“Mechanical characterization of structured sheet materials” by Schumacher, Marschner, Gross and Thomaszewski
Conference:
Type(s):
Entry Number: 148
Title:
- Mechanical characterization of structured sheet materials
Session/Category Title: Disorder Matter: From Shells to Rods and Grains
Presenter(s)/Author(s):
Moderator(s):
Abstract:
We propose a comprehensive approach to characterizing the mechanical properties of structured sheet materials, i.e., planar rod networks whose mechanics and aesthetics are inextricably linked. We establish a connection between the complex mesoscopic deformation behavior of such structures and their macroscopic elastic properties through numerical homogenization. Our approach leverages 3D Kirchhoff rod simulation in order to capture nonlinear effects for both in-plane and bending deformations. We apply our method to different families of structures based on isohedral tilings—a simple yet extensive and aesthetically interesting group of space-filling patterns. We show that these tilings admit a wide range of material properties, and our homogenization approach allows us to create concise and intuitive descriptions of a material’s direction-dependent macromechanical behavior that are easy to communicate even to non-experts. We perform this characterization for an extensive set of structures and organize these data in a material browser to enable efficient forward exploration of the aesthetic-mechanical space of structured sheet materials. We also propose an inverse design method to automatically find structure parameters that best approximate a user-specified target behavior.
References:
1. Ergun Akleman, Jianer Chen, Qing Xing, and Jonathan L. Gross. 2009. Cyclic Plain-weaving on Polygonal Mesh Surfaces with Graph Rotation Systems. ACM Trans. Graph. 28, 3. Google ScholarDigital Library
2. Miklós Bergou, Basile Audoly, Etienne Vouga, Max Wardetzky, and Eitan Grinspun. 2010. Discrete Viscous Threads. ACM Trans. Graph. 29, 4. Google ScholarDigital Library
3. Katia Bertoldi, Vincenzo VitelliJohanChristensen, and Martin van Hecke. 2017. Flexible mechanical metamaterials. Nature Reviews 2, 17066.Google Scholar
4. 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. ACM Trans. Graph. 29, 4. Google ScholarDigital Library
5. Bernd Bickel, Moritz Bächer, Miguel A. Otaduy, Wojciech Matusik, Hanspeter Pfister, and Markus Gross. 2009. Capture and Modeling of Non-linear Heterogeneous Soft Tissue. ACM Trans. Graph. 28, 3. Google ScholarDigital Library
6. Desai Chen, David I. W. Levin, Wojciech Matusik, and Danny M. Kaufman. 2017. Dynamics-aware Numerical Coarsening for Fabrication Design. ACM Trans. Graph. 36, 4. Google ScholarDigital Library
7. Desai Chen, David I. W. Levin, Shinjiro Sueda, and Wojciech Matusik. 2015. Data-driven Finite Elements for Geometry and Material Design. ACM Trans. Graph. 34, 4. Google ScholarDigital Library
8. Timothy G. Clapp, Hong Peng, Tushar K. Ghosh, and Jeffrey W. Eischen. 1990. Indirect measurement of the moment-curvature relationship for fabrics. Textile Research Journal 60, 9, 525–533.Google ScholarCross Ref
9. Corentin Coulais, Eial Teomy, Koen de Reus, Yair Shokef, and Martin van Hecke. 2016. Combinatorial design of textured mechanical metamaterials. Nature, 529–532.Google Scholar
10. Géry de Saxcé and Claude Vallée. 2013. Invariant Measures of the Lack of Symmetry with Respect to the Symmetry Groups of 2D Elasticity Tensors. Journal of Elasticity 111, 1, 21–39.Google ScholarCross Ref
11. Jérémie Dumas, An Lu,Sylvain Lefebvre, Jun Wu, and Christian Dick. 2015. By-example Synthesis of Structurally Sound Patterns. ACM Trans. Graph. 34, 4. Google ScholarDigital Library
12. Marc L.M. François, Letian Chen, and Michel Coret. 2017. Elasticity and symmetry of triangular lattice materials. International Journal of Solids and Structures 129, Supplement C, 18–27.Google ScholarCross Ref
13. Marc G. D. Geers, Erica W. C. Coenen, and Varvara G. Kouznetsova. 2007. Multi-scale computational homogenization of structured thin sheets. Modelling and Simulation in Materials Science and Engineering 15, 4, S393–S404.Google ScholarCross Ref
14. Branko Grünbaum and G C Shephard. 1986. Tilings and Patterns. W. H. Freeman & Co., New York, NY, USA. Google ScholarDigital Library
15. Behrooz Hassani and Ernest Hinton. 1998. A review of homogenization and topology optimization I-homogenization theory for media with periodic structure. Computers & Structures 69, 6, 707–717.Google ScholarCross Ref
16. Robert G. Hutchinson and Norman A. Fleck. 2006. The structural performance of the periodic truss. Journal of the Mechanics and Physics of Solids 54, 4, 756–782.Google ScholarCross Ref
17. Chyanbin Hwu. 2010. Anisotropic Elastic Plates. Springer US.Google Scholar
18. Caigui Jiang, Chengcheng Tang, Amir Vaxman, Peter Wonka, and Helmut Pottmann. 2015. Polyhedral Patterns. ACM Trans. Graph. 34, 6. Google ScholarDigital Library
19. Jonathan M. Kaldor, Doug L. James, and Steve Marschner. 2010. Efficient Yarn-based Cloth with Adaptive Contact Linearization. ACM Trans. Graph. 29, 4. Google ScholarDigital Library
20. Craig S. Kaplan. 2009. Introductory Tiling Theory for Computer Graphics. Morgan & Claypool Publishers. Google ScholarDigital Library
21. Craig S. Kaplan and David H. Salesin. 2000. Escherization. In Proceedings of the 27th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’00). 499–510. Google ScholarDigital Library
22. Craig S. Kaplan and David H. Salesin. 2004. Islamic Star Patterns in Absolute Geometry. ACM Trans. Graph. 23, 2, 97–119. Google ScholarDigital Library
23. Lily Kharevych, Patrick Mullen, Houman Owhadi, and Mathieu Desbrun. 2009. Numerical Coarsening of Inhomogeneous Elastic Materials. ACM Trans. Graph. 28, 3. Google ScholarDigital Library
24. Dennis Kochmann and Katia Bertoldi. 2017. Exploiting Microstructural Instabilities in Solids and Structures: From Metamaterials to Structural Transitions. Applied Mechanics Reviews 69, 050801.Google ScholarCross Ref
25. Mina Konaković, Keenan Crane, Bailin Deng, Sofien Bouaziz, Daniel Piker, and Mark Pauly. 2016. Beyond Developable: Computational Design and Fabrication with Auxetic Materials. ACM Trans. Graph. 35, 4. Google ScholarDigital Library
26. Yijing Li and Jernej Barbič. 2015. Stable Anisotropic Materials. IEEE Trans. on Visualization and Computer Graphics 21, 10, 1129–1137. Google ScholarDigital Library
27. Jianxing Liu and Yihui Zhang. 2018. Soft network materials with isotropic negative Poisson’s ratios over large strains. Soft Matter 14, 693–703. Issue 5.Google ScholarCross Ref
28. Qiang Lu and Rui Huang. 2009. Nonlinear mechanics of single-atomic-layer graphene sheets. International Journal of Applied Mechanics 1, 3, 443–467.Google ScholarCross Ref
29. Jonàs Martínez, Jérémie Dumas, and Sylvain Lefebvre. 2016. Procedural Voronoi Foams for Additive Manufacturing. ACM Trans. Graph. 35, 4. Google ScholarDigital Library
30. Jonàs Martínez, Jérémie Dumas, Sylvain Lefebvre, and Li-Yi Wei. 2015. Structure and Appearance Optimization for Controllable Shape Design. Proc. of ACM SIGGRAPH Asia 34, 6. Google ScholarDigital Library
31. Jonàs Martínez, Haichuan Song, Jérémie Dumas, and Sylvain Lefebvre. 2017. Orthotropic K-nearest Foams for Additive Manufacturing. ACM Trans. Graph. 36, 4. Google ScholarDigital Library
32. Vittorio Megaro, Jonas Zehnder, Moritz Bächer, Stelian Coros, Markus Gross, and Bernhard Thomaszewski. 2017. A Computational Design Tool for Compliant Mechanisms. ACM Trans. Graph. 36, 4. Google ScholarDigital Library
33. Eder Miguel, Derek Bradley, Bernhard Thomaszewski, Bernd Bickel, Wojciech Matusik, Miguel A. Otaduy, and Steve Marschner. 2012. Data-Driven Estimation of Cloth Simulation Models. Comput. Graph. Forum 31, 2, 519–528. Google ScholarDigital Library
34. Eder Miguel, Rasmus Tamstorf, Derek Bradley, Sara C. Schvartzman, Bernhard Thomaszewski, Bernd Bickel, Wojciech Matusik, Steve Marschner, and Miguel A. Otaduy. 2013. Modeling and Estimation of Internal Friction in Cloth. ACM Trans. Graph. 32, 6. Google ScholarDigital Library
35. Matthieu Nesme, Paul G. Kry, Lenka Jeřábková, and François Faure. 2009. Preserving Topology and Elasticity for Embedded Deformable Models. ACM Trans. Graph. 28, 3. Google ScholarDigital Library
36. William J. O’Donnell and Bernard F. Langer. 1962. Design of Perforated Plates. ASME Journal of Engineering for Industry 84, 3, 307–319.Google ScholarCross Ref
37. Victor Ostromoukhov. 2007. Sampling with Polyominoes. ACM Trans. Graph. 26, 3. Google ScholarDigital Library
38. Simon Pabst, Sybille Krzywinski, Andrea Schenk, and Bernhard Thomaszewski. 2008. Seams and Bending in Cloth Simulation. In Workshop in Virtual Reality Interactions and Physical Simulation “VRIPHYS” (2008).Google Scholar
39. Julian Panetta, Abtin Rahimian, and Denis Zorin. 2017. Worst-case Stress Relief for Micro structures. ACM Trans. Graph. 36, 4. Google ScholarDigital Library
40. Julian Panetta, Qingnan Zhou, Luigi Malomo, Nico Pietroni, Paolo Cignoni, and Denis Zorin. 2015. Elastic Textures for Additive Fabrication. ACM Trans. Graph. 34, 4. Google ScholarDigital Library
41. Jesús Pérez, Miguel A. Otaduy, and Bernhard Thomaszewski. 2017. Computational Design and Automated Fabrication of Kirchhoff-plateau Surfaces. ACM Trans. Graph. 36, 4. Google ScholarDigital Library
42. Jesús Pérez, Bernhard Thomaszewski, Stelian Coros, Bernd Bickel, José A. Canabal, Robert Sumner, and Miguel A. Otaduy. 2015. Design and Fabrication of Flexible Rod Meshes. ACM Trans. Graph. 34, 4. Google ScholarDigital Library
43. Catalin R. Picu. 2011. Mechanics of random fiber networks—a review. Soft Matter 7, 6768–6785. Issue 15.Google ScholarCross Ref
44. Hang Jerry Qi and Mary C. Boyce. 2005. Stress-strain behavior of thermoplastic polyurethanes. Mechanics of Materials 37, 8, 817–839.Google ScholarCross Ref
45. Ahmad Rafsanjani and Damiano Pasini. 2016. Bistable auxetic mechanical metamaterials inspired by ancient geometric motifs. Extreme Mechanics Letters 9, 291–296.Google ScholarCross Ref
46. 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. Google ScholarDigital Library
47. Christian Schumacher, Bernhard Thomaszewski, and Markus Gross. 2016. Stenciling: Designing Structurally-Sounds Surfaces with Decorative Patterns. Comput. Graphics Forum 35, 5, 101–110.Google ScholarDigital Library
48. Chengcheng Tang, Xiang Sun, Alexandra Gomes, Johannes Wallner, and Helmut Pottmann. 2014. Form-finding with Polyhedral Meshes Made Simple. ACM Trans. Graph. 33, 4. Google ScholarDigital Library
49. Huamin Wang, James F. O’Brien, and Ravi Ramamoorthi. 2011. Data-driven Elastic Models for Cloth: Modeling and Measurement. ACM Trans. Graph. 30, 4. Google ScholarDigital Library
50. Jan Wilhelm and Erwin Frey. 2003. Elasticity of Stiff Polymer Networks. Phys. Rev. Lett. 91, 108103. Issue 10.Google ScholarCross Ref
51. Hongyi Xu, Funshing Sin, Yufeng Zhu, and Jernej Barbič. 2015. Nonlinear Material Design Using Principal Stretches. ACM Trans. Graph. 34, 4. Google ScholarDigital Library
52. Lizhi Xu, Terry C. Shyu, and Nicholas A. Kotov. 2017. Origami and Kirigami Nanocomposites. ACS Nano 11, 8, 7587–7599.Google ScholarCross Ref
53. Jonas Zehnder, Stelian Coros, and Bernhard Thomaszewski. 2016. Designing Structurally-sound Ornamental Curve Networks. ACM Trans. Graph. 35, 4. Google ScholarDigital Library
54. 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. Google ScholarDigital Library
55. Kun Zhou, Xin Huang, Xi Wang, Yiying Tong, Mathieu Desbrun, Baining Guo, and Heung-Yeung Shum. 2006. Mesh Quilting for Geometric Texture Synthesis. ACM Trans. Graph. 25, 3, 690–697. Google ScholarDigital Library
