| NSF Org: |
CMMI Division of Civil, Mechanical, and Manufacturing Innovation |
| Recipient: |
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| Initial Amendment Date: | November 2, 2021 |
| Latest Amendment Date: | November 2, 2021 |
| Award Number: | 2105811 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Siddiq Qidwai
sqidwai@nsf.gov (703)292-2211 CMMI Division of Civil, Mechanical, and Manufacturing Innovation ENG Directorate for Engineering |
| Start Date: | November 1, 2021 |
| End Date: | October 31, 2024 (Estimated) |
| Total Intended Award Amount: | $498,773.00 |
| Total Awarded Amount to Date: | $498,773.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
1 NASSAU HALL PRINCETON NJ US 08544-2001 (609)258-3090 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
87 Prospect Avenue Princeton NJ US 08544-2020 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | Mechanics of Materials and Str |
| Primary Program Source: |
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| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.041 |
ABSTRACT
Mechanics plays a fundamental role in the optimality of engineering structures at various scales. Starting in the late nineteenth century, the field of structural optimization grew out of key observations on the criticality of load path and its implication on spatial deformation. Yet, as the field has evolved in pursuit of complex engineering challenges, its focus has shifted towards formulations of tractable optimization statements more than on mechanics guiding structural optimization. This award will support the development of a general topology optimization framework based on local stress constraints that will bring the fundamental principles of mechanics at the center of structural optimality. The theoretical and computational framework will be bridged with advanced additive manufacturing techniques for convergent outcomes. The work will empower the next generation of engineers to solve challenging structural optimization problems involving a large number of local constraints, and to connect topology optimization and additive manufacturing in an inexpensive and easy?to?use way for education at all levels. Guided by theoretical, computational, experimental, and manufacturing challenges, the award will provide educational opportunities to K?12 students through university programs and integration of research with the graduate curriculum, and support dissemination of the findings to the industry and the broader community through computer codes, outreach meetings, and workshops.
This research advances the theory needed to effectively couple mechanics and optimization of highly constrained problems, the computational framework needed to solve such problems, and the manufacturing approach to fabricate the resultant spatially varying multi?lattice parts. From a mathematical perspective, a tailored augmented Lagrangian approach will be employed to solve the stress?constrained mass minimization problem by incorporating local stresses. Specific contributions will include: (i) unifying local formulations of the stress?constrained topology optimization problems to handle a wide range of failure criteria with a single strength function and analytically deriving worst?case stress states from infinite load cases that can be used to define the stress constraints; (ii) reformulating the stress constrained problem to handle an arbitrary number of linear, nonlinear, and/or microstructural materials and deriving interfacial behavior that can be used to enforce stress constraints at material interfaces; and (iii) engineering and experimentally validating functionally?graded, single? and multi?lattice optimized parts using novel manufacturing techniques, such as gray?scale digital light processing (g-DLP) without expensive stereolithography (STL) files. The research will explore a multi?phase design space with on demand structural fidelity.
This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
This research contributed to the fundamental understanding that mechanics plays in the optimality of engineering structures, at different scales. Starting in the late 1800’s, the field of structural optimization grew out of key observations from James Clerk Maxwell and A.G.M. Michell about the mechanics of frame structures (i.e., load path and its implication on the associated strain field). Yet, as the field has evolved in pursuit of engineering challenges, it has shifted away from fundamental principles in order to fit within the confines of a tractable optimization statement. Thus, this project has advanced engineering mechanics to enable us to return to first principles while contributing to modern aspects of topology optimization as outlined below.
This research has advanced knowledge in the theory needed to effectively couple mechanics and optimization, the computations needed to solve such problems, and the engineering needed to manufacture the resulting, spatially-varying multi-lattice parts. To this effect, we have established a consistent and unified stress-constrained topology optimization (TopOpt) framework with infinite load cases. We mathematically formulated stress-constrained, mass minimization problems, consistent with the local definition of stress (according to Cauchy) in classical continuum mechanics, that unifies failure criteria of ductile and pressure-dependent materials and accommodates infinite load cases. This framework is capable of handling lots (e.g. millions) of local stress constraints.
Moreover, we explored stress-constrained TopOpt with spatially-varying properties. We investigated the composite design space using multi-material TopOpt for an arbitrary number of linear, nonlinear(e.g., hyperelastic), and/or microstructural materials, with stress constraints. This investigation was extended to spinodal architected materials.
We advanced g-DLP (gray-scale digital light processing) AM (advanced manufacturing) with multi-material and multi-lattice embedding. We showed how physical realizations of the optimized structures behave compared to the predicted response by experimentally validating single- and multi- property parts, with one or multiple scales, 3D-printed using g-DLP.
The broader goals of this project contributed to advance mechanics principles so that TopOpt can be translated to the industry and national lab environment to effectively handle engineering problems. In this regard, we have also advanced the connection of TopOpt and AM in an accessible (inexpensive and easy-to-use) way for education at all levels. The research advanced under this project has been integrated with the engineering curriculum both at Georgia Tech and at Princeton University. The research was disseminated broadly in several courses, symposia conference and outreach activities.
Five representative publications:
[1] F. V. Senhora, E. D. Sanders, and G. H. Paulino. “Unbiased mechanical cloaks.” Proc. Natl. Acad. Sci. U.S.A. 122 (19) e2415056122, 2025. (NOTE: The 2 attached images are from this article)
https://doi.org/10.1073/pnas.2415056122
[2] A. Nale, A. Chiozzi, F. V. Senhora, and G. H. Paulino. “Large-scale additive manufacturing of optimally-embedded spinodal material architectures.” Additive Manufacturing, 101, 104700, 2025.
https://doi.org/10.1016/j.addma.2025.104700
[3] J. Russ, and G. H. Paulino. “On topology optimization with gradient-enhanced damage: An alternative formulation based on linear physics.” J. Mech. Phys. Solids, 173, 105204, 2023.
https://doi.org/10.1016/j.jmps.2023.105204.
[4] F. V. Senhora, I.F.M. Menezes, and G. H. Paulino. “Topology optimization with local stress constraints and continuously varying load direction and magnitude: towards practical applications.” Proc. R. Soc. A, 479, 2271, 20220436, 2023 [COVER article].
https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2022.0436
[5] O. Giraldo-Londoño, J.B. Russ, M. A. Aguiló, and G. H. Paulino. “Limiting the first principal stress in topology optimization: a local and consistent approach.” Struct Multidisc Optim 65, 254, 2022.
https://doi.org/10.1007/s00158-022-03320-y
Last Modified: 06/12/2025
Modified by: Glaucio Paulino
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