically (FEM) tested by designed specimens with different cell topology, cell size, strut diameter, and number of cells in the sample thickness. Also, results from uniaxial compression tests are used to validate the tensile properties. The specimens are manufactured in different orientations in the building volume by laser powder bed fusion with Polyamide 12. The effects of the pores morphology, distribution, and inherent anisotropy are investigated using X-ray computed tomography analysis. This data is also used to tune a numerical model.ResultsThe numerical analysis showed a uniform stress distribution; experimentally, the fracture is localised inside the gauge length in respect of the ISO standard. Remarkably, among the different strut-based architectures, the elongation at break is, in the best case, 50% of the corresponding bulk material, while the tensile strengths are comparable. Vertical printed specimens exhibited a slight decrease in tensile strength, and the elongation at break was lower than 50% compared to the counterparts built along the horizontal orientation. Modifying the numerical model according to process-related dimensional deviations between the actual and the nominal structures significantly improved the numerical results. The remaining deviation highlighted the incorrectness of modelling the lattice material from the bulk properties.ConclusionDensity gradation is a reliable approach for describing the tensile behaviour of polymeric lattice structures. However, the lower amount of porosity and the different shape in the lattice led to a different material mechanical performance with respect to the corresponding bulk counterpart. Therefore, for polymeric lattice structures, the relationship between process-design-material appears crucial for correctly representing the structure behaviour.

Data-driven XGBoost model for maximum stress prediction of additive manufactured lattice structures

Lattice structures created using additive manufacturing technology inevitably produce inherent defects that seriously affect their mechanical properties. Predicting and analysing the effect of defects on the maximum stress is very important for improving the lattice structure design and process. This study mainly used the finite element method to calculate the lattice structure constitutive equation. The increase in defect type and quantity leads to difficulty in modelling and reduces calculation accuracy. We established a data-driven extreme gradient enhancement (XGBoost) with hyperparameter optimization to predict the maximum stress of the lattice structure in additive manufacturing. We used four types of defect characteristics that affect the mechanical properties—the number of layers, thick-dominated struts (oversize), thin-dominated struts (undersizing), and bend-dominated struts (waviness)—as the input parameters of the model. The hyperparameters of the basic XGBoost model were optimised according to the diversity of the inherent defect characteristics of the lattice structure, while the parameters selected by experience were replaced using the Gaussian process method in Bayesian optimization to improve the model’s generalisation ability. The prediction datasets included the type and number of defects obtained via computer tomography and the calculation results of the finite element model with the corresponding defects implanted. The root mean square error and R-squared error of the maximum stress prediction were 17.40 and 0.82, respectively, indicating the effectiveness of the model proposed in this paper. Furthermore, we discussed the influence of the four types of defects on the maximum stress, among which the thick strut defect had the greatest influence.

Imperfections and computational modeling of lattice structures developed through powder bed fusion – A short review

Additive manufactured lattice structures (AMLS) are widely preferred for a variety of engineering applications because they offer superior performance over traditional structures. AMLS are not error-free, and therefore estimating their mechanical properties with decent computational accuracy remains a challenge that can be eliminated by including the errors in the CAD model. A typical numerical analysis begins with the development of an idealized computational model, neglecting manufacturing errors such as strut surface imperfections, strut waviness, and variances in strut diameter, leading to oversimplification. Likewise, the inclusion of defects in the computational model creates complex finite element meshes, increasing the level of complexity of the analysis and limiting the number of unit cells used to develop the model, emphasizing the need for a simplified model to include the induced defects will the manufacturing process into the lattice structures. This review article presents different strategies adopted to develop computational models with a range of manufacturing errors for finite element analysis, and the results are compared to an idealized model to estimate the deformation properties with a higher degree of accuracy and correlations to experiments.

A virtual stylus method for non-destructive roughness profile measurement of additive manufactured lattice structures

Surface roughness is traditionally evaluated with contact profilometry; however, these methods are not compatible with complex additive manufactured lattice structures due to limited physical access. For these scenarios, computed tomography (CT) is often used to provide qualitative insight into surface roughness but does not directly yield roughness profile data. This research describes a hybrid approach for the non-destructive quantification of roughness profile data for lattice structures based on the mathematical reconstruction and interpretation of CT data. Formal analyses are applied to propose the theoretical minimum CT voxel size required to characterise surface roughness for a specified sampling length. The method is verified against optical data for nominally flat metallic specimens and applied to metallic and polymeric cylinders fabricated by powder bed fusion and material extrusion respectively. This research also assesses the influence of CT reconstruction thresholding as a process variable and finds that roughness profile data is only weakly influenced by thresholding settings, due to scattering effects at the surface — a novel finding that provides certainty for the industrial application of this method. The ability of the proposed method to accurately characterise the inherent surface roughness of these processes as well as the effect of specimen orientation is thus demonstrated, enabling full geometric characterisation supporting subsequent certification analysis. The method can be algorithmically implemented in combination with the generative design of complex lattice structures to support structural certification requirements.

Effects of Pore Size Parameters of Titanium Additively Manufactured Lattice Structures on the Osseointegration Process in Orthopedic Applications: A Comprehensive Review

Architected materials are increasingly applied in form of lattice structures to biomedical implant design for the purpose of optimizing the implant’s biomechanical properties. Since the porous design of the lattice structures affects the resulting properties of the implant, its parameters are being investigated by numerous research articles. The design-related parameters of the unit cells for a strut-architected material are mainly the pore size and the strut thickness. Until today, researchers have not been able to decide on the perfect values of the unit cell parameters for the osseointegration process and tissue regeneration. Based on in vivo and in vitro experiments conducted in the field, researchers have suggested a range of values for the parameters of the lattice structures where osseointegration is in acceptable status. The present study presents a comprehensive review of the research carried out until today, experimenting and proposing the optimum unit cell parameters to generate the most suitable lattice structure for the osseointegration procedure presented in orthopedic applications. Additional recommendations, research gaps, and instructions to improve the selection process of the unit cell parameters are also discussed.

Evaluating the Stress-Strain Relationship of the Additively Manufactured Lattice Structures.

Extensive amount of research on additively manufactured (AM) lattice structures has been made to develop a generalized model that can interpret how strongly operational variables affect mechanical properties. However, the currently used techniques such as physics models and multi-physics simulations provide a specific interpretation of those qualities, and are not general enough to assess the mechanical properties of AM lattice structures of different topologies produced on different materials via several fabrication methods. To tackle this problem, this study develops an optimal deep learning (DL) model based on more than 4000 data points, which has been optimized by analyzing three different hyper-parameters optimization schemes including gradient boost regression trees (GBRT), gaussian process (GP), and random forest (RF) with different data distribution schemes such as normal distribution, nth root transformation, and robust scaler. With the robust scaler and nth root transformation, the accuracy of the model increases from R2 = 0.85 (for simple distribution) to R2 = 0.94 and R2 = 0.88, respectively. After feature engineering and data correlation, the stress, unit cell size, total height, width, and relative density are chosen to be the input parameters to model the strain. The optimal DL model is able to predict the strain of different topologies of lattices (such as circular, octagonal, Gyroid, truncated cube, Truncated cuboctahedron, Rhombic do-decahedron, and many others) with decent accuracy (R2 = 0.936, MAE = 0.05, and MSE = 0.025). The parametric sensitivity analysis and explainable artificial intelligence (by using DeepSHAP library) based insights confirm that stress is the most sensitive input to the strain followed by the relative density from the modeling perspective of the AM lattices. The findings of this study would be helpful for the industry and the researchers to design AM lattice structures of different topologies for various engineering applications.

LPBF Manufactured Functionally Graded Lattice Structures Obtained by Graded Density and Hybrid Poisson's Ratio.

The additive manufacturing (AM) of innovative lattice structures with unique mechanical properties has received widespread attention due to the capability of AM processes to fabricate freeform and intricate structures. The most common way to characterize the additively manufactured lattice structures is via the uniaxial compression test. However, although there are many applications for which lattice structures are designed for bending (e.g., sandwich panels cores and some medical implants), limited attention has been paid toward investigating the flexural behavior of metallic AM lattice structures with tunable internal architectures. The purpose of this study was to experimentally investigate the flexural behavior of AM Ti-6Al-4V lattice structures with graded density and hybrid Poisson’s ratio (PR). Four configurations of lattice structure beams with positive, negative, hybrid PR, and a novel hybrid PR with graded density were manufactured via the laser powder bed fusion (LPBF) AM process and tested under four-point bending. The manufacturability, microstructure, micro-hardness, and flexural properties of the lattices were evaluated. During the bending tests, different failure mechanisms were observed, which were highly dependent on the type of lattice geometry. The best response in terms of absorbed energy was obtained for the functionally graded hybrid PR (FGHPR) structure. Both the FGHPR and hybrid PR (HPR) structured showed a 78.7% and 62.9% increase in the absorbed energy, respectively, compared to the positive PR (PPR) structure. This highlights the great potential for FGHPR lattices to be used in protective devices, load-bearing medical implants, and energy-absorbing applications.

Deep learning-based X-ray computed tomography image reconstruction and prediction of compression behavior of 3D printed lattice structures

Complex thermal processing during laser powder bed fusion ( L -PBF) inevitably induces heterogenous and anisotropic defects, which can affect the macromechanical response of components. The initial morphological features of L -PBF printed samples can be reconstructed with X-ray micro-computed tomography (μCT) scans and the effects of defects on the mechanical properties of the sample can be predicted using image-based finite element modeling. However, due to balling phenomena, several powder particles adhere to the surface of the lattice structure and the mechanical properties of these particles differ from that of the parent material. The predicted modulus and strength of the direct reconstructed models are much higher than the experimental values because of overestimated particle effect. Therefore, these particles should be removed from the CT images before high-fidelity numerical simulation. This paper proposes a new image segmentation method based on a U-Net convolutional neural network to remove adhered particles on the L -PBF manufactured lattice structure from μCT slices. High-fidelity image-based finite element models were constructed with and without the deep learning-based image preprocessing. The results were compared with those obtained from simulations using an ideal CAD model and experimental results. The proposed deep learning-based preprocessing method enables high-precision reconstruction and efficient finite element simulation prediction of additive manufactured lattice structures.

A Digital-Twin Methodology for the Non-destructive Certification of Lattice Structures

Additively manufactured (AM) lattice structures are applied in high-value applications such as lightweight aerospace design and biomedical implants. However, uncertainties of the geometry of as-manufactured AM lattice structures results in uncertainties in the associated mechanical response. This research proposes a non-destructive digital-twin certification methodology that quantifies the functional response of individual strut elements (and associated statistical distributions) from x-ray micro-computed tomography (µCT) data for as-manufactured AM lattice structures. This methodology may be algorithmically applied, as is required for the cost-effective certification of high-value lattice structures. The proposed methodology is demonstrated for a digital twin of over 2000 strut elements within a Ti-6AI-4V lattice fabricated with laser-based powder bed fusion. This digital twin allows various geometric or functional analyses to be performed, and in this case is demonstrated by acquiring statistical distributions of the predicted critical buckling load as a function of the strut element build orientation.

Parametric design workflow of periodic lattice structures for additive manufacturing: A case study

With additive manufacturing, greater degrees of design freedoms can be afforded via design optimization and mass customization of part geometries. One way to leverage the geometrical and hierarchical complexities of additively manufactured parts is the manufacturing of functionally-graded lattice structures – a tall order for conventional manufacturing technologies. Yet, the selection of suitable unit cell types and strut diameters to generate lattice structures with desirable mechanical performance for specific applications remains a challenge for engineers due to the lack of computational design support tools integrating domain experts’ knowledge and past empirical outcomes across the stages of the engineering design process. This study proposes a digital design workflow which aids decision-making by redefining design features as parametric problems to be solved using algorithmic methods. Using a visual programming application, the 3D model is first parameterized, then fed into a simulation and optimization workflow. Solutions are then generated by iterating all possibilities within the ranges of the design parameters given by the human designer. The methodology presented here is examined through a case study of a bike saddle for fabrication via Multi Jet Fusion, taking into consideration the minimum unit cell gap and minimum strut diameter to ensure the model’s printability. Preliminary results indicated that comparisons between different design alternatives can be made easily via the visualization and feedback of the interface. The potential of such an integrated workflow can be further demonstrated in products that can benefit from the mechanical advantages of lattice structures, such as orthotics, personalized sports equipment, and more.