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Suggested Citation:"4 Topology Optimization and Multi-Physics." National Academies of Sciences, Engineering, and Medicine. 2021. 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:"4 Topology Optimization and Multi-Physics." National Academies of Sciences, Engineering, and Medicine. 2021. 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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Page 27
Suggested Citation:"4 Topology Optimization and Multi-Physics." National Academies of Sciences, Engineering, and Medicine. 2021. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 28
Suggested Citation:"4 Topology Optimization and Multi-Physics." National Academies of Sciences, Engineering, and Medicine. 2021. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 29
Suggested Citation:"4 Topology Optimization and Multi-Physics." National Academies of Sciences, Engineering, and Medicine. 2021. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 30
Suggested Citation:"4 Topology Optimization and Multi-Physics." National Academies of Sciences, Engineering, and Medicine. 2021. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 31
Suggested Citation:"4 Topology Optimization and Multi-Physics." National Academies of Sciences, Engineering, and Medicine. 2021. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 32
Suggested Citation:"4 Topology Optimization and Multi-Physics." National Academies of Sciences, Engineering, and Medicine. 2021. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 33
Suggested Citation:"4 Topology Optimization and Multi-Physics." National Academies of Sciences, Engineering, and Medicine. 2021. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 34
Suggested Citation:"4 Topology Optimization and Multi-Physics." National Academies of Sciences, Engineering, and Medicine. 2021. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 35
Suggested Citation:"4 Topology Optimization and Multi-Physics." National Academies of Sciences, Engineering, and Medicine. 2021. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 36
Suggested Citation:"4 Topology Optimization and Multi-Physics." National Academies of Sciences, Engineering, and Medicine. 2021. Exploiting Advanced Manufacturing Capabilities: Topology Optimization in Design: Proceedings of a Workshop. Washington, DC: The National Academies Press. doi: 10.17226/26362.
×
Page 37

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4 Topology Optimization and Multi-Physics Most topology optimizers consider a single physical domain, such as stress- strain analysis for structural design or electromagnetic analysis for photonic crystal design. For the workshop’s second session, speakers were asked to consider chal- lenges and opportunities that combine multiple physical processes. For example: How might we create an optimal design for both mechanical properties along with fluid-structure interactions; or how might we create an optimal design for a chemi- cally reacting flow in the presence of a distributed catalyst? The session focused on the methods required for multi-functional topology optimization and the software intelligence required to search these design spaces. Carlos Levi, University of California, Santa Barbara, introduced the speakers: Graeme Milton, University of Utah; Ryan Watkins, NASA Jet Propulsion Labora- tory (JPL); and Reinhard Radermacher, University of Maryland. William Paul King, University of Illinois, moderated a short Q&A following each speaker’s remarks. THE ROLE OF BOUNDS IN TOPOLOGY OPTIMIZATION Graeme Milton, University of Utah Milton described experiments at the intersection of topology optimization and bounds that explore how the two together could push past known material behav- iors and expand what is possible. Studying bounds, he said, can help in the quest to identify opportunities for topology optimization and lead to surprising results, while using topology optimization can suggest room for improvement in bounds. 26 PREPUBLICATION COPY—Uncorrected Proofs

T o p o lo g y O p t i m i z at i o n and M u lt i - P h y s i c s 27 Microstructure Bounds Microstructure bounds have been studied and analyzed without topology optimization for decades. For electromagnetic absorption and refraction, Milton attained three points on the bound in 1980.1 More recently, in 2019, Christian Kern identified three additional new points on the bound, with results depending on the material parameters. A new optimal bound was also established, corresponding to coated sphere microstructures. There are many real-world applications to which this approach can be applied, such as effective smoke screens, innovative cancer treatments, and improved solar cells.2,3 Using Topology Optimization Coupling bounds with topology optimization makes sense, Milton said, ­because bounds provide global targets, and they can also predict which ­materials to start with. As an example put forward by Owen Miller, designers might compare graphene with aluminum zinc oxide for the purpose of scattering and absorbing electro­ magnetic radiation. In 1997, bounds with thermal expansion and bulk modulus were realized using topology optimization, showing that by mixing three materials that all expand when heated, one could get a composite that contracts when heated.4 In addition, when applying topology optimization, results approach the theoretical bounds.5 Milton also shared findings illustrating how human intuition and topology optimization can come together: researchers trying to understand why a material expanded sideways when it was stretched achieved similar design structures first using intuitive models and bounds and then topology optimizations.6,7 1    G.W. Milton, 1980, Bounds on the complex dielectric constant of a composite material, Applied Physics Letters 37(3), https://doi.org/10.1063/1.91895. 2    X. Huang, I.H. El-Sayed, and W. Qian, 2006, Cancer cell imaging and photothermal therapy in the near-infrared region by using gold nanorods, Journal of the American Chemical Society 128(6): 2115-2120, https://doi.org/10.1021/ja057254a. 3    H.A. Atwater and A. Polman, 2010, Plasmonics for improved photovoltaic devices, Nature ­Materials 9: 205-213, https://doi.org/10.1038/nmat2629. 4    O. Sigmund and S. Torquato, 1997, Design of materials with extreme thermal expansion using a three-phase topology optimization method, Journal of the Mechanics and Physics of Solids 45(6): 1037-1067, https://doi.org/10.1016/S0022-5096(96)00114-7. 5    O.D. Miller, C.W. Hsu, M.T.H. Reid, W. Qiu, B.G. DeLacy, J.D. Joannopoulos, M. Soljacic, and S.G. Johnson, 2014, Fundamental limits to extinction by metallic nanoparticles, Physical Review ­Letters 112(12): 123903, https://doi.org/10.1103/PhysRevLett.112.123903. 6    G. Milton, 1992, Composite materials with Poisson’s ratios close to −1, Journal of the Mechanics and Physics of Solids 40: 1105-1137, https://doi.org/10.1016/0022-5096(92)90063-8. 7    U.D. Larsen, O. Sigmund, and S. Bouwstra, 1997, Design and fabrication of compliant mecha- nisms and material structures with negative Poisson’s ratio, Journal of Microelectromechanical Systems 6(2): 99-106, https://doi.org/10.1109/84.585787. PREPUBLICATION COPY—Uncorrected Proofs

28 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 Pushing Past Known Behavior Studying mathematical possibilities through bounds, Milton said, teaches peo- ple to believe that what is not obviously forbidden may be actually possible. That belief should motivate scientists to search for and probe interesting behavior, he said. For example, for a difficult topic like negative thermal expansion, the same equation applied to the equivalent problem of response of a material immersed in water results in the surprising material property that the material expands when the water pressure is increased, almost similar to negative expansion resulting from materials with positive thermal expansion.8 The work is not simple, but once something is revealed to be possible, an explanation usually follows. In another example, Milton described several optimizations to characterize the elasticity of materials. A large range of properties was found, but there is clearly a missing bound in the simultaneous maximization of shear resistance and compres- sion. Bounds on spontaneous emission of radiation, radiative transfer of energy, and surface-enhanced Raman scattering of the material indicated the potential for orders of magnitude improvement that in some cases have been subsequently achieved by topology optimization. Further optimizations may reveal more, Milton suggested.9 Other experiments involving heat transfer, Raman spectroscopy, and the Strehl ratio also suggest that improvements in topology optimizations could expand what is currently known. In one paper, Milton and Marc Briane were able to use a chainmail design to demonstrate a reversal of the Hall voltage, later confirmed by numerical simulation and physical experiments. Adding topology optimization, he suggested, could create further surprising insights.10 However, experiments have also shown that in some cases, topology optimization is not necessary, for example in plane-wave scattering, Smith-Purcell radiation, and high-efficiency plasmonic radiators.11,12,13 8    J. Qu, M. Kadic, A. Naber, and M. Wegener, 2017, Micro-structured two-component 3D meta- materials with negative thermal-expansion coefficient from positive constituents, Scientific Reports 7: 40643, https://doi.org/10.1038/srep40643. 9    R.E. Christiansen, J. Michon, M. Benzaouia, O. Sigmund, and S.G. Johnson, 2019, Inverse design of nanoparticles for enhanced Raman scattering, Physics Optics, https://arxiv.org/abs/1911.05002. 10    M. Briane and G. Milton, 2009, Homogenization of the three-dimensional hall effect and change of sign of the Hall coefficient, Archive for Rational Mechanics and Analysis 193(3): 715-736, https:// doi.org/10.1007/s00205-008-0200-y. 11    O.D. Miller, A.G. Polimeridis, M.T.H. Reid, C.W. Hsu, B.G. DeLacy, J.D. Joannopoulos, M. ­Solacic, and S.G. Johnson, 2016, Fundamental limits to optical response in absorptive systems, Optics Express 24(4): 3329-3364, https://doi.org/10.1364/OE.24.003329. 12   Y. Yang, A. Massuda, and C. Roques-Carmes, 2018, Maximal spontaneous photon emission and energy loss from free electrons, Nature Physics 14: 894-899, https://doi.org/10.1038/s41567-018-0180-2. 13   Y. Yang, O.D. Miller, T. Christensen, J.D. Joannopoulos, and M. Soljacic, 2017, Low-loss plasmonic dielectric nanoresonators, Nano Letters 17(5): 3238-3245, https://doi.org/10.1021/acs.nanolett.7b00852. PREPUBLICATION COPY—Uncorrected Proofs

T o p o lo g y O p t i m i z at i o n and M u lt i - P h y s i c s 29 Q&A Manoj Kolel-Veetil, Naval Research Laboratory, wondered if topology optimi- zation could be used to envision quantum entanglement, and Milton replied that it was a question worth studying. In response to a question by Benard, Milton also affirmed that metamaterial behaviors could be successfully used in miniaturization, for example, for antenna design. King asked about the implications of systems that populate all the way up to a bound, and Milton replied that the manufacturing process makes a huge differ- ence in reaching the bound, regardless of if topology optimization is used or not. DESIGNING OPTICAL INSTRUMENTS FOR SPACE APPLICATIONS: MULTI-PHYSICS TOPOLOGY OPTIMIZATION Ryan Watkins, NASA Jet Propulsion Laboratory Watkins, who is steeped in all aspects of design work at JPL and spearheads the organization’s topology optimization work, described how his team used topology optimization to design a bracket for a star tracker. Topology Optimization for Space Applications Topology optimizations are extremely well suited to the design problems JPL faces, Watkins said, because each spacecraft is unique and demands high perfor- mance with a limited mass budget. In addition, JPL tends to manufacture items in very low quantities and is therefore not restricted by supply chain and mass production limitations that often prevent topology optimization’s often complex geometries from being economical. For example, he said, JPL has successfully used SIMP-based methodologies to design a new lander concept for Europa (a moon of Jupiter) and also, more generally, to solve difficult design problems. In those cases, JPL formulates the problem to account for, among other things, the dynamic interactions during a launch, the temperature changes in space (a nonlinear problem), and manufactur- ing limitations. Designing a Star Tracker Bracket Star trackers are one of the most commonly used optical instruments on space missions, as they help spacecraft orient themselves in space. It is essential to know where the instrument is pointing and any potential deviations within a millidegree of configuration; as a result, the bracket on a star tracker has very tight pointing PREPUBLICATION COPY—Uncorrected Proofs

30 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 requirements. It is also important to design for multiple environments. For ex- ample, in space, it can be extremely hot or cold, which can cause non-uniform deformation because spacecraft are made up of different materials that react dif- ferently to extreme temperatures. The current bracket design, created with a typical JPL methodology, was not meeting pointing requirements, and so Watkins’ team turned to topology optimization to solve several problems: achieve the tight point- ing requirement, reduce the cost and schedule associated with manufacturing the product, and cut down on the design time associated with a structural/thermal/ optically coupled problem. Topology optimization is a way to solve these general problems by uniting siloed design teams, which decreases the design time and interaction problems. It can also help designs meet requirements for the highly dynamic launch environ- ment and the temperature changes in space. In addition, it can help in the additive manufacturing phase, where the design must also be able to withstand the manu- facturing environment itself. Using Topology Optimization For this specific problem, the team’s design objectives had to balance maxi- mizing stiffness, minimizing mass, and maximizing instrument performance. To accomplish these objectives, they followed a SIMP-based optimization workflow that optimized the design, realized a manufacturable geometry, and verified that the realized design met the original constraints and requirements. Watkins detailed the bracket design’s workflow, including the resulting mass, load and stress constraints, buckling, temperature ranges, and post-processing smoothing. Even with topology optimization, the team struggled to create a component that met every constraint. Specific struggles included conventional penalty continu- ation methods and the intricacies associated with uncertain interfaces between the spacecraft and instrument. The hardest challenge of all, Watkins said, was eliminat- ing erratic constraint violations on realization of a topology optimization solution. However, he said, the team has not given up; as a next step, they plan to add shape optimization as a final step to the process in hopes of perfecting the workflow. Q&A In response to a question from Benard, Watkins stated that commercial soft- ware has fundamental limitations, such as emphasizing structural problems, with few or no options for thermal problems. In fact, he said, he often finds himself overly simplifying problems in order to be able to apply software. Ole Sigmund, DTU Technical University of Denmark, commented that commercial software is often frustrating, and users have to be more demanding as consumers in order to PREPUBLICATION COPY—Uncorrected Proofs

T o p o lo g y O p t i m i z at i o n and M u lt i - P h y s i c s 31 force improvements. Watkins agreed, noting that he is actively looking for better alternatives. Milton suggested adding an actuator to his design, but Watkins noted that ­going beyond basic optical design currently poses significant challenges. Lastly, King asked how risk and uncertainty are addressed in the space context. Watkins said that although JPL performs a battery of tests, further formalizing that process would help reduce risk. The most common approach now, he noted, is to build two copies of a design in order to test one to failure and proof-load the other. TOPOLOGY OPTIMIZED HEAT EXCHANGERS: THEIR POTENTIAL, DESIGN, AND MANUFACTURING CHALLENGES Reinhard Radermacher, University of Maryland Radermacher and his team are using topology optimization to redesign the heat exchangers inside heating and cooling devices, research that could enable compa- nies to manufacture air conditioners and heat pumps that are much smaller and far more energy efficient than the products available today. He described how his team built a design from scratch using topology optimization and the challenges and advantages to that approach. Heat exchangers enable heat transfer, which is described by the equation Q = UA ΔT. The surface area that separates the two fluids, “A,” is crucial. The com- pactness of the heat exchanger and the material utilization must scale with the area. Traditional air conditioning heat exchangers range from 5- to 10-millimeter-wide tubes, and micro-channel heat exchangers are in the 1 millimeter range. However, in the sub-millimeter range, systems get very complex and especially compact, which raises exciting possibilities. 3D printing may be a tool to implement such designs, Radermacher said.14 Designing from Scratch Unfortunately, nothing in the sub-millimeter range has been built before, so finding design data was a challenge. To create a starting geometry, Radermacher’s team designed and optimized heat exchangers virtually before building prototypes. Their methodology was to automate the evaluation of the performance of genera- tions of heat exchanger geometries in terms of, for example, the tube shape and 14    D. Bacellar, V. Aute, H. Zhiwei, and R. Radermacher, 2016, Airside friction and heat transfer characteristics for staggered tube bundle in crossflow configuration with diameters from 0.5 mm to 2.0 mm, International Journal of Heat and Mass Transfer 98: 448-454, https://doi.org/10.1016/j. ijheatmasstransfer.2016.02.072. PREPUBLICATION COPY—Uncorrected Proofs

32 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 spacing; conduct computational fluid dynamics analyses; perform post-processing of the data; develop metamodels; and finally print and then test the most promis- ing designs. Next, promising designs were put through an optimization framework, adding manufacturing constraints to develop designs that could be prototyped using the manufacturing technologies available today.15 After a decade of work, a large part of this process is now automated, which significantly reduces engineering time. It also results in very useful correlations that can be applied to any heat exchanger design based on that design space. Comparing their most promising designs to baseline automotive heat ­exchangers, the team found that their designs all achieved maximum compact- ness, though the most promising of them were not manufacturable. NURBS-Tube HX was the only design that was 3D printable at relaxed specifications, and the team validated that all the prototypes met industry standards and could be very productive. R ­ adermacher also described work by a number of other researchers to create novel designs for 3D-printed heat exchangers. Challenges and Advantages Designing new heat exchangers with topology optimization has several chal- lenges. First, it is difficult to predict the performance of shapes that have not existed before, due to both lack of design data and feasible shape evolution to avoid leak- ing flow paths. It is also hard to know the smallest possible feature size that can be manufactured, how to integrate complex headers, and how to tune the machine parameters of 3D printers. In addition, before a prototype is available, it is difficult to evaluate and optimize a design further, as well as judging its reproducibility. However, Radermacher said, the approach also has several advantages. The newly developed optimization framework reduces the number of tests required. In addition, it can be used to change shape and topology simultaneously, create un- paralleled compactness, and enable hybrid 3D-traditional manufacturing. Finally, the designs are shape-conforming, so they could be fitted to the hull of a ship, a jet engine, or the hood of a car. There is still much to learn about using topology optimization to realize brand-new designs. Looking forward, Radermacher concluded by suggesting that designers could benefit by learning from nature, such as by using the human lung to inspire innovative, manufacturable heat exchange technology. 15    O. Abdelaziz, V. Aute, S. Azarm, and R. Radermacher, 2010, Approximation-assisted optimiza- tion for novel compact heat exchanger designs, HVAC&R Research 16(5): 707-728, https://doi.org/ 10.1080/10789669.2010.10390929. PREPUBLICATION COPY—Uncorrected Proofs

T o p o lo g y O p t i m i z at i o n and M u lt i - P h y s i c s 33 Q&A King asked if Radermacher had deconstructed the printed heat exchanger to learn more, and Radermacher answered that the team plans to do so after run- ning other tests. Levi and another participant suggested that the printing process can also affect surface smoothness, which can in turn affect heat transfer. While ­Radermacher agreed that there are tradeoffs between surface smoothness and roughness, he said he sees reproducibility as the larger challenge. King asked if Radermacher had looked at other fluid path shapes, and ­Radermacher answered that the team usually designs the geometry first and has not yet experimented with computer-designed flow channels, though he agreed that such an approach is worth future exploration. In response to Levi, he also noted that there is currently no known way to evaluate the pressure drop in an additively manu- factured part versus a standard tube, but that such capability must be developed. PANEL DISCUSSION ON TOPOLOGY OPTIMIZATION AND MULTI-MATERIALS King introduced the three panelists who had been invited to address topology optimization and multi-materials: Alicia Kim, University of California, San Diego; Kimberly Saviers, United Technologies Research Center (UTRC); and Rebecca Dylla-Spears, Lawrence Livermore National Laboratory (LLNL). Following their remarks, Levi moderated an open discussion. Alicia Kim is developing level set topology optimizations to solve multiscale, multi-physics problems in order to achieve multifunctionality. Level set methods are very different from other optimizations, as they have the ability to change a topology as the optimization runs, both quickly and at a large scale. Kim has used this method to optimize for more than 3.2 billion elements, and she expects to be able to do more. The process creates crisp, continuous, and smooth topologies. Level set topology optimization uses implicit signed distance function, which originated in image processing and mapping software, to represent boundaries. The resulting equations create stable solutions with no filtering or regularization needed, and while there are Courant-Friedrichs-Lewy restrictions, it is still possible to achieve large-scale optimizations. Multi-materials are expected to have multifunctionality, where the different behaviors of different materials, at the microscopic level, can be used to solve com- plex problems, for example, in structural mechanics, heat exchange, and thermal fluids. Kim expressed her belief that level set topology optimization is the key to producing manufacturable multi-material designs with multifunctionality. Her team is working on several coupled multi-physics problems, including optimized heat-exchanging load-carrying battery packs for NASA aircraft, using PREPUBLICATION COPY—Uncorrected Proofs

34 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 lightning holes for cooling, and multiscale designs, such as interfitting octets. In addition, she has added multifunctionalities to a structure with a meta-­material that was optimized with different microstructural variations for temperature and mechanical load. Finally, her team has implemented topology optimization into multidisciplinary design optimization in order to create larger, systems-level optimizations. Kimberly Saviers, the second speaker, works on internal aerospace functions, in particular, flow ducts and heat exchangers for temperature reduction, which she believes would benefit from combining thermal and fluid aspects by adding the study of convection in addition to conduction. To that end, she shared designs for flow types from topology optimizations, although without thermal aspects, point- ing out that the structures vary greatly for air versus water flow. In automotive ducts, topology optimizations have made some improvements in minimizing the flow separation to reduce pressure drop, which is important for space constraints. Pressure drop can also increase fuel burn, and lowering fuel burn will lower costs, Saviers pointed out. She also shared potential designs for flow ducts, one in which fluid is discouraged from traveling in a certain direction and another one in which fluid goes through a branching pattern for cooling purposes. Saviers has used topology optimization to improve conventionally manufac- tured heat exchangers. Noting that the design of heat exchangers has essentially remained the same for decades, she said that additive manufacturing capabilities will enable new designs. For example, one new design was calculated to have two times greater heat transfer and two times less pressure drop than conventional models, and the 3D-printed prototype also showed improved results. In addition, topology optimization tools have achieved reduced wall temperatures. To build on these promising prototypes, Saviers said the next step is to scale up the topology optimization techniques to manufacture real world, industry-ready products. The third speaker, Rebecca Dylla-Spears, began by noting that rather than aiming to find new ways to produce optics that could be fabricated conventionally, LLNL researchers are focused on opening up the optical design space generally, pur- suing interesting technologies that can expand possibilities and take advantage of multiple advanced manufacturing capabilities, including additive manufacturing. Typically, optical components are made from material with uniform compo- sition and therefore uniform material properties. Dylla-Spears detailed research ­focused on creating new optical materials with tunable material properties im- parted through local control of bulk composition, structure, or surface. Optics with bulk compositional gradients are made with direct ink writing, at room tem- perature and with a controlled flow rate; they have been demonstrated in yttrium aluminum garnet with a neodymium dopant gradient, as well as in silica glass with PREPUBLICATION COPY—Uncorrected Proofs

T o p o lo g y O p t i m i z at i o n and M u lt i - P h y s i c s 35 gradient in refractive index.16,17 Structural gradients can provide enhanced stiffness per weight and are well suited for mirrors. Local control of surface features over large areas leads to anti-reflective metasurfaces.18 In addition, these techniques can be used to produce optics with uniform material properties, she noted. Dylla-Spears expressed her view that using topology optimization for additively manufactured optics has great potential, particularly for optimized lightweighting, athermalization, and thermal management.19,20,21 Additive manufacturing also makes it possible to change materials within a structure, opening up other exciting possibilities. In addition, the optics themselves, not just their mounts and supports, can also be optimized for size, weight, surface, and power reduction. Finally, she suggested that applying topology optimization to the entire system, not just a few components, and incorporating metamaterials and multi-materials, could create game-changing designs.22 DISCUSSION Haydn Wadley, University of Virginia, moderated wrap-up discussions at the end of each day of the workshop. In this first day’s wrap-up, participants asked the speakers to elaborate further on opportunities topology optimization offers 16    K. Jones, Z.M. Seeley, N.J. Cherepy, E.B. Duoss, and S.A. Payne, 2018, Direct ink write fab- rication of transparent ceramic gain media, Optical Materials 75: 19-25, https://doi.org/10.1016/ j.optmat.2017.10.005. 17    N.A. Dudukovic, L.L. Wong, D.T. Nguyen, J.F. Destino, T.D. Yee, F.J. Ryerson, T. Suratwala, E.B. Duoss, and R. Dylla-Spears, 2018, Tuning nanoparticle suspension viscoelasticity for multimaterial 3D printing of silica-titania glass, ACS Applied Nano Materials 1(8), LLNL-JRNL-749401, https:// www.osti.gov/servlets/purl/1476223. 18    J.Y. Hoang, T. Nguyen, N.J. Ray, M.A. Johnson, W.A. Steele, J.M. Chesser, S.H. Baxamusa, S. Elhadj, J.T. McKeown, M.J. Matthews, and E. Feigenbaum, 2019, Scalable light-printing of substrate- engraved free-form metasurfaces, ACS Applied Materials & Interfaces 11(25): 22684-22691, https:// doi.org/10.1021/acsami.9b07135. 19    G. Liu, L. Guo, X. Wang, and Q. Wu, 2018, Topology and parametric optimization based lightweight design of a space reflective mirror, Optical Engineering 57(7): 075101, https://doi. org/10.1117/1.OE.57.7.075101. 20    K.R. Bryant and D. Hayduke, 2018, “Additive Manufacturing Volume Optimization for Athermal Optics,” Proceedings Volume 10627, Advanced Optics for Defense Applications: UV through LWIR III, SPIE Defense + Security Event, https://doi.org/10.1117/12.2306080. 21    L. Wang, J. Liang, Z. Zhang, and Y. Yang, 2019, Nonprobabilistic reliability oriented topological optimization for multi-material heat-transfer structures with interval uncertainties, Structural and Multidisciplinary Optimization 59: 1599-1620, https://doi.org/10.1007/s00158-018-2146-5. 22    S. Koppen, M. van der Kolk, F.C.M. van Kempen, J. de Vreugd, and M. Langelaar, 2018, Topology optimization of multicomponent optomechanical systems for improved optical performance, Struc­ tural and Multidisciplinary Optimization 58: 885-901, https://doi.org/10.1007/s00158-018-1932-4. PREPUBLICATION COPY—Uncorrected Proofs

36 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 the context of optics, heat exchangers, interfaces, acoustics, and self-healing polymers. Optics Design One participant asked how to find allowables for gradients with multi-­materials, which Dylla-Spears said was an important challenge. In glass, she said, researchers are working to increase the refractive index change, but overall, progress will require significant modeling development, in parallel with experimentation, to account for known and unknown phenomena. In general, she added, broad problems are dif- ficult to solve. What is needed is more effort and resources and also a narrowing of the parameter space, as Jonathan Berger, Nama Development LLC, had suggested, to achieve particular solutions. Levi asked if there were tools to help balance multi-physics processes. Dylla- Spears said that she hopes to make a stable of tools one day, but they do not exist yet. As the community that would benefit most from such tools, she suggested optical designers should be motivated to develop them instead of relying on commercially- developed solutions. Brett Compton, University of Tennessee, suggested that the optics problems Dylla-Spears described were unique in that they do not go from gradient to binary and that could be beneficially applied to other problems. Dylla-Spears agreed, not- ing that the gradients can be as steep as tens or hundreds of microns, depending on the approach. Heat Exchangers Watkins pointed out that one of JPL’s biggest successes with additive manu- facturing has come from two-phase heat exchangers, and he asked if UTRC had a similar experience. Saviers replied that her group does some two-phase work and said that applying topology optimization to that would be an intriguing idea. Eric Amis, University of Akron, asked about directional heat flow needs. Kim replied that it should be possible to use her group’s heat exchanger designs for that if the material is the same and only the geometry is changed. It may also help to control the orientation of filler materials in a composite. Compton noted that he believes it is possible to use topology optimization to control both heat flow direc- tion and filler material orientation. Levi asked about the durability of these novel heat exchanger designs in a real-world environment, particularly in the presence of air pollution and other contaminants. Radermacher answered that any hollow part can invite debris, which can cause problems, and there are few data available to use for modeling that sce- nario. Understanding the bounds would help, as would adding filtering capabilities, PREPUBLICATION COPY—Uncorrected Proofs

T o p o lo g y O p t i m i z at i o n and M u lt i - P h y s i c s 37 he said. Levi added that the human factor, an essential design consideration, will always be an important factor, as well. Radermacher posited that, if surface roughness is beneficial, it may be pos- sible to convert any debris into an advantage, perhaps smoothing a passage and creating a pressure drop with the exchanger; Levi agreed that such an approach could theoretically work. Saviers agreed that surface roughness was critical to heat exchange performance, because of the different length scales, which should also be incorporated into topology optimization methods. Interfaces, Acoustics, and Self-Healing Polymers Kolel-Veetil asked if interface interactions could be integrated into topology optimization. Kim replied that several researchers are working on interface stresses, but this work is at a very early stage. For some problems, such as an unpredictable impact shockwaves, the physics are not fully understood, and the problems can be neither modeled nor optimized. Kolel-Veetil also wondered if the fluid flow approach could be harnessed for air flow, for example, to reduce noise from jet engines. Saviers answered that a UTRC acoustics group is working on noise problems, a primary concern for aerospace, and it could be a multi-physics problem. Sigmund pointed at the general statement: “if it can be modeled, it can be optimized,” which also includes acoustics. Kim is also working in acoustics, specifically coupling its physics with structural mechanics instead of the usual temperature and fluids. In her experience, disci- plinary boundaries impede efforts to integrate mechanical designs with acoustics requirements—a “not my department” attitude. She sees personalities and culture as a major barrier in integrating functionalities and creating multi-material systems and multi-functional structures. Ned Thomas, Rice University, asked about self-healing capabilities for poly- mer systems. Kim replied that self-healing polymers and topology optimization have not yet been pursued together, but some researchers have begun modeling fracturing and reliability constraints. She said more work is needed, especially to account for the multiscale mechanics of fracturing. She concluded by noting that it is tempting to optimize to perfection, but those goals can be a trap that leads to unstable or non-fail-safe designs, as Thompson and Hunt showed.23 23    J.M.T. Thompson and C.W. Hunt, 1973, Dangers of structural optimization, Engineering Opti­ mization 1(2): 99-110, https://doi.org/10.1080/03052157408960580. PREPUBLICATION COPY—Uncorrected Proofs

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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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