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Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop (2022)

Chapter: 3 Topology Optimization and Advanced Manufacturing Technologies

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Suggested Citation:"3 Topology Optimization and Advanced Manufacturing Technologies." National Academies of Sciences, Engineering, and Medicine. 2022. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
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Suggested Citation:"3 Topology Optimization and Advanced Manufacturing Technologies." National Academies of Sciences, Engineering, and Medicine. 2022. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
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Suggested Citation:"3 Topology Optimization and Advanced Manufacturing Technologies." National Academies of Sciences, Engineering, and Medicine. 2022. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 15
Suggested Citation:"3 Topology Optimization and Advanced Manufacturing Technologies." National Academies of Sciences, Engineering, and Medicine. 2022. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 16
Suggested Citation:"3 Topology Optimization and Advanced Manufacturing Technologies." National Academies of Sciences, Engineering, and Medicine. 2022. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 17
Suggested Citation:"3 Topology Optimization and Advanced Manufacturing Technologies." National Academies of Sciences, Engineering, and Medicine. 2022. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 18
Suggested Citation:"3 Topology Optimization and Advanced Manufacturing Technologies." National Academies of Sciences, Engineering, and Medicine. 2022. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 19
Suggested Citation:"3 Topology Optimization and Advanced Manufacturing Technologies." National Academies of Sciences, Engineering, and Medicine. 2022. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 20
Suggested Citation:"3 Topology Optimization and Advanced Manufacturing Technologies." National Academies of Sciences, Engineering, and Medicine. 2022. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 21
Suggested Citation:"3 Topology Optimization and Advanced Manufacturing Technologies." National Academies of Sciences, Engineering, and Medicine. 2022. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 22
Suggested Citation:"3 Topology Optimization and Advanced Manufacturing Technologies." National Academies of Sciences, Engineering, and Medicine. 2022. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 23
Suggested Citation:"3 Topology Optimization and Advanced Manufacturing Technologies." National Academies of Sciences, Engineering, and Medicine. 2022. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 24
Suggested Citation:"3 Topology Optimization and Advanced Manufacturing Technologies." National Academies of Sciences, Engineering, and Medicine. 2022. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 25

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3 Topology Optimization and Advanced Manufacturing Technologies The workshop’s first session focused on how topology optimization might ­ etter incorporate manufacturability along with functional design of materials and b structures. Without consideration for manufacturability, topology optimization can result in designs that are theoretically optimal but that could never be realized. Speakers were asked to consider three questions: What new methods are required to simultaneously optimize a design and its manufacture? What new manufacturing technologies are enabled by doing so? And, What are the step change improvements that can be created in the underlying manufacturing technologies? Angus Kingon, Brown University, introduced the speakers: James Guest, Johns Hopkins University; Christopher M. Spadaccini, Lawrence Livermore N ­ ational Lab- oratory (LLNL); and Matthew R. Begley, University of California, Santa ­Barbara. Katherine T. Faber, California Institute of Technology, moderated a short discussion following each presentation. TOPOLOGY OPTIMIZATION WITH EMBEDDED MANUFACTURING CONSTRAINTS AND CONSIDERATIONS James Guest, Johns Hopkins University Guest discussed the importance of embedding manufacturability, and its con- straints, into topology optimization, with an emphasis on smaller-scale compo- nents. Doing so will require understanding manufacturing realities, maintaining physical meaning, and pursuing new directions. 13

14 E x p l o i t i n g A d va n c e d M a n u fa c t u r i n g C a pa b i l i t i e s Understanding Manufacturing Realities As topology optimization has evolved, researchers are moving beyond the design of academic problems to focus on real applications, which require manufac- turing. Creating effective solutions for applications will require an understanding of many facets surrounding material behavior during manufacturing, including sensitivity to flaws, failure, and load uncertainties. These manufacturing realities, Guest stressed, should be incorporated into topology optimization algorithms during the design process through a rigorous, mathematically consistent manner independent of the problem formulation or modeling tools, rather than having a designer manually repairing the design pre- ceding fabrication. In three-dimensional (3D) additive manufacturing, build direction, feature sizes, and layer height must also be considered. Design optimality is ultimately dependent on the build direction: that is, building from the bottom up may require a very differ- ent design than building from the top down, as does choosing different feature sizes and layer heights. For example, a thermal heat sink has very different optimal topolo- gies when manufactured at different build directions and different layer heights. As expected, a finer print resolution allows for a design that offers better performance, but Guest pointed out that there is a point of diminishing returns in this respect. Another key manufacturing issue is that layer-based additive manufacturing often uses support structures during fabrication; that use and subsequent removal adds cost and time to the process. However, Guest noted, it is sometimes possible to eliminate the need for supports by designing structures with self-supporting angles. Overhang constraints are another consideration affecting tradeoffs between per- formance, cost, and manufacturability, and they can be incorporated into ­topology optimization design methods.1 Maintaining Physical Meaning The design process must also maintain physical meaning, for example, by ­using specific length scales and exact dimension measurements. Guest’s team builds structures out of “manufacturing primitives”—the smallest feature one can add or subtract during a manufacturing process.2 These primitives are the building blocks of designs, which are computationally assembled in a manner that mimics 1    A.T. Gaynor and J.K. Guest, 2016, Topology optimization considering overhang constraints: Eliminating sacrificial support material in additive manufacturing through design, Structural and Multidisciplinary Optimization 5(5): 1157-1172. 2    J.K. Guest, J.H. Prévost, and T. Belytschko, 2004, Achieving minimum length scale in topology optimization using nodal design variables and projection functions, International Journal for Numerical Methods in Engineering 61(2): 238-254, https://doi.org/10.1002/nme.1064.

T o p o lo g y O p t i m i z at i o n and A d va n c e d M a n u fa c t u r i n g T e c h n o l o g i e s 15 the manufacturing process. The physics governing performance of the engineer- ing component is then applied on top of that, for example, to reflect the perfor- mance requirements and manufacturability of a structural component. Using this ­approach guarantees that a converged design can be manufactured using the specified process. Recent Work and Future Directions Guest shared a few examples of his work and discussed promising advancements toward additive manufacturing, carbon nanotube yarns, architected ­materials, and 3D woven materials. Guest’s team has applied their topology optimization algorithms to a bracket in the Parker Solar Probe, which is funded by NASA, and was able to eliminate more than half of the mass of the conventional design and manufacture it with- out the use of support structures. They have also created efficient fluidic systems, again manufactured without support structures, demonstrating how topology optimization, with manufacturing constraint-informed design, can create designs for real-world applications. While topology optimization typically assumes that structures are monolithic, Guest noted that many materials and components are actually composed of dis- crete embedded objects. Examples of such objects are fibers and carbon nanotube yarns, which offer very high strength and stiffness but cannot be designed using traditional multi-material methods as the objects do not overlap, though they can be surrounded with a matrix material.3 Architected materials will also be important, Guest said. As Ole Sigmund, DTU Technical University of Denmark, noted in his presentation, closed-walled struc- tures are much more effective than ­stochastic foams or truss networks, although they are more challenging to manufacture. Guest said it is possible to open up pores in architected materials without losing too much stiffness to improve permeability and flow rate in such applications as heat exchangers and bone and tissue scaffolds. Finally, 3D woven materials are very promising. Single metallic wires can be combined into lattices, with a weaving pattern that can be optimized for such properties as stiffness, flow, or thermal transport. They can be made with additive manufacturing, akin to textile manufacturing, which is a highly scalable process, although there are tradeoffs among performance, manufacturability, and cost.4 3    J.M. Gardner, C.J. Stelter, E.A. Yasin, and E.J. Siochi, 2016, High Temperature Thermoplastic Addi­ tive Manufacturing Using Low-Cost, Open-Source Hardware, NASA/TM-2016-219344, https://ntrs. nasa.gov/search.jsp?R=20170000214. 4    S.H. Ha, H.Y. Lee, K.J. Hemker, and J.K. Guest, 2019, Topology optimization of 3D woven ­materials using a ground structure design variable representation, Journal of Mechanical Design, Transactions of the ASME 141(6): 061403.

16 E x p l o i t i n g A d va n c e d M a n u fa c t u r i n g C a pa b i l i t i e s In closing, Guest reiterated how topology optimization can improve the design process for engineered systems across a wide variety of applications. He stressed the need to embrace manufacturing considerations and constraints when using this approach, as well as to improve understanding of material properties and manu- facturing variations. He emphasized the value of collaboration between engineers and commercial application designers to inspire new materials and methods to achieve manufacturability. Q&A William Paul King, University of Illinois, Urbana-Champaign, asked whether Guest considered process tolerances and variations as manufacturing constraints. Guest replied that yes, variations due to randomness should be incorporated into the design in order to increase robustness. It is also possible to incorporate reli- ability, although that is more difficult because reliability is its own optimization problem. Another idea is to have a “worst-case scenario” design to deal with un- predictable variations. Graeme Milton, University of Utah, asked if Guest used topology optimization for the 3D weave he described. Guest said yes, but he added that the details of the implementation depend on whether the weave is a continuum of multiple long wires or short finite fibers. OPTIMAL DESIGN, ARCHITECTED MATERIALS, AND ADVANCED MANUFACTURING TECHNOLOGIES Christopher M. Spadaccini, Lawrence Livermore National Laboratory Spadaccini, director of the Additive Manufacturing Initiative (AMI) at LLNL, shared information about recent work from LLNL’s Center for Engineered ­Materials, Manufacturing and Optimization, as well as from the Center for Design Optimiza- tion (CDO), and he detailed several custom advanced manufacturing technolo- gies. LLNL views additive manufacturing as part of an ecosystem of sophisticated fabrication systems that begins with design, moves into synthesis of materials, incorporates the manufacturing process itself, and finishes with qualification and certification to ensure performance. The AMI and CDO seek to improve overall optimization, design, and manu- facturability with the larger goal of solving multiscale, multi-physics, large-scale problems and nonlinear dynamics for manufacturing, both today and in the future. Spadaccini described how this work is advancing the field and paving the way for the manufacturing of components with high-performance materials.

T o p o lo g y O p t i m i z at i o n and A d va n c e d M a n u fa c t u r i n g T e c h n o l o g i e s 17 Recent Work from LLNL’s Center for Design Optimization New manufacturing processes are expanding the possibilities for design com- plexity and multi-material structures. To continue to move the field forward, the CDO created Livermore Design Optimization code (LiDO), a topology optimiza- tion program with current capability for linear elastic structures that is being ex- panded to include other physics and nonlinear phenomena. Topology optimization is a very computationally intensive work, and LiDO utilizes massively parallel, high- performance computing approaches in order to address design complexity, scale, and manufacturability. While LiDO is currently used only for research, ­Spadaccini said that it should be more widely applicable soon. Spadaccini’s team has used LiDO to design architected materials for various projects, such as microscale trusses, a bridge design infilled with lattices, and struc- tures to respond to transient phenomena such as load speed or impact.5,6 Current and Future Manufacturing Technologies Spadaccini described several manufacturing technologies used or developed at LLNL over the past decade. Microstereolithography, developed several years ago and fairly widespread now, is a 3D-printing technique based on light and photo­chemistry that converts liquids to solid structures. It can be used to cre- ate multi-material designs, nanoparticle suspensions, and combined with post- processing and coatings that can, for example, achieve negative thermal expan- sion performance.7 The process can also be scaled up with large-area projection microstereolithography. Designing for multilevel hierarchical structures also shows excellent prog- ress.8 It has been possible to develop new feedstock for microstereolithography to create and print new materials that are architected, not stochastic, and are also 5    W. Chen, S. Watts, J.A. Jackson, W.L. Smith, D.A. Tortorelli, and C.M. Spada, 2019, Stiff isotropic lattices beyond the Maxwell criterion, Science Advances 5(9), https://doi.org/10.1126/sciadv.aaw1937. 6    M. Wallin, N. Ivarsson, and D. Tortorelli, 2018, Stiffness optimization of non-linear elastic structures, Computer Methods in Applied Mechanics and Engineering 330: 292-307, https://doi. org/10.1016/j.cma.2017.11.004. 7    Q. Wang, J.A. Jackson, Q. Ge, J.B. Hopkins, C.M. Spadaccini, and N.X. Fang, 2016, Lightweight mechanical metamaterials with tunable negative thermal expansion, Physical Review Letters 117(17): 175901, https://doi.org/10.1103/PhysRevLett.117.175901. 8    X. Zheng, W. Smith, J.A. Jackson, B. Moran, H. Cui, D. Chen, J. Ye, N. Fang, N. Rodriguez, T. Weisgraber, and C.M. Spadaccini, 2016, Multiscale metallic metamaterials, Nature Materials 15(10): 1100-1106, https://doi.org/10.1038/nmat4694.

18 E x p l o i t i n g A d va n c e d M a n u fa c t u r i n g C a pa b i l i t i e s hierarchical. One of these is graphene aerogel, which offers remarkable surface area and electrical conductivity and is well suited for building supercapacitor electrodes.9 Another process, direct ink writing, is particularly useful for soft materials. Designer “inks” are extruded and used to create complex designs written in silicone, graphene aerogel, nanoporous gold, glass, or printed carbon fiber. Spadaccini described several promising future technologies, including volu- metric additive manufacturing, which would create an entire 3D structure in one operation through the superposition of light beams, akin to a hologram (but not actually a hologram).10 This method has been improved on with computed axial lithography, essentially inverse tomography, with the same results. This technol- ogy enables complex geometries and results in soft materials with good surface finishes.11 Spadaccini also briefly mentioned overprinting, which eliminates the need for a support structure; parallel two-photon lithography, where time-domain focusing brings nanoscale size effects to the macroscale; and diode-based additive manufacturing, which is a two dimensional (2D), selective laser melting of ­metallic components. Q&A Manoj Kolel-Veetil, Naval Research Laboratory, asked about printing volu- metric processes with 3D or 4D shapes. Spadaccini answered that there are a few limitations to overcome, but the process is geometrically diverse and flexible, so it is possible, depending on the material used. Ned Thomas, Rice University, asked for more details about projected light beam liquid polymerization. Spadaccini answered that one complicating factor is the behavior of light in a changing environment, especially on the chemistry side, but diffusion is limited with a photo absorber. With computed axial lithography, it is more crucial to not diffuse the light, and Spadaccini said the team is still learn- ing how to best understand and control what light can do as the material changes. It may also be possible to harness the power of light refraction for fabrication, he added. 9    R.M Hensleigh, H. Cui, J.S. Oakdale, J.C. Ye, P.G. Campbell, E.B. Duoss, C.M. Spadaccini, X. Zheng, and M.A. Worsley, 2018, Additive manufacturing of complex micro-architected graphene aerogels, Materials Horizons 6: 1035-1041, https://doi.org/10.1039/C8MH00668G. 10    M. Shusteff, A.E.M. Browar, B.E. Kelly, J. Henriksson, T.H. Weisgraber, R.M. Panas, N.X. Fang, and C.M. Spadaccini, 2017, One-step volumetric additive manufacturing of complex polymer struc- tures, Science Advance 3(12), https://doi.org/10.1126/sciadv.aao5496. 11    B.E. Kelly, I. Bhattacharya, H. Heidari, M. Shusteff, C.M. Spadaccini, and H.K. Taylor, 2019, Volumetric additive manufacturing via tomographic reconstruction, Science 363(6431): 1075-1079, https://doi.org/10.1126/science.aau7114.

T o p o lo g y O p t i m i z at i o n and A d va n c e d M a n u fa c t u r i n g T e c h n o l o g i e s 19 PROCESS-INFORMED SIMULATIONS OF PRINTED COMPONENTS FOR OPTIMIZATION FRAMEWORKS Matthew R. Begley, University of California, Santa Barbara Begley shared his work on printing bone implants, done with several govern- ment and industry collaborators, as an illustration of the challenges to achieve consistent application and performance with 3D-printed structures. He stressed the importance of understanding microscale features in a design and process interactions during manufacturing and described several experiments to expand that understanding. Printing Bone Implants The 3D printing of bone implants is a growing market with both off-the-shelf and customizable options. For a custom implant, a surgeon defines the volume, infill, and shape in order to correct each particular patient’s problem and ensure robustness. These calculations are extraordinarily complex and require tradeoffs, for example, between relative density and allowable stress. However, Begley’s team has developed software to generate and analyze feasible implant designs in minutes. An important advancement in this area is the ability to grow synthetic bone that can handle strain in the same way as natural bone. Effective bone implants require high strain transference, in addition to other needs, and finding a solu- tion that satisfies all these needs requires counterintuitive thinking and balancing tradeoffs, all of which happens at the millimeter scale, where every behavior has consequences. For example, heat transfer and other microstructural changes that occur during manufacturing can create significant changes in performance. Understanding the Printing Process To achieve consistent performance, it is critical to understand what happens during the printing process, such as the heat transfer described above, and how that affects the final product, Begley said. The topology optimization “engine” to achieve consistent performance requires accurate performance predictions of a candidate design based on many properties, including cell type, porosity, and shape. It is also necessary to weigh how the process, and all the interactions between the geometry, will affect performance. For example, the build direction can substantially change the shape of struts and thus their performance in various dimensions, such as hardness, modulus, load capacity, and yield stress. Begley’s team is still working to understand why these microstructural issues exist and how the process could be adjusted to account for them.

20 E x p l o i t i n g A d va n c e d M a n u fa c t u r i n g C a pa b i l i t i e s Modeling Nodes and Defects to Expand Understanding Modeling nodes for thin-walled intersections illustrates another example of the complexities of the process interactions involved. Build direction is taken into consideration during modeling, but in this case, node composition is more impor- tant. Testing various node designs for thin walls and struts, Begley’s team discovered that changing the print direction creates dramatic differences in properties. Those differences are not well understood, even with modeling or beam theory, but what is clear is that manufacturing dramatically affects properties and performance in ways that cannot be explained with current models. Begley’s lab is also working to understand defects. Because defects cannot be avoided entirely, they are seeking to understand and predict the effects of defects in order to incorporate defect resiliency into topology optimizations. So far, his team has demonstrated that modeling defects with beam elements is helpful, and the team hopes to create efficient simulations to quantify how topologies behave in the presence of defects. Q&A Ryan Watkins, NASA Jet Propulsion Laboratory (JPL), asked if internal voids or surface finish problems affect performance. Begley answered that low temperature applications can be more forgiving of unwanted voids, but at high temperatures they are a problem, although it is possible to eliminate or minimize them. Surface roughness can be good or bad, depending on the application. For example, bone implants can be effective even if very crevassed, which enables giving more weight to fatigue and functionality of the printed implant and less to surface roughness. In all designs, tradeoffs must be made, and in general, all materials systems and processing require a certain level of control for acceptable performance. PANEL DISCUSSION ON THE EMERGING SYNERGY BETWEEN TOPOLOGY OPTIMIZATION, MANUFACTURING, AND MATERIALS Faber introduced the three speakers who had been invited to address the s­ynergies between topology optimization, manufacturing, and materials: Claus Pedersen, Dassault Systèmes Simulia Corp; David Chapin, GE Additive; and ­Jonathan Berger, Nama Development LLC. Kingon moderated an open discussion following their remarks. Claus Pedersen described his team’s approach to topology optimization, which was recognized with first prize at the 2019 U.S. Association for Computational Mechanics Topology Optimization Roundtable, hosted at Sandia National Labo- ratories. The event challenged teams to optimize a suspension component for a

T o p o lo g y O p t i m i z at i o n and A d va n c e d M a n u fa c t u r i n g T e c h n o l o g i e s 21 Formula 1 race car by minimizing mass while staying within allowable parameters (stress, stiffness, and modal eigenfrequencies). Teams provided designs for three versions of the part, manufactured with additive manufacturing, milling, and cast- ing, respectively, as well as three materials: aluminum, titanium, and steel. Pedersen’s team completed the end-to-end work in less than a single day ­using the 3DEXPERIENCE (3DX) platform functional generative design. In addi­ tion, the team did not stop at design, but brought the work all the way through computer-aided design (CAD) model­ing using automated CAD-reconstruction and validations including additive manufacturing process simulation validation. They then simulated processing with thermo-mechanical analysis, which provided insights on the tradeoffs between different manufacturing approaches. “End-to- end” means optimization in the full digital thread going from CAD to computer- aided engineering modeling to topology optimization, including manufacturing constraints, automated validations of optimization results, detailed automated CAD-reconstructions including their automated validation for design require- ments, and process simulations. Pedersen also showed various examples addressing the importance of realistic modeling having such nonlinearities as contacts and material and geometrical nonlinearities in optimization. Additionally, an iterative algebraic multi-grid solver in the Abaqus software was shown for a large scale nonlinear industrial topology optimization including preloading, distribution couplings, and contacts. Pedersen stressed the importance of accounting for transient phenomena (e.g., impact) in nonparametric optimization, which provides significantly more insight than static design load methods alone and frequently static approximated loads cause false designs for the transient applications. Pedersen also described examples of multi- physics optimization in which the 3DX platform was used to create variations in generative designs. The second speaker, David Chapin, was part of the team that helped develop GE’s presence in the additive manufacturing sector. He and his team were tasked to design a new fuel nozzle, a mission that expanded to encompass the entire ­materials, manufacturing, supply chain, and production process. In addition to supplying machines and materials, GE Additive has a consulting service, with engineers from a range of disciplines, serving multiple industries and leading customers through training, identification, and design. Chapin said that having multiple experts—materials scientists, design engineers, process engineers, and others—creates a true understanding of the function of the part and how it can best be manufactured. At Kingon’s request, Chapin described the design process at GE Additive. Teams use several tools, for example, to shorten their design cycle, run models and itera- tions, or accelerate topology optimization. Many of the topology optimization tools are used during the conceptual phase of the design process, especially for complex

22 E x p l o i t i n g A d va n c e d M a n u fa c t u r i n g C a pa b i l i t i e s problems to help initial iterations, Chapin noted. When developing the fuel nozzle, the team developed the material and process for it in parallel with the design for the nozzle itself, a common process at GE Aviation. The final speaker was Jonathan Berger, who discussed his research identify- ing a fabricable geometry that can attain Hashin-Shtrikman theoretical upper bounds for lightweight stiffness.12 In addition, he has identified two other material mesostructures, one with a maximum shear modulus and one with a maximum Young’s modulus, both under the conditions of cubic symmetry, as two other high- performance unit cell designs. Similarly, he has found that with the right combination of geometries, it is pos- sible to design an isometric material geometry with good performance, achieving the upper bounds, that could be created using additive manufacturing. In fact, he found it possible to build different stiffness and strength into structures, making the design very versatile, a similar analysis to that of Gibson.13 The preliminary results from Berger’s optimization models show twofold weight savings, pointing toward the future ability to produce systems with increased stiffness using these more detailed models and analyses. Berger is also working with NASA on a different approach, in which one op- timal meso microstructure is identified, built, and used as a known quantity in multiple designs and products. Following these presentations, Kingon moderated a discussion that covered materials information, when to use topology optimization, achieving manufac- turability, the importance of certification and testing, and future steps to advance the field. Materials Information Carlos Levi, University of California, Santa Barbara, asked if researchers are developing new materials optimized for existing manufacturing tool sets. Chapin replied that there is a lot of work on materials for various existing additive manufac- turing modalities and to characterize those materials can be costly and time consum- ing. He suggested that new, faster, cheaper predictive tools would advance the field. He also noted that in the aerospace industry, a program with a large volume tied to it can withstand several development iterations to create a consistent product, but for smaller, custom orders, predictive capabilities would be needed to enable sound 12    J.B. Berger, H.N. Wadley, and R.M. McMeeking, 2017, Mechanical metamaterials at the theo- retical limit of isotropic elastic stiffness, Nature 543: 533-537, https://doi.org/10.1038/nature21075. 13    L.J. Gibson, 1984, Optimization of stiffness in sandwich beams with rigid foam cores, Materials Science and Engineering 67(2): 125-135, https://doi.org/10.1016/0025-5416(84)90043-0.

T o p o lo g y O p t i m i z at i o n and A d va n c e d M a n u fa c t u r i n g T e c h n o l o g i e s 23 business cases. Pedersen added that existing material data do not, without difficulty, account for manufacturing stresses, which are an important consideration. Reinhard Radermacher, University of Maryland, asked the panel what the smallest feasible feature size was, both today and in the future. Chapin responded that the answer depended on what technology was being used, but that with laser powder bed fusion printing techniques his team has demonstrated the ability to achieve features smaller than 10 thousandths of an inch thick. When to Use Topology Optimization King asked how researchers can know which problems, out of a hundred com- ponents or a million parts, would benefit from topology optimization. ­Pedersen answered that many factors come into play, such as whether the problem is a part or tool, whether it is a critical component, what the costs are, or if there will be downstream effects. Berger noted that, unfortunately, economic drivers such as part count reduction are usually weighted more heavily than performance improvement. Chapin agreed that costs are often emphasized, and he said that it is necessary to create a business case for customers by stressing life-cycle costs, part durability, and supply chain issues. The ideal customer can look beyond parts, he continued, and come to understand how functions can be enhanced to improve performance, even if an exact value cannot be assigned. Pedersen added that aviation and auto- motive manufacturers are starting to look at how different components interface and assess how better assembly can optimize savings, suggesting they might be ready to look beyond economics for a single component design. Kingon noted that larger companies are more able to balance tradeoffs and make large investments in optimization, but smaller companies need a simplified model. Pedersen agreed, adding that his company has several automated optimiza- tions that smaller companies could access. Several attendees from government agencies commented on opportunities they see for topology optimization in the contexts of their organizations. Julie ­Christodoulou, Office of Naval Research, stated that optimization is well aligned with the Navy’s goals of streamlining systems, reducing weight, and simplify- ing structure. Watkins, JPL, shared that using topology optimization and addi- tive manufacturing in the space industry is beneficial but requires scrutiny as to whether conventional design philosophies—such as industry standard factors of safety—need specialized formulation. William Benard, Army Research Laboratory, added that threat-response is critical to the Department of Defense, and topology optimization could be used to quickly design for new threats.

24 E x p l o i t i n g A d va n c e d M a n u fa c t u r i n g C a pa b i l i t i e s Achieving Manufacturability Haydn Wadley, University of Virginia, pointed out that while there is general agreement about designing effective structures, their benefits are limited if they cannot yet be manufactured. Berger agreed but noted that it should be relatively simple to create a machine that makes one specific topology, especially if tools from other industries are adopted and modified. It may be unlikely that one general machine can make everything, but progress can be made by narrowing the goal to very specific applications. Ole Sigmund, DTU Technical University of Denmark, asked about reaching mass manufacturability. Berger agreed that it was not possible yet, and there are several factors to consider, such as scale, multiple material systems, process, and characterization. He reiterated that the best motivation will be one specific appli- cation. Nama Development LLC is getting closer to that with its work for NASA, but right now there is no clear solution, he said. In response to a question by Frank Zok, University of California, Santa Barbara, Berger noted that researchers are working on specific optimizations for closed-shell structures, but they are very difficult to make and create performance reductions. Kolel-Veetil asked if manufacturing processes were material-agnostic, and Chapin answered that they can be and in situ data monitoring and predictive capabilities can be used to tailor processing power or speed to a particular alloy. The Importance of Certification and Testing When asked if topology optimization introduces certification challenges, Berger replied that it does, and they need to be addressed. For example, internal porosity creates a host of issues. Kingon added that it is critically important to in- clude test structures that guarantee performance after processing, and they should be included in consulting and software packages as well. Chapin agreed, noting that in the aviation industry, the certification/qualification process includes robust testing, which would be extended for any new materials system. Jennifer Wolk, Office of Naval Research, noted that the Navy is very interested in certification and qualification, as it is an important way to combine computational and experimental tools to build understanding of a new microstructure and its prop- erties. Certifications also help minimize risk and enable quality assurance so that new technologies, however exciting, can be manufactured and implemented safely. Benard suggested consulting the Federal Aviation Administration on verifica- tion and validation testing. He sees additive manufacturing as very valuable if it can evolve to the point where designing, building, and testing is quick and inexpensive. Verification and validation testing inspire confidence in a product, he continued, and it is possible to learn methods from other agencies or fields.

T o p o lo g y O p t i m i z at i o n and A d va n c e d M a n u fa c t u r i n g T e c h n o l o g i e s 25 Future Steps to Advance the Field Thomas said he sees amazing potential for the field, but it is important to plan now for two things: (1) sustainability and recyclability of materials, to avoid adding more waste to the world; and (2) the ability to maintain or repair the com- plex ­machinery that will be needed. Berger agreed, noting that repairing complex ­material geometries is not currently possible. Right now, he suggested, the best way forward is to avoid wading through all the complexities and interactions that can exist in additive manufacturing, which cannot be addressed simultaneously or generically, and identify a tractable problem with manageable elements and clear economic gains. Chapin stressed the importance of reducing the time required to characterize new materials. Additive manufacturing is very different from traditional manu- facturing, and a poor understanding of how new materials behave has created un­realistic expectations, he said. He added that it is also important to develop industry standards around the additive manufacturing process in general. Pedersen noted that the current trial-and-error approach to testing should also be replaced with faster prediction techniques to include a host of materials characteristics, from buckling and plastic strains to recyclability and design and manufacturing processes.

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Topology optimization is a digital method for designing objects in order to achieve the best structural performance, sometimes in combination with other physical requirements. Topology optimization tools use mathematical algorithms, such as the finite element method and gradient computation, to generate designs based on desired characteristics and predetermined constraints. Initially a purely academic tool, topology optimization has advanced rapidly and is increasingly being applied to the design of a wide range of products and components, from furniture to spacecraft.

To explore the potential and challenges of topology optimization, the National Academies of Sciences, Engineering, and Medicine hosted a two-day workshop on November 19-20, 2019, Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design. The workshop was organized around three main topics: how topology optimization can incorporate manufacturability along with functional design; challenges and opportunities in combining multiple physical processes; and approaches and opportunities for design of soft and compliant structures and other emerging applications. Speakers identified the unique strengths of topology optimization and explored a wide range of techniques and strengths of topology optimization and explored a wide range of techniques and achievements in the field to date. This publication summarizes the presentations and discussion of the workshop.

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