Design of Three-Dimensional, Triply Periodic Unit Cell Scaffold Structures for Additive Manufacturing

2018 ◽  
Vol 140 (7) ◽  
Author(s):  
Mazher Iqbal Mohammed ◽  
Ian Gibson
Keyword(s):  
Additive Manufacturing ◽  
Periodic Structures ◽  
Three Dimensional ◽  
Unit Cell ◽  
Final Size ◽  
Fused Filament Fabrication ◽  
Cell Structures ◽  
Triply Periodic ◽  
Unit Cells ◽  
Scaffold Structure

Highly organized, porous architectures leverage the true potential of additive manufacturing (AM) as they can simply not be manufactured by any other means. However, their mainstream usage is being hindered by the traditional methodologies of design which are heavily mathematically orientated and do not allow ease of controlling geometrical attributes. In this study, we aim to address these limitations through a more design-driven approach and demonstrate how complex mathematical surfaces, such as triply periodic structures, can be used to generate unit cells and be applied to design scaffold structures in both regular and irregular volumes in addition to hybrid formats. We examine the conversion of several triply periodic mathematical surfaces into unit cell structures and use these to design scaffolds, which are subsequently manufactured using fused filament fabrication (FFF) additive manufacturing. We present techniques to convert these functions from a two-dimensional surface to three-dimensional (3D) unit cell, fine tune the porosity and surface area, and examine the nuances behind conversion into a scaffold structure suitable for 3D printing. It was found that there are constraints in the final size of unit cell that can be suitably translated through a wider structure while still allowing for repeatable printing, which ultimately restricts the attainable porosities and smallest printed feature size. We found this limit to be approximately three times the stated precision of the 3D printer used this study. Ultimately, this work provides guidance to designers/engineers creating porous structures, and findings could be useful in applications such as tissue engineering and product light-weighting.

An Executable Notation, With Illustrations From Elementary Crystallography

1994 ◽  
Author(s):  
Donald B. Mclntyre
Keyword(s):  
Plate Tectonics ◽  
Periodic Structures ◽  
Dimensional Space ◽  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Cubic Symmetry ◽  
Multiple Data ◽  
Special Cases ◽  
Unit Cells ◽  
Crystallographic Axes

Elementary crystallography is an ideal context for introducing students to mathematical geology. Students meet crystallography early because rocks are made of crystalline minerals. Moreover, morphological crystallography is largely the study of lines and planes in real three-dimensional space, and visualizing the relationships is excellent training for other aspects of geology; many algorithms learned in crystallography (e.g., rotation of arrays) apply also to structural geology and plate tectonics. Sets of lines and planes should be treated as entities, and crystallography is an ideal environment for introducing what Sylvester (1884) called "Universal Algebra or the Algebra of multiple quantity." In modern terminology, we need SIMD (Single Instruction, Multiple Data) or even MIMD. This approach, initiated by W.H. Bond in 1946, dispels the mysticism unnecessarily associated with Miller indices and the reciprocal lattice; edges and face-normals are vectors in the same space. The growth of mathematical notation has been haphazard, new symbols often being introduced before the full significance of the functions they represent had been understood (Cajori, 1951; Mclntyre, 1991b). Iverson introduced a consistent notation in 1960 (e.g., Iverson 1960, 1962, 1980). His language, greatly extended in the executable form called J (Iverson, 1993), is used here. For information on its availability as shareware, see the Appendix. Publications suitable as tutorials in , J are available (e.g., Iverson. 1991; Mclntyre, 1991 a, b; 1992a,b,c; 1993). Crystals are periodic structures consisting of unit cells (parallelepipeds) repeated by translation along axes parallel to the cell edges. These edges define the crystallographic axes. In a crystal of cubic symmetry they are orthogonal and equal in length (Cartesian). Those of a triclinic crystal, on the other hand, are unequal in length and not at right angles. The triclinic system is the general case; others are special cases. The formal description of a crystal gives prominent place to the lengths of the axes (a, b, and c) and the interaxial angles ( α, β, and γ). A canonical form groups these values into a 2 x 3 table (matrix), the first row being the lengths and the second the angles.

Design for Additive Manufacturing: Effectiveness of Unit Cell Design Guidelines As Ideation Tools

2019 ◽  
Author(s):  
I’Shea Boyd ◽  
Mohammad Fazelpour
Keyword(s):  
Additive Manufacturing ◽  
Effective Properties ◽  
Cellular Materials ◽  
Design Guidelines ◽  
Unit Cell ◽  
Cell Design ◽  
Recent Approach ◽  
Wide Range ◽  
Unit Cells ◽  
High Flexibility

Abstract The periodic cellular materials are comprised of repeatable unit cells. Due to outstanding effective properties of the periodic cellular materials such as high flexibility or high stiffness at low relative density, they have a wide range of applications in lightweight structures, crushing energy absorption, compliant structures, among others. Advancement in additive manufacturing has led to opportunities for making complex unit cells. A recent approach introduced four unit cell design guidelines and verified them through numerical simulation and user studies. The unit cell design guidelines aim to guide designers to re-design the shape or topology of a unit cell for a desired structural behavior. While the guidelines were identified as ideation tools, the effectiveness of the guidelines as ideation tools has not been fully investigated. To evaluate the effectiveness of the guidelines as ideation tools, four objective metrics have been considered: novelty, variety, quality, and quantity. The results of this study reveal that the unit cell design guidelines can be considered as ideation tools. The guidelines are effective in aiding engineers in creating novel unit cells with improved shear flexibility while maintaining the effective shear modulus.

Structure-unit cell-based approach on three-dimensional representative braided preforms from four-step braiding: Experimental determination of effects of structure-process parameters on predetermined yarn path

2011 ◽  
Vol 82 (3) ◽  
pp. 220-241 ◽  
Author(s):  
Kadir Bilisik ◽  
Nesrin Sahbaz
Keyword(s):  
Cell Structure ◽  
Three Dimensional ◽  
Unit Cell ◽  
Number Of Layers ◽  
Cell Structures ◽  
Cell Dimensions ◽  
Unit Cell Dimensions ◽  
Surface Angle ◽  
Unit Cell Structure

The aim of this study was to understand the effects of braid pattern and the number of layers on three-dimensional (3D) braided unit cell structures. Various unit cell-based representative 3D braided preforms were developed. Data generated from these structures included unit cell dimensions, yarn angle, and yarn length in the unit cell structures. It was shown that braid patterns affected the 3D braided unit cell structures. The 1 × 1 braid pattern made fully interconnected integral 3D braided unit cell structures, whereas the 2 × 1 braid pattern created disconnected braid layers that were connected to the structures edges. When the number of layers increased, 3D braided unit cell thickness also increased. Braid pattern slightly affected the braider yarn angle, whereas the number of layers did not influence it. It was observed that the number of layers considerably affected the yarn length in the unit cell structure. Increasing the layer number from five to 10 layers created a yarn path in the unit cell edge regions called the ‘multilayer yarn length’. This yarn path was not observed below five-layer 3D braided unit cell structures. In jamming conditions, minimum jamming decreased the width of the unit cell structure, but maximum jamming increased its width. On the other hand, minimum jamming decreased the surface angle of the unit cell structure, whereas maximum jamming increased the surface angle. In addition, it was realized that jamming conditions influenced the density of the unit cell but did not affect the yarn length in the unit cell structures.

Design and Analysis of Lattice Structures for Additive Manufacturing

2016 ◽  
Vol 138 (12) ◽  
Author(s):  
Christiane Beyer ◽  
Dustin Figueroa
Keyword(s):  
Additive Manufacturing ◽  
Lattice Structure ◽  
Cost Savings ◽  
Unit Cell ◽  
Cnc Machining ◽  
Numerical Control ◽  
Full Potential ◽  
Lattice Structures ◽  
Cell Structures ◽  
Bending Load

Additive manufacturing (AM) enables time and cost savings in the product development process. It has great potential in the manufacturing of lighter parts or tools by the embedding of cellular/lattice structures that consume less material while still distributing the necessary strength. Less weight and less material consumption can lead to enormous energy and cost savings. Although AM has come a long way over the past 25–30 years since the first technology was invented, the design of parts and tools that capitalize on the technology do not yet encompass its full potential. Designing for AM requires departing from traditional design guidelines and adopting new design considerations and thought structures. Where previous manufacturing techniques (computer numerical control (CNC) machining, casting, etc.) often necessitated solid parts, AM allows for complex parts with cellular and lattice structure implementation. The lattice structure geometry can be manipulated to deliver the level of performance required of the part. The development and research of different cell and lattice structures for lightweight design is of significant interest for realizing the full potential of AM technologies. The research not only includes analysis of existing software tools to design and optimize cell structures, but it also involves design consideration of different unit cell structures. This paper gives a solid foundation of an experimental analysis of additive manufactured parts with diverse unit cell structures in compression and flexural tests. Although the research also includes theoretical finite element analysis (FEA) of the models, the results are not considered here. As an introduction, the paper briefly explains the basics of stress and strain relationship and summarizes the test procedure and methods. The tests concentrate primarily on the analysis of 3D printed polymer parts manufactured using PolyJet technology. The results show the behavior of test specimens with different cell structures under compression and bending load. However, the research has been extended and is still ongoing with an analysis of selective laser melted test specimens in aluminum alloy AlSi10Mg.

scholarly journals Characteristic Mode Analysis of Unit Cells of Metal-Only Infinite Arrays

2019 ◽  
Vol 8 (2) ◽  
pp. 134-142 ◽  
Author(s):  
Y. Haykir ◽  
O. A. Civi
Keyword(s):  
Periodic Structures ◽  
Unit Cell ◽  
Mode Analysis ◽  
Radiation Characteristics ◽  
Characteristic Mode ◽  
Unit Cell Size ◽  
Characteristic Modes ◽  
Unit Cells ◽  
Physical Insight ◽  
Cost Efficient

Characteristic mode analysis of metal only unit cells of periodic structures is performed using Method of Moments based formulation. Ewald’s transformation is incorporated for a fast and cost efficient solution and the advantages over spatial Green’s function are discussed. The influence of the unit cell size on the characteristic modes is demonstrated. Various metal-only reflectarray elements are compared and their radiation characteristics are interpreted using the theory of characteristic modes. It is shown that characteristic modes of the unit cell can help us to understand the radiation and scattering behavior of the unit cell and this physical insight can be used in periodic array unit cell design.

scholarly journals A 3D weaving infill pattern for fused filament fabrication

2021 ◽  
Author(s):  
Yuan Yao ◽  
Cheng Ding ◽  
Mohamed Aburaia ◽  
Maximilian Lackner ◽  
Lanlan He
Keyword(s):  
Additive Manufacturing ◽  
Three Dimensional ◽  
Layer By Layer ◽  
Fused Filament Fabrication ◽  
Repetitive Structure ◽  
Mechanical Linkage ◽  
Manufacturing Technologies ◽  
Dimensional Object ◽  
Anisotropy Of Mechanical Properties ◽  
3D Weaving

Abstract The Fused Filament Fabrication process is the most used additive manufacturing process due to its simplicity and low operating costs. In this process, a thermoplastic filament is led through an extruder, melted, and applied to a building platform by the axial movements of an automated Cartesian system in such a way that a three-dimensional object is created layer by layer. Compared to other additive manufacturing technologies, the components produced have mechanical limitations and are often not suitable for functional applications. To reduce the anisotropy of mechanical strength in fused filament fabrication (FFF), this paper proposes a 3D weaving deposit path planning method that utilizes a 5-layer repetitive structure to achieve interlocking and embedding between neighbor slicing planes to improve the mechanical linkage within the layers. The developed algorithm extends the weaving path as an infill pattern to fill different structures and makes this process feasible on a standard three-axis 3D printer. Compared with 3D weaving printed parts by layer-to-layer deposit, the anisotropy of mechanical properties inside layers is significantly reduced to 10.21% and 0.98%.

A Conceptual Design and Modeling Framework for Integrated Additive Manufacturing

2018 ◽  
Vol 140 (8) ◽  
Author(s):  
Hossein Mokhtarian ◽  
Eric Coatanéa ◽  
Henri Paris ◽  
Mouhamadou Mansour Mbow ◽  
Franck Pourroy ◽  
...  
Keyword(s):  
Additive Manufacturing ◽  
Process Model ◽  
Conceptual Modeling ◽  
Three Dimensional ◽  
Integrated Model ◽  
Performance Model ◽  
Process Equipment ◽  
3D Printer ◽  
Fused Filament Fabrication ◽  
Modeling Framework

Modeling and simulation for additive manufacturing (AM) is commonly used in industry. Nevertheless, a central issue remaining is the integration of different models focusing on different objectives and targeting different levels of details. The objective of this work is to increase the prediction capability of characteristics and performances of additively manufactured parts and to co-design parts and processes. The paper contributes to this field of research by integrating part's performance model and additive technology process model into a single early integrated model. The paper uses the dimensional analysis conceptual modeling (DACM) framework in an AM perspective to generate causal graphs integrating the AM equipment and the part to be printed. DACM offers the possibility of integrating existing knowledge in the model. The framework supported by a computer tool produces a set of governing equations representing the relationships among the influencing variables of the integrated model. The systematic identification of the weaknesses and contradictions in the system and qualitative simulation of the system are some of the potential uses of the model. Ultimately, it is a way to create better designs of machines and parts, to control and qualify the manufacturing process, and to control three-dimensional (3D) printing processes. The DACM framework is tested on two cases of a 3D printer using the fused filament fabrication (FFF) powder bed fusion. The analysis, applied to the global system formed of the 3D printer and the part, illustrates the existence of contradictions. The analysis supports the early redesign of both parts and AM process (equipment) and later optimization of the control parameters.

scholarly journals Selective Laser Sintering Fabricated Thermoplastic Polyurethane/Graphene Cellular Structures with Tailorable Properties and High Strain Sensitivity

2019 ◽  
Vol 9 (5) ◽  
pp. 864 ◽  
Author(s):  
Alfredo Ronca ◽  
Gennaro Rollo ◽  
Pierfrancesco Cerruti ◽  
Guoxia Fei ◽  
Xinpeng Gan ◽  
...  
Keyword(s):  
Thermoplastic Polyurethane ◽  
Selective Laser Sintering ◽  
Three Dimensional ◽  
Laser Sintering ◽  
Gauge Factor ◽  
Strain Sensitivity ◽  
Porous Structures ◽  
Compression Tests ◽  
Triply Periodic ◽  
Unit Cells

Electrically conductive and flexible thermoplastic polyurethane/graphene (TPU/GE) porous structures were successfully fabricated by selective laser sintering (SLS) technique starting from graphene (GE)-wrapped thermoplastic polyurethane (TPU) powders. Several 3D mathematically defined architectures, with porosities from 20% to 80%, were designed by using triply periodic minimal surfaces (TMPS) equations corresponding to Schwarz (S), Diamond (D), and Gyroid (G) unit cells. The resulting three-dimensional porous structures exhibit an effective conductive network due to the segregation of graphene nanoplatelets previously assembled onto the TPU powder surface. GE nanoplatelets improve the thermal stability of the TPU matrix, also increasing its glass transition temperature. Moreover, the porous structures realized by S geometry display higher elastic modulus values in comparison to D and G-based structures. Upon cyclic compression tests, all porous structures exhibit a robust negative piezoresistive behavior, regardless of their porosity and geometry, with outstanding strain sensitivity. Gauge factor (GF) values of 12.4 at 8% strain are achieved for S structures at 40 and 60% porosity, and GF values up to 60 are obtained for deformation extents lower than 5%. Thermal conductivity of the TPU/GE structures significantly decreases with increasing porosity, while the effect of the structure architecture is less relevant. The TPU/GE porous structures herein reported hold great potential as flexible, highly sensitive, and stable strain sensors in wearable or implantable devices, as well as dielectric elastomer actuators.

Experimental Electron Microscopy of Determining B. subtilis Alpha-Amylase Crystals

1990 ◽  
Vol 48 (1) ◽  
pp. 104-105
Author(s):  
Jingqiang Zhang ◽  
Ye Qiaozhen ◽  
Lu Xinying ◽  
Zhou Suiwen ◽  
Luo Jinxian
Keyword(s):  
Electron Microscopy ◽  
Low Dose ◽  
High Vacuum ◽  
Three Dimensional ◽  
High Sensitivity ◽  
Unit Cell ◽  
Alpha Amylase ◽  
Aqueous Environment ◽  
Information Need ◽  
Unit Cells

The structure determination of unstained biological molecules by electron microscopy would be straightforward but for two factors: One is their high sensitivity to electron damage and the other is the loss of three-dimensional order that generally takes place when the specimen's natural aqueous environment is replaced by the high vacuum of the electron microscope. In order to surmounting these difficulties, following methods would be used: (i) Phase contrast; (ii) For vacuum preservation the aqueous medium is replaced by glucose; (iii) Low dose (le/Å2.S) electron microscopy is used to prevent specimen from electron damage. However, a low dose image will not display the projected structure of a molecule or unit cell directly, because contrast and S/N are very low. Nenertheless, provided that the object is comprised of a large enough number of unit cells and that the periodicities are precisely maintained, all the information need to reconstruct the “average” molecule or unit cell will be available by computer. In order to recontrast the object, one needs to determine the Fourier amplitude and phase for each reflection. Fourier analysis of the micrograph data provide the phase and the measurement of the electron diffraction pattern provide the amplitudes. In this paper an experimental method of determining molecular structure of B. subtilis alpha-amylase crystal is discussed.

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