Abstract
Mechanical metamaterials enable customizing the elastic properties of physical objects by altering their fine-scale structure. A broad gamut of effective material properties can be produced even from a single fabrication material by optimizing the geometry of a periodic microstructure tiling. Past work has extensively studied the capabilities of microstructures in the small-displacement regime, where periodic homogenization of linear elasticity yields computationally efficient optimal design algorithms. However, many applications involve flexible structures undergoing large deformations for which the accuracy of linear elasticity rapidly deteriorates due to geometric nonlinearities. Design of microstructures at finite strains involves a massive increase in computation and is much less explored; no computational tool yet exists to design metamaterials emulating target hyperelastic laws over finite regions of strain space.
We make an initial step in this direction, developing algorithms to accelerate homogenization and metamaterial design for nonlinear elasticity and building a complete framework for the optimal design of planar metamaterials. Our nonlinear homogenization method works by efficiently constructing an accurate interpolant of a microstructure's deformation over a finite space of macroscopic strains likely to be endured by the metamaterial. From this interpolant, the homogenized energy density, stress, and tangent elasticity tensor describing the microstructure's effective properties can be inexpensively computed at any strain. Our design tool then fits the effective material properties to a target constitutive law over a region of strain space using a parametric shape optimization approach, producing a directly manufacturable geometry. We systematically test our framework by designing a catalog of materials fitting isotropic Hooke's laws as closely as possible. We demonstrate significantly improved accuracy over traditional linear metamaterial design techniques by fabricating and testing physical prototypes.
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- Jérémie Allard, Franccois Faure, Hadrien Courtecuisse, Florent Falipou, Christian Duriez, and Paul G. Kry. 2010. Volume Contact Constraints at Arbitrary Resolution. ACM Trans. Graph. 29, 4, Article 82 (jul 2010), 10 pages. Google ScholarDigital Library
- Moritz Bächer, Bernd Bickel, Emily Whiting, and Olga Sorkine-Hornung. 2017. Spin-it: Optimizing moment of inertia for spinnable objects. Commun. ACM 60, 8 (2017), 92--99. Google ScholarDigital Library
- Changyeob Baek, Andrew O Sageman-Furnas, Mohammad K Jawed, and Pedro M Reis. 2018. Form finding in elastic gridshells. Proceedings of the National Academy of Sciences 115, 1 (2018), 75--80.Google ScholarCross Ref
- Reza Behrou, Maroun Abi Ghanem, Brianna C. Macnider, Vimarsh Verma, Ryan Alvey, Jinho Hong, Ashley F. Emery, Hyunsun Alicia Kim, and Nicholas Boechler. 2021. Topology optimization of nonlinear periodically microstructured materials for tailored homogenized constitutive properties. Composite Structures 266 (6 2021). Google ScholarCross Ref
- Amit H Bermano, Thomas Funkhouser, and Szymon Rusinkiewicz. 2017. State of the art in methods and representations for fabrication-aware design. In Computer Graphics Forum, Vol. 36. Wiley Online Library, 509--535.Google Scholar
- Katia Bertoldi, Vincenzo Vitelli, Johan Christensen, and Martin Van Hecke. 2017. Flexible mechanical metamaterials. Google ScholarCross Ref
- Gaurav Bharaj, David I.W. Levin, James Tompkin, Yun Fei, Hanspeter Pfister, Wojciech Matusik, and Changxi Zheng. 2015. Computational design of metallophone contact sounds. ACM Transactions on Graphics 34, 6 (2015), 1--13. Google ScholarDigital Library
- Bernd Bickel, Moritz Bächer, Miguel A. Otaduy, Hyunho Richard Lee, Hanspeter Pfister, Markus Gross, and Wojciech Matusik. 2010. Design and fabrication of materials with desired deformation behavior. (2010), 1. Google ScholarDigital Library
- Eric Brown, Nicholas Rodenberg, John Amend, Annan Mozeika, Erik Steltz, Mitchell R. Zakin, Hod Lipson, and Heinrich M. Jaeger. 2010. Universal robotic gripper based on the jamming of granular material. Proceedings of the National Academy of Sciences 107, 44 (2010), 18809--18814. arXiv:https://www.pnas.org/doi/pdf/10.1073/pnas.1003250107 Google ScholarCross Ref
- Paolo Celli, Connor McMahan, Brian Ramirez, Anton Bauhofer, Christina Naify, Douglas Hofmann, Basile Audoly, and Chiara Daraio. 2018. Shape-morphing architected sheets with non-periodic cut patterns. Soft matter 14, 48 (2018), 9744--9749.Google Scholar
- Antoine Chan-Lock, Jesús Pérez, and Miguel A Otaduy. 2022. High-Order Elasticity Interpolants for Microstructure Simulation. In Computer Graphics Forum, Vol. 41. Wiley Online Library, 63--74.Google Scholar
- Desai Chen, David IW Levin, Shinjiro Sueda, and Wojciech Matusik. 2015. Data-driven finite elements for geometry and material design. ACM Transactions on Graphics (TOG) 34, 4 (2015), 1--10.Google ScholarDigital Library
- Desai Chen, Mélina Skouras, Bo Zhu, and Wojciech Matusik. 2018. Computational discovery of extremal microstructure families. Science advances 4, 1 (2018), eaao7005.Google Scholar
- Tian Chen, Julian Panetta, Max Schnaubelt, and Mark Pauly. 2021a. Bistable Auxetic Surface Structures. ACM Trans. Graph. 40, 4, Article 39 (July 2021), 9 pages. Google ScholarDigital Library
- Tian Chen, Mark Pauly, and Pedro M Reis. 2021b. A reprogrammable mechanical metamaterial with stable memory. Nature 589, 7842 (2021), 386--390.Google Scholar
- Xiang Chen, Changxi Zheng, Weiwei Xu, and Kun Zhou. 2014. An asymptotic numerical method for inverse elastic shape design. ACM Transactions on Graphics (TOG) 33, 4 (2014), 1--11.Google ScholarDigital Library
- Francisco Chinesta, Roland Keunings, and Adrien Leygue. 2013. The proper generalized decomposition for advanced numerical simulations: a primer. Springer Science & Business Media.Google Scholar
- R. M. Christensen. 1987. Sufficient Symmetry Conditions for Isotropy of the Elastic Moduli Tensor. Journal of Applied Mechanics 54, 4 (12 1987), 772--777. arXiv:https://asmedigitalcollection.asme.org/appliedmechanics/article-pdf/54/4/772/5459546/772_1.pdf Google ScholarCross Ref
- Anders Clausen, Fengwen Wang, Jakob S. Jensen, Ole Sigmund, and Jennifer A. Lewis. 2015. Topology Optimized Architectures with Programmable Poisson's Ratio over Large Deformations. Advanced Materials 27 (10 2015), 5523--5527. Issue 37. Google ScholarCross Ref
- Qiaodong Cui, Timothy Langlois, Pradeep Sen, and Theodore Kim. 2020. Fast and Robust Stochastic Structural Optimization. In Computer Graphics Forum, Vol. 39. Wiley Online Library, 385--397.Google Scholar
- Franccois Faure, Jérémie Allard, Florent Falipou, and Sébastien Barbier. 2008. Image-based collision detection and response between arbitrary volumetric objects. In ACM SIGGRAPH/Eurographics Symposium on Computer Animation. Eurographics Association, 155--162.Google Scholar
- Ruslan Guseinov, Eder Miguel, and Bernd Bickel. 2017. CurveUps: Shaping objects from flat plates with tension-actuated curvature. ACM Transactions on Graphics (TOG) 36, 4 (2017), 1--12.Google ScholarDigital Library
- Babak Haghpanah, Ladan Salari-Sharif, Peyman Pourrajab, Jonathan Hopkins, and Lorenzo Valdevit. 2016. Multistable Shape-Reconfigurable Architected Materials. Advanced Materials 28 (9 2016), 7915--7920. Issue 36. Google ScholarCross Ref
- David Harmon, Daniele Panozzo, Olga Sorkine, and Denis Zorin. 2011. Interference Aware Geometric Modeling. ACM Transactions on Graphics (proceedings of ACM SIGGRAPH ASIA) 30, 6 (2011), 137:1--137:10.Google Scholar
- Alexandra Ion, Johannes Frohnhofen, Ludwig Wall, Robert Kovacs, Mirela Alistar, Jack Lindsay, Pedro Lopes, Hsiang-Ting Chen, and Patrick Baudisch. 2016. Metamaterial mechanisms. In Proceedings of the 29th annual symposium on user interface software and technology. 529--539.Google ScholarDigital Library
- Lishuai Jin, Antonio Elia Forte, Bolei Deng, Ahmad Rafsanjani, and Katia Bertoldi. 2020. Kirigami-Inspired Inflatables with Programmable Shapes. Advanced Materials 32, 33 (2020), 2001863. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/adma.202001863 Google ScholarCross Ref
- David Jourdan, Mélina Skouras, Etienne Vouga, and Adrien Bousseau. 2022. Computational Design of Self-Actuated Surfaces by Printing Plastic Ribbons on Stretched Fabric. In Computer Graphics Forum, Vol. 41. Wiley Online Library, 493--506.Google Scholar
- Muamer Kadic, Tiemo Bückmann, Nicolas Stenger, Michael Thiel, and Martin Wegener. 2012. On the practicability of pentamode mechanical metamaterials. Applied Physics Letters 100, 19 (2012), 191901.Google ScholarCross Ref
- Lily Kharevych, Patrick Mullen, Houman Owhadi, and Mathieu Desbrun. 2009. Numerical coarsening of inhomogeneous elastic materials. ACM Transactions on graphics (TOG) 28, 3 (2009), 1--8.Google Scholar
- Yujin Kim, Kuk Hui Son, and Jin Woo Lee. 2021. Auxetic structures for tissue engineering scaffolds and biomedical devices. Materials 14, 22 (2021), 6821.Google ScholarCross Ref
- Hajer Lamari, Amine Ammar, Patrice Cartraud, Grégory Legrain, Francisco Chinesta, and Frédéric Jacquemin. 2010. Routes for efficient computational homogenization of nonlinear materials using the proper generalized decompositions. Archives of Computational methods in Engineering 17, 4 (2010), 373--391.Google Scholar
- Timothy Langlois, Ariel Shamir, Daniel Dror, Wojciech Matusik, and David IW Levin. 2016. Stochastic structural analysis for context-aware design and fabrication. ACM Transactions on Graphics (TOG) 35, 6 (2016), 1--13.Google ScholarDigital Library
- Antoine Laurain and Kevin Sturm. 2016. Distributed shape derivative via averaged adjoint method and applications. ESAIM: Mathematical Modelling and Numerical Analysis 50 (7 2016), 1241--1267. Issue 4. Google ScholarCross Ref
- B. A. Le, J. Yvonnet, and Q. C. He. 2015. Computational homogenization of nonlinear elastic materials using neural networks. Internat. J. Numer. Methods Engrg. 104 (12 2015), 1061--1084. Issue 12. Google ScholarCross Ref
- Ryan H Lee, Erwin A B Mulder, and Jonathan B Hopkins. 2022. Mechanical neural networks: Architected materials that learn behaviors. https://www.science.orgGoogle Scholar
- Minchen Li, Zachary Ferguson, Teseo Schneider, Timothy Langlois, Denis Zorin, Daniele Panozzo, Chenfanfu Jiang, and Danny M. Kaufman. 2020. Incremental Potential Contact: Intersection- and Inversion-free Large Deformation Dynamics. ACM Trans. Graph. (SIGGRAPH) 39, 4, Article 49 (2020).Google ScholarDigital Library
- Lin Lu, Andrei Sharf, Haisen Zhao, Yuan Wei, Qingnan Fan, Xuelin Chen, Yann Savoye, Changhe Tu, Daniel Cohen-Or, and Baoquan Chen. 2014. Build-to-last: Strength to weight 3D printed objects. ACM Transactions on Graphics 33, 4 (2014). Google ScholarDigital Library
- Luigi Malomo, Jesús Pérez, Emmanuel Iarussi, Nico Pietroni, Eder Miguel, Paolo Cignoni, and Bernd Bickel. 2018. FlexMaps: Computational design of flat flexible shells for shaping 3D objects. SIGGRAPH Asia 2018 Technical Papers, SIGGRAPH Asia 2018 37, 6 (2018), 1--14. Google ScholarDigital Library
- Andrew G. Mark, Stefano Palagi, Tian Qiu, and Peer Fischer. 2016. Auxetic metamaterial simplifies soft robot design. In 2016 IEEE International Conference on Robotics and Automation (ICRA). 4951--4956. Google ScholarDigital Library
- Jonàs Martínez, Jérémie Dumas, Sylvain Lefebvre, and Li Yi Wei. 2015. Structure and appearance optimization for controllable shape design. ACM Transactions on Graphics 34, 6 (2015). Google ScholarDigital Library
- Przemyslaw Musialski, Thomas Auzinger, Michael Birsak, Michael Wimmer, and Leif Kobbelty. 2015. Reduced-order shape optimization using offset surfaces. ACM Transactions on Graphics 34, 4 (2015). Google ScholarDigital Library
- Przemyslaw Musialski, Christian Hafner, Florian Rist, Michael Birsak, Michael Wimmer, and Leif Kobbelt. 2016. Non-linear shape optimization using local subspace projections. ACM Transactions on Graphics 35, 4 (2016), 1--13. Google ScholarDigital Library
- Praveen Babu Nakshatrala, Daniel A Tortorelli, and KB Nakshatrala. 2013. Nonlinear structural design using multiscale topology optimization. Part I: Static formulation. Computer Methods in Applied Mechanics and Engineering 261 (2013), 167--176.Google ScholarCross Ref
- Igor Ostanin, George Ovchinnikov, Davi Colli Tozoni, and Denis Zorin. 2018. A parametric class of composites with a large achievable range of effective elastic properties. Journal of the Mechanics and Physics of Solids 118 (2018), 204--217.Google ScholarCross Ref
- Jifei Ou, Mélina Skouras, Nikolaos Vlavianos, Felix Heibeck, Chin-Yi Cheng, Jannik Peters, and Hiroshi Ishii. 2016. aeroMorph-heat-sealing inflatable shape-change materials for interaction design. In Proceedings of the 29th Annual Symposium on User Interface Software and Technology. 121--132.Google ScholarDigital Library
- Julian Panetta, Florin Isvoranu, Tian Chen, Emmanuel Siéfert, Benoît Roman, and Mark Pauly. 2021. Computational inverse design of surface-based inflatables. ACM Transactions on Graphics (TOG) 40, 4 (2021), 1--14.Google ScholarDigital Library
- Julian Panetta, Mina Konaković-Luković, Florin Isvoranu, Etienne Bouleau, and Mark Pauly. 2019. X-Shells: A New Class of Deployable Beam Structures. ACM Trans. Graph. 38, 4, Article 83 (July 2019), 15 pages. Google ScholarDigital Library
- Julian Panetta, Haleh Mohammadian, Emiliano Luci, and Vahid Babaei. 2022. Shape from Release: Inverse Design and Fabrication of Controlled Release Structures. ACM Transactions on Graphics (TOG) 41, 6 (2022), 1--14.Google ScholarDigital Library
- Julian Panetta, Abtin Rahimian, and Denis Zorin. 2017. Worst-case Stress Relief for Microstructures. ACM Trans. Graph. 36, 4, Article 122 (July 2017), 16 pages. Google ScholarDigital Library
- Julian Panetta, Qingnan Zhou, Luigi Malomo, Nico Pietroni, Paolo Cignoni, and Denis Zorin. 2015. Elastic Textures for Additive Fabrication. ACM Trans. Graph. 34, 4, Article 135 (July 2015), 12 pages. Google ScholarDigital Library
- Jesús Pérez, Miguel A Otaduy, and Bernhard Thomaszewski. 2017. Computational design and automated fabrication of kirchhoff-plateau surfaces. ACM Transactions on Graphics (TOG) 36, 4 (2017), 1--12.Google ScholarDigital Library
- Stefan Pillwein and Przemyslaw Musialski. 2021. Generalized deployable elastic geodesic grids. ACM Transactions on Graphics (TOG) 40, 6 (2021), 1--15.Google ScholarDigital Library
- Ileana Pirozzi, Ali Kight, Rohan Shad, Amy Kyungwon Han, Seraina A. Dual, Robyn Fong, Allison Jia, William Hiesinger, Paul Yock, and Mark Cutkosky. 2022. RVEX: Right Ventricular External Device for Biomimetic Support and Monitoring of the Right Heart. Advanced Materials Technologies 7, 8 (2022), 2101472. arXiv:https://onlinelibrary.wiley.com/doi/pdf/10.1002/admt.202101472 Google ScholarCross Ref
- Romain Prévost, Emily Whiting, Sylvain Lefebvre, and Olga Sorkine-Hornung. 2013. Make it stand: Balancing shapes for 3D fabrication. ACM Transactions on Graphics 32, 4 (2013). Google ScholarDigital Library
- Ahmad Rafsanjani, Katia Bertoldi, and André R. Studart. 2019. Programming soft robots with flexible mechanical metamaterials. Science Robotics 4, 29 (2019), eaav7874. arXiv:https://www.science.org/doi/pdf/10.1126/scirobotics.aav7874 Google ScholarCross Ref
- Karthikayen Raju, Tong-Earn Tay, and Vincent Beng Chye Tan. 2021. A review of the FE2 method for composites. Multiscale and Multidisciplinary Modeling, Experiments and Design 4 (2021), 1--24.Google ScholarCross Ref
- Xin Ren, Raj Das, Phuong Tran, Tuan Duc Ngo, and Yi Min Xie. 2018. Auxetic metamaterials and structures: a review. Smart materials and structures 27, 2 (2018), 023001.Google Scholar
- Yingying Ren, Uday Kusupati, Julian Panetta, Florin Isvoranu, Davide Pellis, Tian Chen, and Mark Pauly. 2022. Umbrella meshes: elastic mechanisms for freeform shape deployment. ACM Transactions on Graphics 41, ARTICLE (2022), 1--15.Google Scholar
- Christian Schumacher, Bernd Bickel, Jan Rys, Steve Marschner, Chiara Daraio, and Markus Gross. 2015. Microstructures to Control Elasticity in 3D Printing. ACM Trans. Graph. 34, 4, Article 136 (July 2015), 13 pages.Google ScholarDigital Library
- Christian Schumacher, Steve Marschner, Markus Cross, and Bernhard Thomaszewski. 2018a. Mechanical Characterization of Structured Sheet Materials. ACM Trans. Graph. 37, 4, Article 148 (July 2018), 15 pages. Google ScholarDigital Library
- Christian Schumacher, Jonas Zehnder, and Moritz Bächer. 2018b. Set-in-stone: Worst-case optimization of structures weak in tension. SIGGRAPH Asia 2018 Technical Papers, SIGGRAPH Asia 2018 38, 6 (2018). Google ScholarDigital Library
- Mélina Skouras, Bernhard Thomaszewski, Stelian Coros, Bernd Bickel, and Markus Gross. 2013. Computational design of actuated deformable characters. ACM Transactions on Graphics (TOG) 32, 4 (2013), 1--10.Google ScholarDigital Library
- Yuanping Song, Robert M. Panas, Samira Chizari, Lucas A. Shaw, Julie A. Jackson, Jonathan B. Hopkins, and Andrew J. Pascall. 2019. Additively manufacturable micro-mechanical logic gates. Nature Communications 10 (12 2019). Issue 1. Google ScholarCross Ref
- Georg Sperl, Rahul Narain, and Chris Wojtan. 2020. Homogenized Yarn-Level Cloth. ACM Trans. Graph. 39, 4, Article 48 (aug 2020), 16 pages. Google ScholarDigital Library
- Ondrej Stava, Juraj Vanek, Bedrich Benes, Nathan Carr, and Radomír Mvech. 2012. Stress relief: Improving structural strength of 3D printable objects. ACM Transactions on Graphics 31, 4 (2012). Google ScholarDigital Library
- Stratasys. 2021. Digital Materials Data Sheet. https://www.stratasys.com/siteassets/materials/materials-catalog/mds_pj_digitalmaterialsdatasheet_0122a-1.pdf?v=49c186Google Scholar
- Davi Colli Tozoni, Jérémie Dumas, Zhongshi Jiang, Julian Panetta, Daniele Panozzo, and Denis Zorin. 2020. A low-parametric rhombic microstructure family for irregular lattices. ACM Transactions on Graphics (TOG) 39, 4 (2020), 101--1.Google ScholarDigital Library
- Erva Ulu, James McCann, and Levent Burak Kara. 2017. Lightweight structure design under force location uncertainty. ACM Transactions on Graphics 36, 4 (2017), 1--13. Google ScholarDigital Library
- Pauli Virtanen, Ralf Gommers, Travis E. Oliphant, Matt Haberland, Tyler Reddy, David Cournapeau, Evgeni Burovski, Pearu Peterson, Warren Weckesser, Jonathan Bright, Stéfan J. van der Walt, Matthew Brett, Joshua Wilson, K. Jarrod Millman, Nikolay Mayorov, Andrew R. J. Nelson, Eric Jones, Robert Kern, Eric Larson, C J Carey, İlhan Polat, Yu Feng, Eric W. Moore, Jake VanderPlas, Denis Laxalde, Josef Perktold, Robert Cimrman, Ian Henriksen, E. A. Quintero, Charles R. Harris, Anne M. Archibald, Antônio H. Ribeiro, Fabian Pedregosa, Paul van Mulbregt, and SciPy 1.0 Contributors. 2020. SciPy 1.0: Fundamental Algorithms for Scientific Computing in Python. Nature Methods 17 (2020), 261--272. Google ScholarCross Ref
- Fengwen Wang, Ole Sigmund, and Jakob Søndergaard Jensen. 2014. Design of materials with prescribed nonlinear properties. Journal of the Mechanics and Physics of Solids 69 (2014), 156--174.Google ScholarCross Ref
- Yifan Wang, Liuchi Li, Douglas Hofmann, José E Andrade, and Chiara Daraio. 2021. Structured fabrics with tunable mechanical properties. Nature 596, 7871 (2021), 238--243.Google Scholar
- Yifan Wang, Brian Ramirez, Kalind Carpenter, Christina Naify, Douglas C. Hofmann, and Chiara Daraio. 2019. Architected lattices with adaptive energy absorption. Extreme Mechanics Letters 33 (2019), 100557. Google ScholarCross Ref
- Ron Wein, Eric Berberich, Efi Fogel, Dan Halperin, Michael Hemmer, Oren Salzman, and Baruch Zukerman. 2023. 2D Arrangements. In CGAL User and Reference Manual (5.5.2 ed.). CGAL Editorial Board. https://doc.cgal.org/5.5.2/Manual/packages.html#PkgArrangementOnSurface2Google Scholar
- A.J. Worsey and B. Piper. 1988. A trivariate Powell-Sabin interpolant. Computer Aided Geometric Design 5, 3 (1988), 177--186. Google ScholarDigital Library
- Jorge Nocedal Stephen J Wright. 2006. Numerical optimization.Google Scholar
- Hongyi Xu, Yijing Li, Yong Chen, and Jernej Barbivc. 2015. Interactive Material Design using Model Reduction. ACM Trans. on Graphics 34, 2 (2015).Google ScholarDigital Library
- Jonas Zehnder, Stelian Coros, and Bernhard Thomaszewski. 2016. Designing Structurally-Sound Ornamental Curve Networks. ACM Trans. Graph. 35, 4, Article 99 (jul 2016), 10 pages. Google ScholarDigital Library
- Jonas Zehnder, Espen Knoop, Moritz Bächer, and Bernhard Thomaszewski. 2017. Metasilicone: Design and Fabrication of Composite Silicone with Desired Mechanical Properties. ACM Trans. Graph. 36, 6, Article 240 (nov 2017), 13 pages. Google ScholarDigital Library
- Hang Zhang, Xiaogang Guo, Jun Wu, Daining Fang, and Yihui Zhang. 2018. Soft mechanical metamaterials with unusual swelling behavior and tunable stress-strain curves. Science advances 4, 6 (2018), eaar8535.Google Scholar
- Qingnan Zhou, Eitan Grinspun, Denis Zorin, and Alec Jacobson. 2016. Mesh Arrangements for Solid Geometry. ACM Trans. Graph. 35, 4, Article 39 (jul 2016), 15 pages. Google ScholarDigital Library
- Qingnan Zhou, Julian Panetta, and Denis Zorin. 2013. Worst-case Structural Analysis. ACM Trans. Graph. 32, 4, Article 137 (July 2013), 12 pages. Google ScholarDigital Library
- Bo Zhu, Mélina Skouras, Desai Chen, and Wojciech Matusik. 2017. Two-Scale Topology Optimization with Microstructures. ACM Trans. Graph. 36, 5, Article 164 (July 2017), 16 pages.Google ScholarDigital Library
- Benliang Zhu, Xianmin Zhang, Hongchuan Zhang, Junwen Liang, Haoyan Zang, Hai Li, and Rixin Wang. 2020. Design of compliant mechanisms using continuum topology optimization: A review. Mechanism and Machine Theory 143 (2020), 103622. Google ScholarCross Ref
Index Terms
- Computational Design of Flexible Planar Microstructures
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