Design of conformal lattice structures using the volumetric distance field based on parametric solid models

Advances in additive manufacturing techniques have enabled the production of parts with complex internal geometries. However, the layer-based nature of additive processes often results in mechanical properties that vary based on the orientation of the feature relative to the build plane. Lattice structures have been a popular design application for additive manufacturing due to their potential uses in lightweight structural applications. Many recent works have explored the modeling, design, and fabrication challenges that arise in the multiscale setting of lattice structures. However, there remains a significant challenge in bridging the simplified computational models used in the design process and the more complex properties actually realized in fabrication. This work develops a design approach that captures orientation-dependent material properties that have been observed in metal AM processes while remaining suitable for use in an iterative design process. Exemplar problems are utilized to investigate the potential design changes and performance improvements that can be attained by taking the directional dependence of the manufacturing process into account in the design of lattice structures.

This study presents a comparative analysis of the influence of open-cell and closed-cell topologies on the manufacturing quality and resultant elasticity of 3D printed thermoplastic polyurethane (TPU) lattice structures. Lattice samples were designed based on various open-cell and closed-cell configurations, varying in unit cell size and fabricated using extrusion-based additive manufacturing (AM) techniques. A microscopic analysis was conducted to assess manufacturing defects, while mechanical compression tests were performed to characterize the elasticity of the samples. The correlation between the obtained results enabled the evaluation of the relationship between the manufacturability of lattice topologies and their stiffness. The findings reveal substantial differences in the manufacturability of the topologies, with open-cell structures exhibiting more pronounced defects. Additionally, the unit cell size and the resulting density of the samples were found to provide design advantages, as closed-cell topologies demonstrated superior load resistance. The accumulation of manufacturing defects was identified as a critical factor influencing deviations in stiffness measurements. This study establishes a foundational framework for lattice structural design, emphasizing the impact of cell topology and unit cell size on mechanical performance. The significance of this research lies in its contribution to the optimization of 3D printed TPU-based lattice structures, providing valuable insights for product design applications.

Polymer foams are extensively utilized because of their superior mechanical and energy-absorbing capabilities; however, foam materials of consistent geometry are difficult to produce because of their random microstructure and stochastic nature. Alternatively, lattice structures provide greater design freedom to achieve desired material properties by replicating mesoscale unit cells. Such complex lattice structures can only be manufactured effectively by additive manufacturing or 3D printing. The mechanical properties of lattice parts are greatly influenced by the lattice parameters that define the lattice geometries. To study the effect of lattice parameters on the mechanical stiffness of lattice parts, 360 lattice parts were designed by varying five lattice parameters, namely, lattice type, cell length along the X, Y, and Z axes, and cell wall thickness. Computational analyses were performed by applying the same loading condition on these lattice parts and recording corresponding strain deformations. To effectively capture the correlation between these lattice parameters and parts’ stiffness, five machine learning (ML) algorithms were compared. These are Linear Regression (LR), Polynomial Regression (PR), Decision Tree (DT), Random Forest (RF), and Artificial Neural Network (ANN). Using evaluation metrics such as mean squared error (MSE), root mean squared error (RMSE), and mean absolute error (MAE), all ML algorithms exhibited significantly low prediction errors during the training and testing phases; however, the Taylor diagram demonstrated that ANN surpassed other algorithms, with a correlation coefficient of 0.93. That finding was further supported by the relative error box plot and by comparing actual vs. predicted values plots. This study revealed the accurate prediction of the mechanical stiffness of lattice parts for the desired set of lattice parameters.

Topology optimization for concurrent design of layer-wise graded lattice materials and structures

Bone cells, including osteoblasts, osteoclasts, and osteocytes, have the ability to develop and maintain bone architecture. Although improved experimental testing approaches are increasing our understanding of the complex structures and functions of bone cells and bone, computational models, particularly finite element analyses, are being used to extend this knowledge and to develop a more theoretical understanding of bone cell behaviors. There are many challenges to developing an accurate and validated computational model due to the complex structure and biomechanical behaviors of the bone cells and bone tissue. A better understanding of the geometry and material properties of bone cells and bone will improve our understanding of the bone's biomechanical behaviors. In this review, we summarize and discuss the different geometric representations and material properties that have been used to model the bone cells. The current status of computational models, a comprehensive overview of the modeling methods for the bone cells, and the challenges for validating the models are presented.

Image-based and in-situ measurement techniques for the characterization of the damage behavior of additively manufactured lattice structures under fatigue loading

Lattice structures are promising materials in the terms of energy absorption, acoustic and vibrational damping, high strength-to-weight ratios and thermal management capabilities. In particular, auxetic lattice structures, among others, show high energy absorption performances due to their characteristic negative Poisson’s ratio. In this study, it is aimed to compare auxetic deformation mechanisms under quasi-static crush loads. Ti6Al4V tensile test specimens were produced with Electron Beam Melting (EBM) Additive Manufacturing (AM) technology. Moreover, a constitutive equation was derived and calibrated according to tensile results. The calibrated data were used to generate non-linear computational crush models including elastoplastic material data, damage initiation criterion, damage evaluation law and element deletion. The computational models are utilized for optimum topology design and mechanical performance prediction of different auxetic cells, including anti-tetrachiral, hexachiral, re-entrant and honeycomb lattice structures that are prone to prematurely fail under crush loading conditions. Consequently, it was found that the chiral auxetic deformation mechanism experienced better energy absorption ability over re-entrant deformation mechanism for metallic lattice structures.

A lattice structure is defined by a network of interconnected structural members whose architecture exhibits some degree of regularity. Although the overall architecture of a lattice may contain many members, its generation can be a simple process in which a unit cell composed of a small amount of members, in comparison to the overall structure, is mapped throughout the Euclidean space. However, finding the right lattice architecture in a vast search space that customizes the behavior of a design for a given purpose, subject to mechanical and manufacturing constraints, is a challenging task. In response to this challenge, this work investigates a Voronoi diagram-based tessellation of a body-centered cubic cell for applications in structural synthesis and computational design of 3D lattice structures. This work contributes by exploring how the Voronoi tessellation can be utilized to parametrically represent the architecture of a lattice structure and what the implications of the parametrization are on the optimization, for which a global direct search method is used. The work considers two benchmark studies, a cubic and a cantilever lattice structure, as well as the effect of isotropic and anisotropic material property models, stemming from applications to additive manufacturing. The results show that the proposed parameterization generates complex search spaces using only four variables and includes four different lattice structure types, a Kelvin cell, a hexagonal lattice, a diamond-core lattice structure, and a box-boom type lattice structure. The global direct search method applied is shown to be effective considering two different material property models from an additive manufacturing (AM) process.

Closed-cell metal foams are cellular solids that show unique properties such as high strength to weight ratio, high energy absorption capacity, and low thermal conductivity. Due to being computation and cost effective, modeling the behavior of closed-cell foams using regular unit cells has attracted a lot of attention in this regard. Recent developments in additive manufacturing techniques which have made the production of rationally designed porous structures feasible has also contributed to recent increasing interest in studying the mechanical behavior of regular lattice structures. In this study, five different topologies namely Kelvin, Weaire–Phelan, rhombicuboctahedron, octahedral, and truncated cube are considered for constructing lattice structures. The effects of foam density and impact velocity on the stress–strain curves, first peak stress, and energy absorption capacity are investigated. The results showed that unit cell topology has a very significant effect on the stiffness, first peak stress, failure mode, and energy absorption capacity. Among all the unit cell types, the Kelvin unit cell demonstrated the most similar behavior to experimental test results. The Weaire–Phelan unit cell, while showing promising results in low and medium densities, demonstrated unstable behavior at high impact velocity. The lattice structures with high fractions of vertical walls (truncated cube and rhombicuboctahedron) showed higher stiffness and first peak stress values as compared to lattice structures with high ratio of oblique walls (Weaire–Phelan and Kelvin). However, as for the energy absorption capacity, other factors were important. The lattice structures with high cell wall surface area had higher energy absorption capacities as compared to lattice structures with low surface area. The results of this study are not only beneficial in determining the proper unit cell type in numerical modeling of dynamic behavior of closed-cell foams, but they are also advantageous in studying the dynamic behavior of additively manufactured lattice structures with different topologies.

The robotic arm is one of the vital components of robot assembly. The purpose of the robotic arm is to transmit power and conduct the desired motion, i.e., translation or rotation. Robotic limbs are designed and constructed to execute certain tasks with a high degree of speed, accuracy, and efficiency. This research focuses on to enhancing the strength-to-weight ratio of robotic arm using certain techniques of additive manufacturing, i.e., topology optimization and lattice structure. Employing the finite element analysis, the impact of weight reduction optimization on structural parameters such as stress and deformation in the current design is assessed using ANSYS R18.1 for FE analysis and Creo parametric 7.0 design software for computer-aided design modeling. Observations reveal that the 0.5 and .4 scale lattice structure designs have deformation of 0.01453mm and 0.01453 mm respectively though the generic design has 0.01043 mm deformation. Notably, the 0.5 scale lattice of the robotic arm exhibits a 31.08% higher equivalent stress than the generic design with 29.3%. reduction in mass of the robotic arm. These findings highlight the efficacy of lattice structures for optimizing the robotic arm’s performance, contributing to advancements in power-efficient robot assembly processes.

Geometric constraint solving is a central topic in many fields such as parametric solid modeling, computer-aided design or chemical molecular docking. A geometric constraint problem consists of a set geometric objects on which a set of constraints is defined. Solving the geometric constraint problem means finding a placement for the geometric elements with respect to each other such that the set of constraints holds. Clearly, the primary goal of geometric constraint solving is to define rigid shapes. However an interesting problem arises when we ask whether allowing parameter constraint values to change with time makes sense. The answer is in the positive. Assuming a continuous change in the variant parameters, the result of the geometric constraint solving with variant parameters would result in the generation of families of different shapes built on top of the same geometric elements but governed by a fixed set of constraints. Considering the problem where several parameters change simultaneously would be a great accomplishment. However the potential combinatorial complexity make us to consider problems with just one variant parameter. Elaborating on work from other authors, we develop a new algorithm based on a new tool we have called h-graphs that properly solves the geometric constraint solving problem with one variant parameter. We offer a complete proof for the soundness of the approach which was missing in the original work. Dynamic geometry is a computer-based technology developed to teach geometry at secondary school, which provides the users with tools to define geometric constructions along with interaction tools such as drag-and-drop. The goal of the system is to show in the user's screen how the geometry changes in real time as the user interacts with the system. It is argued that this kind of interaction fosters students interest in experimenting and checking their ideas. The most important drawback of dynamic geometry is that it is the user who must know how the geometric problem is actually solved. Based on the fact that current user-computer interaction technology basically allows the user to drag just one geometric element at a time, we have developed a new dynamic geometry approach based on two ideas: 1) the underlying problem is just a geometric constraint problem with one variant parameter, which can be different for each drag-and-drop operation, and, 2) the burden of solving the geometric problem is left to the geometric constraint solver. Two classic and interesting problems in many computational models are the reachability and the tracing problems. Reachability consists in deciding whether a certain state of the system can be reached from a given initial state following a set of allowed transformations. This problem is paramount in many fields such as robotics, path finding, path planing, Petri Nets, etc. When translated to dynamic geometry two specific problems arise: 1) when intersecting geometric elements were at least one of them has degree two or higher, the solution is not unique and, 2) for given values assigned to constraint parameters, it may well be the case that the geometric problem is not realizable. For example computing the intersection of two parallel lines. Within our geometric constraint-based dynamic geometry system we have developed an specific approach that solves both the reachability and the tracing problems by properly applying tools from dynamic systems theory. Finally we consider Henneberg graphs, Laman graphs and tree-decomposable graphs which are fundamental tools in geometric constraint solving and its applications. We study which relationships can be established between them and show the conditions under which Henneberg constructions preserve graph tree-decomposability. Then we develop an algorithm to automatically generate tree-decomposable Laman graphs of a given order using Henneberg construction steps.

Additive manufacture (AM) technologies allow innovative structural design, including complex lattice structures. Selective laser melting (SLM) is an AM process that enables the manufacture of space filling lattice structures. Lattice structures are topologically ordered, three-dimensional open-celled structures composed of one or more repeating unit cells. From a mechanical designer viewpoint, a great advantage offered by cellular materials is high strength accompanied by a relatively low mass. Due to their complex structure, fine geometry and the absence of supports structures, the setting of the best parameters to print lattice structures is difficult and could negative influence their mechanical response. This study investigated how different parameters settings influence the compression behaviour of lattice structures in stainless steel 17-4PH (AISI-630) printed by SLM. A comparison between compressive response of structures printed with different parameters is presented and considerations about their behaviour exposed.

Mechanisms of low-frequency bandgap formation and energy absorption of three-dimensional nested hybrid lattice structures

Stiffness design of a multilayer arbitrary BCC lattice structure with face sheets

Wind resistant size optimization of geometrically nonlinear lattice structures using a modified optimality criterion method