Mechanical Properties Of Lattice Structures Research Articles

Development and Comparison of Model-Based and Data-Driven Approaches for the Prediction of the Mechanical Properties of Lattice Structures

AbstractLattice structures have great potential for several application fields ranging from medical and tissue engineering to aeronautical one. Their development is further speeded up by the continuing advances in additive manufacturing technologies that allow to overcome issues typical of standard processes and to propose tailored designs. However, the design of lattice structures is still challenging since their properties are considerably affected by numerous factors. The present paper aims to propose, discuss, and compare various modeling approaches to describe, understand, and predict the correlations between the mechanical properties and the void volume fraction of different types of lattice structures fabricated by fused deposition modeling 3D printing. Particularly, four approaches are proposed: (i) a simplified analytical model; (ii) a semi-empirical model combining analytical equations with experimental correction factors; (iii) an artificial neural network trained on experimental data; (iv) numerical simulations by finite element analyses. The comparison among the various approaches, and with experimental data, allows to identify the performances, advantages, and disadvantages of each approach, thus giving important guidelines for choosing the right design methodology based on the needs and available data.

Prediction of Mechanical Properties of Lattice Structures: An Application of Artificial Neural Networks Algorithms.

The yield strength and Young's modulus of lattice structures are essential mechanical parameters that influence the utilization of materials in the aerospace and medical fields. Currently, accurately determining the Young's modulus and yield strength of lattice structures often requires conduction of a large number of experiments for prediction and validation purposes. To save time and effort to accurately predict the material yield strength and Young's modulus, based on the existing experimental data, finite element analysis is employed to expand the dataset. An artificial neural network algorithm is then used to establish a relationship model between the topology of the lattice structure and Young's modulus (the yield strength), which is analyzed and verified. The Gibson-Ashby model analysis indicates that different lattice structures can be classified into two main deformation forms. To obtain an artificial neural network model that can accurately predict different lattice structures and be deployed in the prediction of BCC-FCC lattice structures, the artificial network model is further optimized and validated. Concurrently, the topology of disparate lattice structures gives rise to a certain discrete form of their dominant deformation, which consequently affects the neural network prediction. In conclusion, the prediction of Young's modulus and yield strength of lattice structures using artificial neural networks is a feasible approach that can contribute to the development of lattice structures in the aerospace and medical fields.

Improving mechanical properties of lattice structures using nonuniform hollow struts

In contrast to constant-strut lattices, the introduction of innovative strut designs has the potential to enhance the mechanical properties of lattice structures. This study presents a Bézier curve-based nonuniform section design for body-centered cubic lattices with hollow struts (BCCH). Periodic boundary conditions are applied to the unit cells, and a finite element (FE) numerical homogenization method is employed to assess their elastic properties. A comprehensive dataset is generated through the FE model, which is subsequently divided into training, validation, and testing sets. The coordinates of the Bézier curve control points serve as inputs to deep learning networks, which are trained on the training dataset. Relative density and elastic properties are treated as two distinct networks, with the validation set utilized to prevent overfitting. The objective function consists of two weighted components: one aims to maximize the relative Young's modulus, while the other ensures that the relative density achieves a specified value. An evolutionary algorithm is employed to optimize the objective function, with variations in the control point coordinates constrained to specific ranges. By leveraging the fast inference ability of the deep learning model, the stiffness and orientation-dependent mechanical properties can be efficiently tailored. Our results demonstrate that the optimized structures demonstrate superior stiffness (+92.8 %) and distributed stress field compared to the benchmark lattice. The design method also enables tailoring of specific mechanical properties, including isotropic elasticity. 3D-printed lattice designs were fabricated and compression tests confirmed agreement with simulation results in terms of stiffness. Additionally, the optimized designs exhibit superior strength (+99.6 %) and toughness compared to the benchmark lattices.

Research on mechanical properties of lattice structure based on selective laser melting technology

Research on mechanical properties of lattice structure based on selective laser melting technology

A two-step modeling method for constructing 3D negative Poisson’s ratio materials with high specific strength based on common lattice structures

The traditional negative Poisson’s ratio (NPR) structure was basically designed based on concave or rotational mechanisms, resulting in relatively low specific strength and limiting its application. This paper proposed a two-step modeling method to establish a connection between the common lattice structures and NPR structures, which can obtain NPR structures with high specific strength. The models with different triaxial compression ratios were obtained through triaxial compression FE simulation to the selected initial configuration. Then, the mechanical properties of these models were studied through uniaxial compression FE simulation and experiments. In the research scope of this paper, the results demonstrate that the lattice structure can get NPR through the two-step modeling method when the Maxwell’s number is less than or equal to zero. The specific strength of the NPR structure obtained through the two-step modeling method was at most 1.5 times higher than that of the traditional 3D star-shaped NPR structure. Due to the high designability and excellent mechanical properties of lattice structures, this work provides a novel method for the manufacture of NPR structures with high specific strength.

Asymptotic homogenization of tesseract lattice structures

One of the main advantages of lattice structures (a type of porous structures) is their high strength-to-weight ratio. The mechanical properties of lattice structures, including static and dynamic properties, are dependent on the type of base repeating unit cell. In this research, we investigate the mechanical properties of lattice structures based on tesseract unit cell. This unit cell is significant due to similarity of its relative density to human bone, especially high-density spongy bone. Up to now, no analytical or homogenization method has been used to analyze the mechanical behavior of this unit cell. In this study, homogenization process based on an Asymptotic method (AH) is used. Then, the accuracy of the homogenization method is evaluated against FE results and experimental tests. We present the analytical solution that relates the geometry of unit cell to normalized Young's modulus, normalized shear modulus, and Poisson's ratio. The mechanical properties of the lattice structures were found to be strongly dependent on the d/l ratio (strut diameter to length ratio). The Young's modulus increased exponentially by increasing the d/l ratio. Compared to the analytical results based on homogenization method, the numerical predictions were higher for the normalized Young's modulus. For instance, for d/l=0.15, the predicted normalized Young's modulus was 0.0316 and 0.0238 for the FE and Homogenization methods, respectively. As a practical application, the range of obtained elastic modulus was 0.13 GPa and 1.23 GPa which is close to the elastic modulus of femur head bone, demonstrating the suitability of the tesseract unit cell to be used as bone replacement biomaterial.

Thermomechanical behavior of auxetic lattices

This study investigates the thermomechanical behavior of auxetic square-grid lattice structures through analytical, numerical, and experimental approaches. These structures have gained prominence in biomedical applications due to their ability to mimic the structural behavior of surrounding tissue, even if the natural tissue is not auxetic. First, analytical relations are derived for elastic modulus, Poisson’s ratio, and yield strength of lattice structures, as well as their thermomechanical behavior under different loading conditions. The mechanical properties of lattice structures are validated using both finite element and experiments. Several 3D-printed specimens with varying thickness-to-length dimensions are heated in a heat chamber to measure their deformations. Results also demonstrate excellent accuracy of the derived analytical relationships, which show that elastic modulus and yield strength increase exponentially with an increase in the thickness-to-length (t/l) ratio, while Poisson’s ratio is largely independent of t/l. Furthermore, it is found that the coefficient of thermal expansion is equivalent to that of the constituent solid material and that thermal stress has a linear relationship with temperature change. These findings have important implications for analyzing lattice structures based on other unit cell types and can be extended to macro-geometries such as tubular or spherical shapes commonly used in biomedical applications.

Study on Thermodynamic Coupling Performance of Multi-Level Lattice Structures

With the development of hypersonic vehicle, the design of heat-resistant and load-bearing surface of hypersonic vehicle has gradually become a key technology affecting its combat effectiveness. As a new type of lightweight and high-strength structure, lattice structure has excellent mechanical properties such as ultra-light, high specific strength and high specific stiffness, and special properties such as vibration reduction, heat dissipation and sound absorption. Among them, the multi-level lattice structure can increase the bearing efficiency of the structure at low relative density, and increase the heat transfer area at the same time, so as to improve the heat protection and bearing capacity of the structure. This study includes three aspects of high temperature out-of-plane compression test, high temperature numerical simulation comparison, and structural optimization for the designed multi-level pyramid lattice, in order to obtain the bearing capacity of the multi-level pyramid lattice at 350°C, and further improve the bearing performance by optimizing the core structure. Through experiments and verification, the multi-level pyramid lattice designed and optimized in this study can further meet the requirements of thermal protection and load-bearing performance of aircraft compared with the single-level pyramid lattice, and can provide a reference for the study of high temperature mechanical properties of lattice structures, the design of new multi-level lattice structures and the engineering application of lattice structures.

Mechanical Properties of Lattice Structures with a Central Cube: Experiments and Simulations.

In this study, a new structure is proposed based on the body-centered cubic (BCC) lattice structure by adding a cubic truss in the center of the BCC structure and denoting it TLC (truss-lattice-cube). The different dimensions of the central cube can notably affect the mechanical properties of the lattice structure. With a fixed length (15 mm) of a unit cell, the optimal size for the central cube is determined to be 5 mm. Quasi-static compressive tests are performed on specimens made of polylactic acid (PLA) using additive manufacturing technology. The deformation characteristics of the new structure are analyzed in detail by experiments and numerical simulations. Compared to the BCC structure, the mechanical properties of the TLC structure were significantly improved. The initial flow stress of the TLC increased by 122% at a strain of 0.1; the specific strength enhanced by 293% at a strain of 0.5; and the specific energy absorption improved by 312% at a strain of 0.6. Printing defects in the lattice structure may remarkably damage its mechanical properties. In this work, incorporation of microcracks into the finite element model allows the simulation to capture the influence of printing defects and significantly improve the predictive accuracy of the simulation.

Experimental study on the influence of abrasive flow machining on the surface quality and mechanical properties of BCC lattice structure manufactured by L-PBF

During the L-PBF process for preparing porous biomaterials, the "spheroidization effect" and the "stair-step effect" lead to defects such as pore clogging and rod diameter thickening in the actual components. These defects affect the part's dimensional accuracy, which in turn has the critical influence on the mechanical properties of the workpiece. Thus, suitable post treatment methods are required to improve the surface quality of porous biomaterials. This paper aims to investigate the effects of abrasive flow machining on the surface quality and mechanical properties of body-centered cubic (BCC) lattice-structured specimens molded by L-PBF at different pressures and abrasive concentrations and their mechanisms. Experimental results indicate that the number of powders adhering to the rod diameter of the member is significantly reduced after the abrasive grain flow process treatment. The roughness of the rod diameter surface is reduced from 17.48 μm to 6.82 μm, and the surface finishing is improved by 60.98%. The abrasive flow machining can effectively eliminate the "spheroidization effect" on the mechanical properties of the lattice structure. The maximum compressive strength of specimens subjected to abrasive flow machining have all been increased. Especially, with the abrasive flow machining under the pressure of 4 MPa and the abrasive grain concentration of 60%, the maximum compressive strength of the specimens was even been increased by 8.89%.

Numerical investigation of the mechanical properties of lattice structures inspired from polycrystalline materials

In this work, polycrystalline-like lattice structures that are inspired by the geometry of polycrystalline materials are designed. They are generated by filling periodic lattice structures into a Voronoi diagram. Then, finite element analyses of two periodic and eight polycrystalline-like lattice structures are performed to compare their mechanical properties. The numerical results show that polycrystalline-like lattice structures consisting of anisotropic rectangular X-type periodic unit cells are isotropic at the macroscale. Moreover, they have a higher specific stiffness and specific strength than periodic lattice structures under compression. Then, the energy absorption capability is investigated. Five energy absorption indicators (energy absorption, energy absorption per unit volume, specific energy absorption per unit mass, crush stress efficiency, and plateau stress) reveal that polycrystalline-like lattice structures are better energy absorption structures. Furthermore, the defect sensitivity of missing struts is discussed. The findings of this work offer a new route for designing novel lattice structures.

Rate-dependent behaviour of additively manufactured topology optimised lattice structures

Lattice structures offer a wide range of tuneable qualities that cannot be achieved with bulk materials. While lattice structures offer a range of tuneable qualities, including isotropic properties achievable in bulk materials, the advent of additive manufacturing (AM) advances research in this domain. Although several studies have characterized the quasi-static mechanical properties of lattice structures, there is limited experimental data available on their rate-dependent behaviour. Additionally, most lattice structures are anisotropic, making them unsuitable for applications where loading directions are unknown. In this study, a topology-optimised unit cell with nearly perfect isotropic stiffness is investigated for its isotropic specific energy absorption under high strain rates. The dynamic response of the structure is evaluated using 3 different materials: CPTi, AlSi10Mg, and 316LSS, and both experimental and numerical methods are employed. The influence of topology and relative density on the mechanical properties of the structure are explored, and the specific energy absorption isotropy is determined by loading the lattices in various orientations numerically. This research fills the gap in knowledge regarding the rate-dependent behaviour of lattice structures and offers insight into the potential for isotropic lattice structures in engineering applications.

The coupled effect of aspect ratio and strut micro-deformation mode on the mechanical properties of lattice structures

Lattice structures have been integrated into various industrial applications owing to their unique compressive properties. Mechanical characterisation is usually done by testing a small specimen which is assumed representative of the utilised lattice. A specimen's aspect ratio (height to diameter/width ratio) is known to affect compressive properties in various engineering materials, yet its influence in lattices has not been investigated thoroughly. In this study, titanium lattice specimens designed with different aspect ratios (ranging from 0.5 to 3.0) and four different topologies (displaying bend and stretch-dominated micro-deformation modes) were fabricated using powder bed fusion and tested in quasi-static compression. Their compressive properties and failure modes were evaluated using acquired stress-strain curves and digital image correlation (DIC) analysis. Reducing the aspect ratio in the bend-dominated lattices increased the measured stiffness of the specimens by up to 40%. Conversely, increasing the aspect ratio of the stretch dominated lattices increased the measured stiffness of the specimens by up to 30%. For both topology types, decreasing the aspect ratio increased the measured strength of the specimens, but the effect was less than that observed for stiffness. Different responses were attributed to gradient strain accumulation and different failure patterns (densification versus shear banding) that were observed depending on the combination of aspect ratio and topology. These findings are particularly important for better predicting the mechanical behaviour of lattice-based components that have aspect ratios outside the range of conventional test specimens.

Enhanced Mechanical Properties of Lattice Structures Enabled by Tailoring Oblique Truss Orientation Angle

The significant effect of the strut angle on the mechanical properties of strut‐based lattice structures is systematically explored through experimental and numerical investigations. The highest values of elastic modulus and yield strength, surpassing those observed in cubic lattices with the same relative density, have been experimentally observed at the strut angle of 71.76°. A correlation among elastic modulus, yield strength, and strut angles in lattices, validated by experimental tests, has been identified through developing a theoretical modelling and conducting a detailed finite element analysis. Transition from a bending dominated deformation mechanism to one dominated by compression within the lattice structures has been realized, contingent upon the tailoring of the strut angle. The deformation mechanism of these lattices is significantly influenced by the interplay between ductile bending and brittle failure of the struts. The superior energy absorption and yield strength demonstrated by the optimized lattice design have been underscored through a comparative analysis with other previously reported lattices. These lightweight structures hold promise for applications in the development of mechanical metamaterials with on‐demand mechanical properties.

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.

Controlling mechanical properties and energy absorption in AlSi10Mg lattice structures through solution and aging heat treatments

The use of Selective Laser Melting (SLM) has gained popularity due to its ability to produce complex-shaped parts, which includes lightweight lattice structures that are appealing to a variety of industries. AlSi10Mg alloy is a favored choice for SLM due to its excellent specific properties. The utilization of AlSi10Mg in lattice structures further reduces their mass while enhancing specific mechanical properties. However, the inherent brittle deformation behavior of as-built AlSi10Mg restricts the energy absorption potential of lattice structures. This study explores the control of mechanical properties and energy absorption in AlSi10Mg lattice structures and bulk tensile samples through solution and aging heat treatments, examining their impact on microstructural transformations. The results show that solution heat treatment decreases the mechanical properties of lattice structures and bulk tensile samples while improving their ductility and energy absorption. This change is attributed to the transformation of the alloy's fine cellular microstructure into coarser Si-precipitates. Subsequent aging treatments lead to increased mechanical properties in lattice structures solution heat treated at 500 and 550 °C, albeit with a slight reduction in energy absorption. Intriguingly, lattice structures heat treated at 460 °C exhibit unchanged mechanical properties and energy absorption, as confirmed by the t-test. Additionally, the absence of the Al5FeSi intermetallic phase suggests that aging did not occur following solution heat treatment at 460 °C. These findings offer valuable insights into manipulating the mechanical properties and energy absorption of AlSi10Mg lattice structures through controlled heat treatments. Such control can significantly enhance the performance and functionality of lattice structures in practical applications.

Compressive mechanical properties of lattice structures filled with silicone rubber

The lattice structure is a periodically repeating three-dimensional open-cell architecture, and the introduction of polymer materials into its gaps results in a lattice structure filled with silicone rubber that can simultaneously exhibit vibration reduction, energy absorption, and other functional characteristics. In this study, the compressive behavior of both the lattice structure and the lattice structure filled with silicone rubber were investigated through a combination of finite element analysis and experimental investigations. The results show that the finite element analysis results are consistent with the experimental ones, and the method can be used to analyze such structures. Lattice structures filled with silicone rubber have better load-bearing capacity compared to lattice structures, and the integration of silicone rubber increases the compressive strength of the lattice structure, reducing the occurrence of structural localization phenomena.

Effect of cell size and wall thickness on the compression performance of triply periodic minimal surface based AlSi10Mg lattice structures

Triply periodic minimal surface (TPMS) are mathematical surfaces with zero mean curvature and are spatially invariant. Recently, these surfaces are investigated for potential application in the manufacturing of cellular materials or lattice structures for a variety of purposes. However, designing such structures is a difficult task as the dedicated design platforms impose higher costs. Therefore, in this study, lattice structures have been designed using an in-house developed opensource tool for different cell sizes and cell wall thicknesses. The lattice structures have been additively manufactured through laser powder bed fusion (LPBF) and their design compliance and manufacturing defects have been investigated through optical micrography and SEM. The lattice structures have been subjected to quasistatic uniaxial compression test in as-manufactured and heat-treated conditions and the resulting compressive stress-strain curves have been analyzed in detail to draw a relationship between the two varying quantities and the mechanical properties of the lattice structure. The results show that there has been small but visible differences between the as-designed and as-manufactured lattice structures. The mechanical properties of lattice structures deteriorated with increasing cell size at constant wall thickness and improved with increasing cell wall thickness at constant unit cell size. The heat treatment procedures homogenized and increased plastic deformation while decreasing the strength and modulus values. Overall the study outlined a significant effect of cell geometry, size, and cell wall thickness on the mechanical properties of the TPMS lattice structures.

Synergetic control mechanism for enhancing energy-absorption of 3D-printed lattice structures

It is difficult for controlling the failure mechanisms to improve the mechanical properties of lattice structures in a specified way. To this end, inspired by biological tissue/alloy microstructure, a novel synergetic control mechanism with gradient- and Orowan-strengthening is proposed to enhance energy-absorption (EA) of lattice. Gradient, Orowan and Grad-Oro lattices with different Reinforcement Phase (RP) spacing are designed and manufactured by 3D-printing with little defect. By experiments, simulations and theoretical analysis, compressive behaviors and failure modes of designed lattices are studied to explore the effects of synergetic control mechanism on mechanical properties. Results show that a 31.0%∼35.1% higher SEA than Matrix lattice is identified for Grad-Oro lattices which also surpass Orowan or Gradient lattices. Then, the transitional failure mechanisms of lattices are revealed to explain the improvement. It is illustrated that Zigzag shear-path induced by the Gradient-Orowan synergism can dissipate more energy than any single mechanism (bypassing shear-path or progressive collapse). It is finally found that closer RP spacing brings about stronger interactions between RP boundaries to affect failure modes like the grain boundary strengthening. This novel concept and structural design method greatly contribute to controllable mechanical design of lattice.

Improving the Mechanical Properties of a Lattice Structure Composed of Struts with a Tri-Directional Elliptical Cylindrical Section via Selective Laser Melting.

In recent years, lattice structures produced via additive manufacturing have been increasingly investigated for their unique mechanical properties and the flexible and diverse approaches available to design them. The design of a strut with variable cross-sections in a lattice structure is required to improve the mechanical properties. In this study, a lattice structure design method based on a strut cross-section composed of a mixture of three ellipses named a tri-directional elliptical cylindrical section (TEC) is proposed. The lattice structures were fabricated via the selective laser melting of 316L alloy. The finite element analysis results show that the TEC strut possessed the high mechanical properties of lattice structures. Compression experiments confirmed that the novel lattice structure with the TEC strut exhibited increases in the elastic modulus, compressive yield strength, and energy absorption capacity of 24.99%, 21.66%, and 20.50%, respectively, compared with the conventional lattice structure at an equal level of porosity.