Material Density Distribution Research Articles

Разработка теории непрерывного формования изделий из ультрадисперсных композиционных порошковых материалов

In article there are discussed the basic results of theoretical investigating continuous ultra-dispersed powder materials pressing process for obtaining lengthy products with nano-crystal structure. Within the framework of the hypothesis about similarity under stress conditions in compressible and incompressible materials in the pressing channel, the pressure distribution along the pressing channel is established. Using G.M. Zhdanovich equation with new material density distribution boundary conditions along the length of the pressing channel is found.

Designing 2D stochastic porous structures using topology optimisation

Functionally graded porous materials have superior properties such as high strength, low thermal conductivity and high energy absorption. More importantly, their density distribution can be customised to best suit different objectives, thus having a wide range of applications. With different manufacturing approaches, the geometry of functionally graded porous materials can be deterministic (e.g., lattice structure) or stochastic (e.g., metal foam). Whilst the design of the former has been extensively studied leveraging the long-established topology optimisation approach, the latter is rarely investigated despite its widespread use in industrial fields, such as aerospace and biomedical. In this study, we propose a novel two-step topology optimisation framework to design 2D stochastic porous structures. In the first step, topology optimisation based on compliance minimisation (or stiffness maximisation) is carried out to obtain the homogenised material density distribution. In the second step, a new de-homogenisation approach is developed to transform the homogenised materials into stochastic porous structures. Several numerical examples are presented to demonstrate the effectiveness of the proposed approach. As a result of employing stochastic materials and the associated density constraint, the optimised porous structures demonstrate higher compliance compared to the optimised structures made of solid materials. Nevertheless, the results indicate that the difference in compliance values between the homogenised structures and de-homogenised porous structures is minor (i.e., less than 6.99%). Furthermore, it is observed that the structural stiffness is only minimally affected by the introduction of geometric stochasticity during de-homogenisation, with variations of less than 1.94%. Therefore, the developed topology optimisation is numerically robust. Various constraints have also been developed, enabling designers to choose structures with the desired stiffness and geometric complexity from a diverse range of novel designs.

A comparison of the joint and independent inversions for magnetic and gravity data over kimberlites in Botswana

AbstractComplementary independent and joint focusing inversion investigations are applied to the magnetic and gravity datasets for two kimberlite pipes, BK54 and BK55, in Botswana. The magnetic data are high resolution and, clearly, indicate two anomalies in the survey area. Independent inversion of this magnetic data provides a focused image of the subsurface with sharp boundaries for both pipes. The extensions of the pipes are close to those estimated by the available boreholes in the area. The spatial resolution of the gravity data is, on the other hand, relatively poor. The BK54 pipe does not appear on the residual gravity anomaly, while the BK55 is characterized by a positive anomaly. Independent inversion of the gravity data provides the geometry of the BK55 but does not identify the BK54 pipe. While there are some lower density materials in the place of the BK54 pipe, no specific target is revealed. Furthermore and relevant is that the reconstructed model for BK55 is not focused. A joint focusing inversion based on the structural cross‐gradient linkage is applied for the combined gravity and magnetic datasets. This algorithm produces structurally similar magnetic susceptibility and density models. A lower density distribution of material, similar to that of the magnetic susceptibility distribution, is revealed for the BK54 pipe. Moreover, in contrast to the result obtained by an independent inversion, the structure for BK54 is connected at depth, and the reconstructed models of BK54 and BK55 share the sparsity. The models are not as sparse as the magnetic susceptibility model that is obtained independently, but they are more focused than the independently obtained density model. A comprehensive comparison of the reconstructed models, and also computational CPU time, for independent and joint inversions is presented.

DEVELOPMENT OF A ROBOT FOR THE MEASUREMENT OF RADIOACTIVE CONTAMINATION AND FERTILITY OF THE SOIL IN FARMLAND

Abstract A tractor-based robot with the capability of real-time assessing and visualizing the radioactive material density and fertility distribution of farmlands has been developed to accelerate the recovery process of the farmlands suffered by the accident of the Fukushima Daiichi Nuclear Power Plant (FDNPP). In a field test at a decontaminated farmland near FDNPP, within-field heterogeneities of soil contamination and fertility are clarified almost in real-time. Results obtained by this robot are consistent with the map by the conventional soil sampling or the history of decontamination activities.

Reliability-based optimization of structural topologies using artificial neural networks

In this paper, a topology optimization approach is presented, where uncertain load and uncertain material parameters are considered. The concept of compliance minimization, i.e., stiffness maximization, is applied based on a plane stress finite element formulation. In order to take uncertain structural load parameters and uncertain material behavior into account, the topology optimization is embedded into a reliability-based design optimization approach. Uncertain structural parameters and design variables are quantified as random variables, intervals and probability boxes (p-boxes). This allows to consider aleatory and epistemic uncertainties by means of polymorphic uncertainty models within the topology optimization. Solving optimization problems with random variables, intervals and p-boxes leads to a high computational effort, because the objective functions and constraints have to evaluated millions of times. To speed up the optimization process, the finite element simulation of the topology optimization is replaced by artificial neural networks. This includes the topology dependent maximal stresses and displacements of the structure, which are used as constraints, and also the material density distribution inside the design domain. The reliability-based optimization of structural topologies approach is applied to a cantilever structure and a single span girder.

In-situ 4-point flexural testing and synchrotron micro X-ray computed tomography of 3D printed hierarchical-porous ultra-high temperature ceramic

3D printed ceramics have received much attention of late due to the ability to manufacture complex near net shapes with a range of structures across multiple length scales. The introduction of hierarchical features offers a wider array of properties, yet with this comes additional unknowns as to their limits including the mechanisms behind failures. The present work applies in-situ Synchrotron micro X-ray computed tomography (μXCT) with 4-point flexural testing to study and further understand the failure pattern of 3D printed hierarchical porous ultra-high temperature ceramics. Samples were imaged at incremental load steps to observe the propagation of defects until final failure, where in the case of the strain tolerant logpile structure a full crack spanning the height and width of the sample was captured and reconstructed revealing a complex tortuous fracture path. The relative strength and density of the structures are related to the sintered microstructure and the printed logpile or honeycomb geometry, which are described using Gibson’s and Ashby’s theory for brittle foams. In addition, tomographic data was used to extract detailed information on porosity and material density distribution within honeycomb and logpile 3D printed lattice structures that was related to the tool path planning of each layer. • First capture and tomographic reconstruction of complex fracture path in 3D printed UHTC logpile lattice structure. • Synchrotron μXCT of honeycomb and logpile lattice structures provided detailed density information. • Relative strength and density were related to microstructure and the 3D printed logpile/honeycomb internal lattice structure. • Logpile structures exhibited tortuous fracture path and resulted in greater strain tolerance compared to honeycomb.

Multi-scale collaborative optimization of lattice structures using laser additive manufacturing

In the present work, an effective and efficient design approach is proposed to obtain a three-dimensional multi-scale graded lattice structure by virtue of multiple control parameters via density-based topology optimization. To balance the computational accuracy and cost, a Parameterized Interpolation of Lattice Structure (PILS) model was established, and the math formula combined two novel designing parameters: relative density at macro-scale and aspect ratio at micro-scale. A multinomial function was employed to describe the explicit association between control parameters and equivalent elastic constants with regard to relative density and aspect ratio, which avoided tedious homogenization computation burden in the structural optimization process. Consequently, the multi-scale collaborative design approach could optimize the macro material density distribution and the micro cell topology in an integrated manner. Numerical examples with respect to compliance optimization were offered to validate the benefits of the proposed approach. Finally, the quasi-static and dynamic compression tests were respectively implemented by universal testing machine and Split Hopkinson Pressure Bar (SHPB) system on lattice structures manufactured by laser powder bed fusion (LPBF). The outcomes reveal that graded lattice structures exhibit remarkably improved load-bearing performance than the uniform lattice structures.

Effects of Gas Diffusion Layer Porosity Distribution on Proton Exchange Membrane Fuel Cell

The effect of the porosity change of the cathode gas diffusion layer (GDL) along the cell length on the proton exchange membrane fuel cell (PEMFC) is evaluated using the calculation model and the numerical method. A detailed analysis of the polarization curve, temperature distribution of the cell center surface, cathode material, and current distribution law is carried out for six different porosity models. It is found that the influence of the GDL porosity on the fuel cell polarization curve increases with the increase in current density, and the influence reaches the maximum at the limit current density. The limit current of the fuel cell is directly proportional to the GDL porosity, and the change of GDL porosity has limited influence on it. The existence of the porosity gradient improves the uniformity of the material and current density distribution on the cathode side. The same conclusion can be obtained using the standard deviation formula to quantitatively express the degree of uniformity. The results show that the existence of the GDL porosity gradient of the PEMFC cathode has a positive effect on the cell performance.

Multi-scale topology optimization with shell and interface layers for additive manufacturing

Abstract This paper contributes a multi-scale topology optimization method for lattice structure design with both shell and lattice-lattice interface layers to enhance the structural aesthetical, mechanical, and manufacturability properties. To improve the robustness, a multi-step algorithm is proposed. The variable thickness sheet (VTS) method and the projection-based regularization mechanism are used to realize the free material optimization with a limited number of lattice microstructures. Then, a series of successive filtering and projection operations are adopted to identify the lattice-lattice interface layers based on the material density distribution. Elements with close densities are grouped into clusters and for elements inside each cluster, they are assumed to have the same periodical lattice microstructure. In the second step, based on the achieved discrete material distribution, the macrostructure with a solid shell layer and the multiple representative lattice microstructures are concurrently optimized with the density-based multi-scale topology optimization method. Several benchmark numerical examples are studied to demonstrate the effectiveness of the proposed method. Finally, additive manufacturing experiments are performed to validate the stiffness enhancement by including the lattice-lattice interface layers.

Deep-learning-based direct inversion for material decomposition.

To develop a convolutional neural network (CNN) that can directly estimate material density distribution from multi-energy computed tomography (CT) images without performing conventional material decomposition. The proposed CNN (denoted as Incept-net) followed the general framework of encoder-decoder network, with an assumption that local image information was sufficient for modeling the nonlinear physical process of multi-energy CT. Incept-net was implemented with a customized loss function, including an in-house-designed image-gradient-correlation (IGC) regularizer to improve edge preservation. The network consisted of two types of customized multibranch modules exploiting multiscale feature representation to improve the robustness over local image noise and artifacts. Inserts with various densities of different materials [hydroxyapatite (HA), iodine, a blood-iodine mixture, and fat] were scanned using a research photon-counting detector (PCD) CT with two energy thresholds and multiple radiation dose levels. The network was trained using phantom image patches only, and tested with different-configurations of full field-of-view phantom and in vivo porcine images. Furthermore, the nominal mass densities of insert materials were used as the labels in CNN training, which potentially provided an implicit mass conservation constraint. The Incept-net performance was evaluated in terms of image noise, detail preservation, and quantitative accuracy. Its performance was also compared to common material decomposition algorithms including least-square-based material decomposition (LS-MD), total-variation regularized material decomposition (TV-MD), and U-net-based method. Incept-net improved accuracy of the predicted mass density of basis materials compared with the U-net, TV-MD, and LS-MD: the mean absolute error (MAE) of iodine was 0.66, 1.0, 1.33, and 1.57mgI/cc for Incept-net, U-net, TV-MD, and LS-MD, respectively, across all iodine-present inserts (2.0-24.0mgI/cc). With the LS-MD as the baseline, Incept-net and U-net achieved comparable noise reduction (both around 95%), both higher than TV-MD (85%). The proposed IGC regularizer effectively helped both Incept-net and U-net to reduce image artifact. Incept-net closely conserved the total mass densities (i.e., mass conservation constraint) in porcine images, which heuristically validated the quantitative accuracy of its outputs in anatomical background. In general, Incept-net performance was less dependent on radiation dose levels than the two conventional methods; with approximately 40% less parameters, the Incept-net achieved relatively improved performance than the comparator U-net, indicating that performance gain by Incept-net was not achieved by simply increasing network learning capacity. Incept-net demonstrated superior qualitative image appearance, quantitative accuracy, and lower noise than the conventional methods and less sensitive to dose change. Incept-net generalized and performed well with unseen image structures and different material mass densities. This study provided preliminary evidence that the proposed CNN may be used to improve the material decomposition quality in multi-energy CT.

Dynamics behavior of porous tin under strong shockwave impact

The dynamic fracture and fragmentation of solid materials subjected to shocks have been widely studied for several decades. Motivations for investigating shock-induced damage behavior are both practical and scientific. In many cases, the loading conditions are two or more continuous shockwaves, causing complex dynamic behavior. Understanding the complex dynamics of metal materials under multiple strong shockwave loadings is important for inertial confinement fusion and impact protection. Under multiple shockwave loadings, the shockwaves not only interact with the material, but also cause interactions among the particles in the porous structure produced by the first impact. These complex dynamics might be revealed by studying the impact response of metals with a clear three-dimensional pore distribution. In this study, experiments were performed on three kinds of porous tin with typical dimensions (millimeters, sub-millimeters, and micrometers) and a clear initial structure. The dynamic behaviors of the porous tins under a 10 GPa-order shockwave loading were characterized by X-ray images, high-speed photography, and photon Doppler velocimetry. The porous tin was not completely compacted after the shockwave, and many particles were ejected at velocities far exceeding the theoretical free-surface velocity. The post-shockwave material density and status of the high-speed ejection were closely related to the initial structure of the porous tin. The distribution characteristics of the material after the shockwave, and the generation mechanism of the high-speed jets, were determined in numerical simulations. After the shock loading, the surface spray was ejected at high speed and the particles inside the porous stucture collided with each other, also at high speed. The particle collisions in the porous structure contributed significantly to the high-speed ejections and the distribution of material density. This study is significant for understanding the dynamic responses of metal materials under multiple shockwave loadings.

Multi-scale design of an architected composite structure with optimized graded properties

A design framework is here presented for the development of an architected solid with targeted mechanical properties thanks to an optimized porosity distribution. A 2D lattice of regular hexagons is considered as core element of a sandwich panel and a Bloch-Floquet-based approach is adopted to derive homogenized equivalent properties. The density distribution of the equivalent continuum is taken as objective function to be minimized in the optimization process. To this end, suitable constraints are designed to avoid empty regions and ensure a minimized density where required by the mechanical actions. A de-homogenization process is carried out on the optimized equivalent continuum to derive the configuration of regular hexagons with optimally varying wall thickness. Static and buckling responses of the optimized architected solid are compared with that of a 2D continuum whose material density distribution is determined through a classical topology optimization. It is shown that the architected 2D solid can absorb higher strain energy, with respect to classically optimized structures, which suffer a buckling-driven collapse below the elasticity threshold. The architected solid is also shown to have an improved energy absorption capability, that may increase considerably its performance, depending on the ductility of the adopted material.

Conceptual structural system layouts via design response grammars and evolutionary algorithms

Two new methods to generate structural system layouts for conceptual building spatial designs are presented. The first method, the design response grammar, uses design rules—configurable by parameters—to develop a structural system layout step by step as a function of a building spatial design's geometry and preliminary assessments of the structural system under development. The second method, design via optimizer assignment, uses an evolutionary algorithm to assign structural components to a building spatial design's geometry. In this work, the methods are demonstrated for two objectives: minimal strain energy (a commonly used objective for structural topology optimization) and minimal structural volume. In a first case study three building spatial designs have been subjected to the methods: Design via optimizer assignment yields a uniformly distributed Pareto front approximation, which incorporates the best performing layouts among both methods. On the other hand, results of the design response grammar show that layouts that correspond to specific positions on the Pareto front (e.g. layouts that perform well for strain energy), share the same parameter configurations among the three different building spatial designs. By generalizing, specific points on the Pareto front approximation have been expressed in terms of parameter configurations. A second case study addresses the use of a generic material and generic dimensions in the assessment of structural system layouts. The study applies a technique similar to topology optimization to optimize the material density distribution of each individual structural component, which can be regarded as a part of determining materials and dimensions in more advanced stages of the design of a system layout. This optimization approach is applied to the layouts that are part of the Pareto front approximations as found by the evolutionary algorithm in the first case study, the study shows that—after optimization—the fronts remain the same qualitatively, suggesting that the methods produce results that are also useful in more advanced design stages. A final case study tests the generalization that is established in the first case study by using the found configurations for the design response grammar, and it is shown that the generated layouts indeed are positioned near the desired positions on the Pareto front approximation found by the evolutionary algorithm. Although the evolutionary algorithm can find better performing solutions among a better distributed Pareto front approximation, the design response grammar uses only a fraction of the computational cost. As such it is concluded that the design response grammar is a promising support tool for the exploration and structural assessment of conceptual building spatial designs. Future research should focus on more types of structural elements; more objectives; new constraints to ensure feasible solutions, especially stress constraints; and the application of state-of-the-art techniques like machine learning to find more generalizations.

Crashworthiness design of graded cellular materials: An asymptotic solution considering loading rate sensitivity

Introducing graded cellular materials into energy absorber may improve the crashworthiness of protective structures. In order to meet the crashworthiness requirement that the impact force does not exceed the value that the protected object can afford, a backward strategy guiding the design of relative density distribution of cellular material is improved by considering the loading rate sensitivity in a shock model. Asymptotic solutions of the relative density distribution are obtained for the cases with or without considering the loading rate sensitivity, when a constant impact force is required. It is found that the second-order approximate solutions of the relative density distribution are good enough to approximate the exact solutions calculated by the fourth-order Runge-Kutta scheme. The validity of the design method is further verified by the cell-based finite element method, and the results indicate that the deformation localization at the proximal end is caused by both the density gradient and inertial effect. It is shown that the average impact force from the design without considering loading rate sensitivity exceeds the affordable value of the protected object, but that considering loading rate sensitivity can well meet the crashworthiness requirement. Therefore, the asymptotic solution of the relative density distribution from the design strategy considering loading rate sensitivity is suitable and convenient to guide the crashworthiness design in practical engineering.

Optimization Methodology for Continuous Heterogeneous Structures: A Preliminary Design of an Engine Mounting Bracket

A numerical methodology is presented which is based on Topology Optimization (TO) approach for designing continuous heterogeneous structures. This method is then exploited to reduce weight and to increase stiffness in mechanical components. Useful guidelines for the evaluation of equivalent material properties of metallic cellular structures are discussed, and they are applied for the optimization process of an engine mounting bracket under realistic loading and boundary conditions. The outcome of TO, which is related to the material density distribution into the design space, is critically reviewed for the definition of bulk, lattice and void regions within the component.

The Influence of Loading Program on the Stimulated Callus Mineralization

The aim of this work is to describe the change of physical properties of the callus material with the use of the proposed mathematical model for callus remodeling. Callus tissue can be considered as a biomaterial where it’s properties change over time due to the stimulated healing process. The proposed model is based on the mechanical stimulus theory. It is used to estimate the stress-stimulated change in the callus, Young’s modulus, and the density in the case of a mandible fracture. Three healing loading programs are discussed and compared: optimal, intermittent, and intermittent with residual load. Here, the optimal loading program is understood as the in-time change of stimulating loads, which results in the shortest necessary healing time and, simultaneously, in the most uniform distribution of material density in the analyzed domain. The necessary healing time is a period after which the callus density (and hence the Young’s modulus) reaches the desired value. The results of the study suggest a significant difference in the value of the callus maximal density between all three analyzed loading programs for a given healing time interval. The highest values of the density are obtained using the optimal loading program, however, all three programs provide satisfactory density distributions. The analytical results are compared with the callus density estimation based on the computer tomography (CT) medical data.

Robust regularization of topology optimization problems with a posteriori error estimators

Abstract Topological optimization finds a material density distribution minimizing a functional of the solution of a partial differential equation (PDE), subject to a set of constraints (typically, a bound on the volume or mass of the material). Using a finite elements discretization (FEM) of the PDE and functional we obtain an integer programming problem. Due to approximation error of the FEM discretization, optimization problem becomes mesh-depended and possess false, physically inadequate optimums, while functional value heavily depends on the fineness of discretization scheme used to compute it. To alleviate this problem, we propose regularization of given functional by error estimate of the FEM discretization. This regularization provides robustness of solutions and improves obtained functional values as well. While the idea is broadly applicable, in this paper we apply our method to the heat conduction optimization. Problems of this type are of practical importance in design of heat conduction channels, heat sinks and other types of heat guides.

3D topology optimization of continuous fiber-reinforced structures via natural evolution method

The method to optimize a topology of 3D continuous fiber-reinforced additively manufactured structures is discussed. The proposed method makes it possible to simultaneously search for density distribution and local reinforcement layup in 3D composite structures of transversely isotropic materials. The approach uses a dynamical systems method to find density distribution, combined with the method for rotation of reinforcement direction to align it in the direction of principal stresses with local minimum compliance. The algorithm is implemented as a built-in material model within Abaqus finite element suite. Both the optimal material density distribution and the distribution of fiber orientation vector are determined for three structural elements used as benchmarks: the bending of simply supported 2D beam under central point load, the loading of 3D cube by vertical load, and the bending of 3D cantilever beam.

Minimization of Warpage for Injection Molded Parts by Inverse Thermal Mold Design

Abstract For injection molding, a controlled heat removal is important to produce dimensional accurate parts efficiently. The following article introduces a new concept called inverse thermal mold design. Using this method, a proper cooling channel system for the injection mold can be produced to achieve minimal part warpage. Based on the postulate of a homogeneous material density distribution within the plastic part to achieve homogenous shrinkage, the method calculates the local cooling demand of the part to derive the cooling channel layout of the mold.

Crashworthiness of graded cellular materials: A design strategy based on a nonlinear plastic shock model

Dynamic behaviors and crashworthiness design of density graded cellular materials are investigated by using theoretical method and finite element simulation. A nonlinear plastic shock model is employed to guide the gradient design of cellular rod under mass impact and cell-based finite element models are used to verify the design strategy. Effects of impact-force parameter on the design of relative density distribution of graded cellular material and on the residual velocity of the striker for different lengths of graded cellular rods are explored. Three cases of design strategy with different impact-force parameters are analyzed and verified. The results reveal that the design strategy is reliable when the impact-force parameter is not less than zero. If the relative density distribution of graded cellular rod increases monotonically, the actual deformation mode of graded cellular rod is identical with the assumed one in the theoretical derivations. It is noticed that a portion of the graded cellular rods close to the distal end is not fully compacted. A scheme with restricting the shock strain not less than a specific value is proposed to shorten the graded cellular rods. Therefore, the desirable crashworthiness of graded cellular materials can be obtained by designing the density distribution of graded cellular materials.