An optimization-based approach to tailor the mechanical response of soft metamaterials undergoing rate-dependent instabilities

Alberdi, Ryan; Hamel, Craig; Talamini, Brandon; Tupek, Michael R.

doi:10.1016/j.cma.2024.117679

Title: An optimization-based approach to tailor the mechanical response of soft metamaterials undergoing rate-dependent instabilities

Journal Article · 24 December 2024 · Computer Methods in Applied Mechanics and Engineering

DOI: https://doi.org/10.1016/j.cma.2024.117679 · OSTI ID:2498462

^[1];

^[1]; Talamini, Brandon ^[2];

^[2]

Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)
Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States)

An optimization-based design framework is proposed to tune the response of soft metamaterials involving both geometric instabilities and nonlinear viscoelastic material behavior. Designing the response of soft metamaterials to harness instabilities and undergo large, tailored configuration changes will enable advancements in soft robotics, shock and vibration mitigation, and flexible electronics. In line with the metamaterial concept, the response of these materials is governed to a large extent by the geometric and topological makeup of their small-scale features. However, the link between structure and response is less intuitive for soft metamaterials due to their reliance upon highly nonlinear responses triggered by geometric instabilities. This is further complicated by the effects of viscoelastic relaxation, which recent studies have shown to alter the emergence of instabilities in non-intuitive ways. Here, these effects are accounted for in our framework to achieve various design objectives, including tailored force–displacement response and maximized energy absorption from both geometric and material effects. To fully automate this process, it is essential to have a completely robust equation solver for forward problems involving instabilities and viscoelastic relaxation. We achieve this by casting the search for stable mechanical equilibrium — i.e. the forward problem — as a minimization problem and utilize a trust region algorithm to robustly handle instabilities and follow energetically-favorable equilibrium paths through critical points.

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Research Organization:: Lawrence Livermore National Laboratory (LLNL), Livermore, CA (United States); Sandia National Laboratories (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE Laboratory Directed Research and Development (LDRD) Program; USDOE National Nuclear Security Administration (NNSA)

Grant/Contract Number:: AC52-07NA27344; NA0003525

OSTI ID:: 2498462

Report Number(s):: LLNL--JRNL-2002293; LLNL--JRNL-870743; SAND--2025-00242J

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Journal Name: Computer Methods in Applied Mechanics and Engineering Vol. 435; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (87)

Multistable Architected Materials for Trapping Elastic Strain Energy Shan, Sicong; Kang, Sung H.; Raney, Jordan R. Advanced Materials, Vol. 27, Issue 29 https://doi.org/10.1002/adma.201501708	journal	June 2015
Tailored Buckling Microlattices as Reusable Light-Weight Shock Absorbers Frenzel, Tobias; Findeisen, Claudio; Kadic, Muamer Advanced Materials, Vol. 28, Issue 28 https://doi.org/10.1002/adma.201600610	journal	May 2016
Multistable Shape-Reconfigurable Architected Materials Haghpanah, Babak; Salari-Sharif, Ladan; Pourrajab, Peyman Advanced Materials, Vol. 28, Issue 36 https://doi.org/10.1002/adma.201601650	journal	July 2016
Mechanically‐Guided Structural Designs in Stretchable Inorganic Electronics Xue, Zhaoguo; Song, Honglie; Rogers, John A. Advanced Materials https://doi.org/10.1002/adma.201902254	journal	July 2019
Bistable and Multistable Actuators for Soft Robots: Structures, Materials, and Functionalities Chi, Yinding; Li, Yanbin; Zhao, Yao Advanced Materials, Vol. 34, Issue 19 https://doi.org/10.1002/adma.202110384	journal	March 2022
Tunable Metamaterials for Impact Mitigation Smith, Lawrence; Hayes, Brandon; Ford, Kurtis Advanced Materials Technologies, Vol. 9, Issue 6 https://doi.org/10.1002/admt.202301668	journal	January 2024
A variational formulation of constitutive models and updates in non-linear finite viscoelasticity Fancello, Eduardo; Ponthot, Jean-Philippe; Stainier, Laurent International Journal for Numerical Methods in Engineering, Vol. 65, Issue 11 https://doi.org/10.1002/nme.1525	journal	January 2006
Tangent operators and design sensitivity formulations for transient non-linear coupled problems with applications to elastoplasticity Michaleris, Panagiotis; Tortorelli, Daniel A.; Vidal, Creto A. International Journal for Numerical Methods in Engineering, Vol. 37, Issue 14 https://doi.org/10.1002/nme.1620371408	journal	July 1994
A variational, finite‐deformation constitutive model for piezoelectric materials Mota, Alejandro; Zimmerman, Jonathan A. International Journal for Numerical Methods in Engineering, Vol. 85, Issue 6 https://doi.org/10.1002/nme.2993	journal	January 2011
Numerical methods for the topology optimization of structures that exhibit snap-through Bruns, T. E.; Sigmund, O.; Tortorelli, D. A. International Journal for Numerical Methods in Engineering, Vol. 55, Issue 10 https://doi.org/10.1002/nme.544	journal	January 2002
Topology optimization of energy absorbing structures with maximum damage constraint: TOPOLOGY OPTIMIZATION INELASTIC DAMAGE Li, Lei; Zhang, Guodong; Khandelwal, Kapil International Journal for Numerical Methods in Engineering, Vol. 112, Issue 7 https://doi.org/10.1002/nme.5531	journal	March 2017
A unified framework for nonlinear path-dependent sensitivity analysis in topology optimization Alberdi, Ryan; Zhang, Guodong; Li, Lei International Journal for Numerical Methods in Engineering, Vol. 115, Issue 1 https://doi.org/10.1002/nme.5794	journal	March 2018
Design of dissipative multimaterial viscoelastic‐hyperelastic systems at finite strains via topology optimization Zhang, Guodong; Khandelwal, Kapil International Journal for Numerical Methods in Engineering, Vol. 119, Issue 11 https://doi.org/10.1002/nme.6083	journal	May 2019
A Heaviside function‐based density representation algorithm for truss‐like buckling‐induced mechanism design Deng, Hao International Journal for Numerical Methods in Engineering, Vol. 119, Issue 11 https://doi.org/10.1002/nme.6084	journal	June 2019
A density‐based boundary evolving method for buckling‐induced design under large deformation Deng, Hao; To, Albert C. International Journal for Numerical Methods in Engineering, Vol. 122, Issue 7 https://doi.org/10.1002/nme.6599	journal	December 2020
Mapped shape optimization method for the rational design of cellular mechanical metamaterials under large deformation Xue, Tianju; Mao, Sheng International Journal for Numerical Methods in Engineering, Vol. 123, Issue 10 https://doi.org/10.1002/nme.6941	journal	March 2022
Large deformations and stability in topology optimization Kemmler, R.; Lipka, A.; Ramm, E. Structural and Multidisciplinary Optimization, Vol. 30, Issue 6 https://doi.org/10.1007/s00158-005-0534-0	journal	July 2005
Isogeometric shape design optimization: exact geometry and enhanced sensitivity Cho, Seonho; Ha, Seung-Hyun Structural and Multidisciplinary Optimization, Vol. 38, Issue 1 https://doi.org/10.1007/s00158-008-0266-z	journal	May 2008
On compliance and buckling objective functions in topology optimization of snap-through problems Lindgaard, Esben; Dahl, Jonas Structural and Multidisciplinary Optimization, Vol. 47, Issue 3 https://doi.org/10.1007/s00158-012-0832-2	journal	August 2012
Topology optimization approaches: A comparative review Sigmund, Ole; Maute, Kurt Structural and Multidisciplinary Optimization, Vol. 48, Issue 6 https://doi.org/10.1007/s00158-013-0978-6	journal	August 2013
Design of buckling-induced mechanical metamaterials for energy absorption using topology optimization Chen, Qi; Zhang, Xianmin; Zhu, Benliang Structural and Multidisciplinary Optimization, Vol. 58, Issue 4 https://doi.org/10.1007/s00158-018-1970-y	journal	April 2018
Failure resistant topology optimization of structures using nonlocal elastoplastic-damage model Li, Lei; Zhang, Guodong; Khandelwal, Kapil Structural and Multidisciplinary Optimization, Vol. 58, Issue 4 https://doi.org/10.1007/s00158-018-1984-5	journal	April 2018
Topology optimization of dissipative metamaterials at finite strains based on nonlinear homogenization Zhang, Guodong; Khandelwal, Kapil Structural and Multidisciplinary Optimization, Vol. 62, Issue 3 https://doi.org/10.1007/s00158-020-02566-8	journal	May 2020
Structural stability and artificial buckling modes in topology optimization Dalklint, Anna; Wallin, Mathias; Tortorelli, Daniel A. Structural and Multidisciplinary Optimization, Vol. 64, Issue 4 https://doi.org/10.1007/s00158-021-03012-z	journal	August 2021
Isogeometric sizing and shape optimization of 3D beams and lattice structures at large deformations Weeger, Oliver Structural and Multidisciplinary Optimization, Vol. 65, Issue 2 https://doi.org/10.1007/s00158-021-03131-7	journal	January 2022
Level-set topology optimization with PDE generated conformal meshes Schmidt, Mathias R.; Barrera, Jorge L.; Mittal, Ketan Structural and Multidisciplinary Optimization, Vol. 67, Issue 10 https://doi.org/10.1007/s00158-024-03870-3	journal	October 2024
Stiffness design of geometrically nonlinear structures using topology optimization Buhl, T.; Pedersen, C. B. W.; Sigmund, O. Structural and Multidisciplinary Optimization, Vol. 19, Issue 2 https://doi.org/10.1007/s001580050089	journal	April 2000
An incremental approach to the solution of snapping and buckling problems Riks, E. International Journal of Solids and Structures, Vol. 15, Issue 7 https://doi.org/10.1016/0020-7683(79)90081-7	journal	January 1979
Shape optimal design using B-splines Braibant, V.; Fleury, C. Computer Methods in Applied Mechanics and Engineering, Vol. 44, Issue 3 https://doi.org/10.1016/0045-7825(84)90132-4	journal	August 1984
Adaptive finite element methods for shape optimization of linearly elastic structures Noboru, Kikuchi; Toshikazu, Torigaki Computer Methods in Applied Mechanics and Engineering, Vol. 57, Issue 1 https://doi.org/10.1016/0045-7825(86)90071-X	journal	August 1986
Structural shape optimization—A survey Haftka, Raphael T.; Grandhi, Ramana V. Computer Methods in Applied Mechanics and Engineering, Vol. 57, Issue 1 https://doi.org/10.1016/0045-7825(86)90072-1	journal	August 1986
A theory of finite viscoelasticity and numerical aspects Reese, Stefanie; Govindjee, Sanjay International Journal of Solids and Structures, Vol. 35, Issue 26-27 https://doi.org/10.1016/S0020-7683(97)00217-5	journal	September 1998
The variational formulation of viscoplastic constitutive updates Ortiz, M.; Stainier, L. Computer Methods in Applied Mechanics and Engineering, Vol. 171, Issue 3-4 https://doi.org/10.1016/S0045-7825(98)00219-9	journal	April 1999
Error estimation and adaptive meshing in strongly nonlinear dynamic problems Radovitzky, R.; Ortiz, M. Computer Methods in Applied Mechanics and Engineering, Vol. 172, Issue 1-4 https://doi.org/10.1016/S0045-7825(98)00230-8	journal	April 1999
Design sensitivity analysis and shape optimization of structural components with hyperelastic material Choi, K. K.; Duan, W. Computer Methods in Applied Mechanics and Engineering, Vol. 187, Issue 1-2 https://doi.org/10.1016/S0045-7825(99)00121-8	journal	June 2000
Numerical analysis perspective in structural shape optimization: A review post 2000 Upadhyay, Bhavik D.; Sonigra, Sunil S.; Daxini, Sachin D. Advances in Engineering Software, Vol. 155 https://doi.org/10.1016/j.advengsoft.2021.102992	journal	May 2021
A variational Cam-clay theory of plasticity Ortiz, M.; Pandolfi, A. Computer Methods in Applied Mechanics and Engineering, Vol. 193, Issue 27-29 https://doi.org/10.1016/j.cma.2003.08.008	journal	July 2004
Toward the topology design of mechanisms that exhibit snap-through behavior Bruns, T. E.; Sigmund, O. Computer Methods in Applied Mechanics and Engineering, Vol. 193, Issue 36-38 https://doi.org/10.1016/j.cma.2004.02.017	journal	September 2004
Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement Hughes, T. J. R.; Cottrell, J. A.; Bazilevs, Y. Computer Methods in Applied Mechanics and Engineering, Vol. 194, Issue 39-41 https://doi.org/10.1016/j.cma.2004.10.008	journal	October 2005
Isogeometric structural shape optimization Wall, Wolfgang A.; Frenzel, Moritz A.; Cyron, Christian Computer Methods in Applied Mechanics and Engineering, Vol. 197, Issue 33-40 https://doi.org/10.1016/j.cma.2008.01.025	journal	June 2008
Full analytical sensitivities in NURBS based isogeometric shape optimization Qian, Xiaoping Computer Methods in Applied Mechanics and Engineering, Vol. 199, Issue 29-32 https://doi.org/10.1016/j.cma.2010.03.005	journal	June 2010
A gradient-based, parameter-free approach to shape optimization Le, Chau; Bruns, Tyler; Tortorelli, Daniel Computer Methods in Applied Mechanics and Engineering, Vol. 200, Issue 9-12 https://doi.org/10.1016/j.cma.2010.10.004	journal	February 2011
Shape optimization of thin walled structures governed by geometrically nonlinear mechanics Firl, Matthias; Bletzinger, Kai-Uwe Computer Methods in Applied Mechanics and Engineering, Vol. 237-240 https://doi.org/10.1016/j.cma.2012.05.016	journal	September 2012
Shape optimization with a level set based mesh evolution method Allaire, G.; Dapogny, C.; Frey, P. Computer Methods in Applied Mechanics and Engineering, Vol. 282 https://doi.org/10.1016/j.cma.2014.08.028	journal	December 2014
Layout design of a bi-stable cardiovascular stent using topology optimization James, Kai A.; Waisman, Haim Computer Methods in Applied Mechanics and Engineering, Vol. 305 https://doi.org/10.1016/j.cma.2016.02.036	journal	June 2016
Condition number analysis and preconditioning of the finite cell method de Prenter, F.; Verhoosel, C. V.; van Zwieten, G. J. Computer Methods in Applied Mechanics and Engineering, Vol. 316 https://doi.org/10.1016/j.cma.2016.07.006	journal	April 2017
Isogeometric shape optimization of smoothed petal auxetic structures via computational periodic homogenization Wang, Zhen-Pei; Poh, Leong Hien; Dirrenberger, Justin Computer Methods in Applied Mechanics and Engineering, Vol. 323 https://doi.org/10.1016/j.cma.2017.05.013	journal	August 2017
Isogeometric shape optimization of nonlinear, curved 3D beams and beam structures Weeger, Oliver; Narayanan, Bharath; Dunn, Martin L. Computer Methods in Applied Mechanics and Engineering, Vol. 345 https://doi.org/10.1016/j.cma.2018.10.038	journal	March 2019
Isogeometric shape optimization of smoothed petal auxetics with prescribed nonlinear deformation Pokkalla, Deepak Kumar; Wang, Zhen-Pei; Poh, Leong Hien Computer Methods in Applied Mechanics and Engineering, Vol. 356 https://doi.org/10.1016/j.cma.2019.07.014	journal	November 2019
Topology optimization for energy dissipation design of lattice structures through snap-through behavior Deng, Hao; Cheng, Lin; Liang, Xuan Computer Methods in Applied Mechanics and Engineering, Vol. 358 https://doi.org/10.1016/j.cma.2019.112641	journal	January 2020
A Newton solver for micromorphic computational homogenization enabling multiscale buckling analysis of pattern-transforming metamaterials van Bree, S. E. H. M.; Rokoš, O.; Peerlings, R. H. J. Computer Methods in Applied Mechanics and Engineering, Vol. 372 https://doi.org/10.1016/j.cma.2020.113333	journal	December 2020
Body-fitted topology optimization of 2D and 3D fluid-to-fluid heat exchangers Feppon, F.; Allaire, G.; Dapogny, C. Computer Methods in Applied Mechanics and Engineering, Vol. 376 https://doi.org/10.1016/j.cma.2020.113638	journal	April 2021
Topology optimization of bistable elastic structures — An application to logic gates Wallin, Mathias; Dalklint, Anna; Tortorelli, Daniel Computer Methods in Applied Mechanics and Engineering, Vol. 383 https://doi.org/10.1016/j.cma.2021.113912	journal	September 2021
Second-order computational homogenisation enhanced with non-uniform body forces for non-linear cellular materials and metamaterials Wu, Ling; Mustafa, Mohib; Segurado, Javier Computer Methods in Applied Mechanics and Engineering, Vol. 407 https://doi.org/10.1016/j.cma.2023.115931	journal	March 2023
Finite strain topology optimization with nonlinear stability constraints Zhang, Guodong; Khandelwal, Kapil; Guo, Tong Computer Methods in Applied Mechanics and Engineering, Vol. 413 https://doi.org/10.1016/j.cma.2023.116119	journal	August 2023
Simultaneous shape and topology optimization of inflatable soft robots Dalklint, Anna; Wallin, Mathias; Tortorelli, Daniel Computer Methods in Applied Mechanics and Engineering, Vol. 420 https://doi.org/10.1016/j.cma.2024.116751	journal	February 2024
Towards understanding the role of viscoelasticity in microstructural buckling in soft particulate composites Xiang, Yuhai; Chen, Dean; Arora, Nitesh Composites Part B: Engineering, Vol. 263 https://doi.org/10.1016/j.compositesb.2023.110850	journal	August 2023
Phase transforming cellular materials Restrepo, David; Mankame, Nilesh D.; Zavattieri, Pablo D. Extreme Mechanics Letters, Vol. 4 https://doi.org/10.1016/j.eml.2015.08.001	journal	September 2015
Nonlinear shape optimization of flexible mechanical metamaterials Medina, Eder; Rycroft, Chris H.; Bertoldi, Katia Extreme Mechanics Letters, Vol. 61 https://doi.org/10.1016/j.eml.2023.102015	journal	June 2023
Topology optimization of pressure dependent elastoplastic energy absorbing structures with material damage constraints Alberdi, Ryan; Khandelwal, Kapil Finite Elements in Analysis and Design, Vol. 133 https://doi.org/10.1016/j.finel.2017.05.004	journal	October 2017
The effect of topology on the shock dynamics of two-dimensional architected materials Luan, Shengzhi; Guest, James K.; Gaitanaros, Stavros International Journal of Impact Engineering, Vol. 190 https://doi.org/10.1016/j.ijimpeng.2024.104987	journal	August 2024
Mechanics of deformation-triggered pattern transformations and superelastic behavior in periodic elastomeric structures Bertoldi, K.; Boyce, M. C.; Deschanel, S. Journal of the Mechanics and Physics of Solids, Vol. 56, Issue 8 https://doi.org/10.1016/j.jmps.2008.03.006	journal	August 2008
Relating pore shape to the non-linear response of periodic elastomeric structures Overvelde, Johannes T. B.; Bertoldi, Katia Journal of the Mechanics and Physics of Solids, Vol. 64 https://doi.org/10.1016/j.jmps.2013.11.014	journal	March 2014
Characteristics of mechanical metamaterials based on buckling elements Findeisen, Claudio; Hohe, Jörg; Kadic, Muamer Journal of the Mechanics and Physics of Solids, Vol. 102 https://doi.org/10.1016/j.jmps.2017.02.011	journal	May 2017
Soft network composite materials with deterministic and bio-inspired designs Jang, Kyung-In; Chung, Ha Uk; Xu, Sheng Nature Communications, Vol. 6, Issue 1 https://doi.org/10.1038/ncomms7566	journal	March 2015
Rapid inverse design of metamaterials based on prescribed mechanical behavior through machine learning Ha, Chan Soo; Yao, Desheng; Xu, Zhenpeng Nature Communications, Vol. 14, Issue 1 https://doi.org/10.1038/s41467-023-40854-1	journal	September 2023
Harnessing instabilities for design of soft reconfigurable auxetic/chiral materials Shim, Jongmin; Shan, Sicong; Košmrlj, Andrej Soft Matter, Vol. 9, Issue 34 https://doi.org/10.1039/c3sm51148k	journal	January 2013
The extreme mechanics of viscoelastic metamaterials Dykstra, David M. J.; Janbaz, Shahram; Coulais, Corentin APL Materials, Vol. 10, Issue 8 https://doi.org/10.1063/5.0094224	journal	August 2022
Digital synthesis of free-form multimaterial structures for realization of arbitrary programmed mechanical responses Li, Weichen; Wang, Fengwen; Sigmund, Ole Proceedings of the National Academy of Sciences, Vol. 119, Issue 10 https://doi.org/10.1073/pnas.2120563119	journal	March 2022
Global Convergence of a a of Trust-Region Methods for Nonconvex Minimization in Hilbert Space Toint, Ph. L. IMA Journal of Numerical Analysis, Vol. 8, Issue 2 https://doi.org/10.1093/imanum/8.2.231	journal	January 1988
Navigating the landscape of nonlinear mechanical metamaterials for advanced programmability Medina, Eder; Farrell, Patrick E.; Bertoldi, Katia Physical Review B, Vol. 101, Issue 6 https://doi.org/10.1103/PhysRevB.101.064101	journal	February 2020
Harnessing Buckling to Design Tunable Locally Resonant Acoustic Metamaterials Wang, Pai; Casadei, Filippo; Shan, Sicong Physical Review Letters, Vol. 113, Issue 1 https://doi.org/10.1103/PhysRevLett.113.014301	journal	July 2014
Pattern Transformation Triggered by Deformation Mullin, T.; Deschanel, S.; Bertoldi, K. Physical Review Letters, Vol. 99, Issue 8 https://doi.org/10.1103/PhysRevLett.99.084301	journal	August 2007
Negative stiffness honeycombs for recoverable shock isolation Correa, Dixon M.; Klatt, Timothy; Cortes, Sergio Rapid Prototyping Journal, Vol. 21, Issue 2 https://doi.org/10.1108/RPJ-12-2014-0182	journal	March 2015
Three-Dimensional-Printed Multistable Mechanical Metamaterials With a Deterministic Deformation Sequence Che, Kaikai; Yuan, Chao; Wu, Jiangtao Journal of Applied Mechanics, Vol. 84, Issue 1 https://doi.org/10.1115/1.4034706	journal	October 2016
Viscoelastic Snapping Metamaterials Dykstra, David M. J.; Busink, Joris; Ennis, Bernard Journal of Applied Mechanics, Vol. 86, Issue 11 https://doi.org/10.1115/1.4044036	journal	September 2019
Strain rate–dependent mechanical metamaterials Janbaz, S.; Narooei, K.; van Manen, T. Science Advances, Vol. 6, Issue 25 https://doi.org/10.1126/sciadv.aba0616	journal	June 2020
Programming soft robots with flexible mechanical metamaterials Rafsanjani, Ahmad; Bertoldi, Katia; Studart, André R. Science Robotics, Vol. 4, Issue 29 https://doi.org/10.1126/scirobotics.aav7874	journal	April 2019
Inflatable soft jumper inspired by shell snapping Gorissen, Benjamin; Melancon, David; Vasios, Nikolaos Science Robotics, Vol. 5, Issue 42 https://doi.org/10.1126/scirobotics.abb1967	journal	May 2020
The Conjugate Gradient Method and Trust Regions in Large Scale Optimization Steihaug, Trond SIAM Journal on Numerical Analysis, Vol. 20, Issue 3 https://doi.org/10.1137/0720042	journal	June 1983
Control of Bifurcation Structures using Shape Optimization Boullé, Nicolas; Farrell, Patrick E.; Paganini, Alberto SIAM Journal on Scientific Computing, Vol. 44, Issue 1 https://doi.org/10.1137/21M1418708	journal	January 2022
A Trust Region Method for Parabolic Boundary Control Problems Kelley, C. T.; Sachs, E. W. SIAM Journal on Optimization, Vol. 9, Issue 4 https://doi.org/10.1137/S1052623496308965	journal	January 1999
Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate Chen, Yanqing; Davis, Timothy A.; Hager, William W. ACM Transactions on Mathematical Software, Vol. 35, Issue 3 https://doi.org/10.1145/1391989.1391995	journal	October 2008
Unstructured grid generation using iterative point insertion and local reconnection Marcum, David L.; Weatherill, Nigel P. AIAA Journal, Vol. 33, Issue 9 https://doi.org/10.2514/3.12701	journal	September 1995
On The Construction of Aircraft Conceptual Geometry for High-Fidelity Analysis and Design Haimes, Robert; Drela, Mark 50th AIAA Aerospace Sciences Meeting including the New Horizons Forum and Aerospace Exposition https://doi.org/10.2514/6.2012-683	conference	January 2012
The Engineering Sketch Pad: A Solid-Modeling, Feature-Based, Web-Enabled System for Building Parametric Geometry Haimes, Robert; Dannenhoffer, John 21st AIAA Computational Fluid Dynamics Conference https://doi.org/10.2514/6.2013-3073	conference	June 2013
Design Sensitivity Calculations Directly on CAD-based Geometry Dannenhoffer, John; Haimes, Robert 53rd AIAA Aerospace Sciences Meeting https://doi.org/10.2514/6.2015-1370	conference	January 2015

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97 MATHEMATICS AND COMPUTING
Bifurcations
Finite deformation viscoelasticity
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Snap-through
Soft metamaterials

Title: An optimization-based approach to tailor the mechanical response of soft metamaterials undergoing rate-dependent instabilities

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