“Physical simulation of environmentally induced thin shell deformation”
Conference:
Type(s):
Entry Number: 146
Title:
- Physical simulation of environmentally induced thin shell deformation
Session/Category Title: Disorder Matter: From Shells to Rods and Grains
Presenter(s)/Author(s):
Abstract:
We present a physically accurate low-order elastic shell model that incorporates active material response to dynamically changing stimuli such as heat, moisture, and growth. Our continuous formulation of the geometrically non-linear elastic energy derives from the principles of differential geometry, and as such naturally incorporates shell thickness, non-zero rest curvature, and physical material properties. By modeling the environmental stimulus as local, dynamic changes in the rest metric of the material, we are able to solve for the corresponding shape changes by integrating the equations of motions given this non-Euclidean rest state. We present models for differential growth and shrinking due to moisture and temperature gradients along and across the surface, and incorporate anisotropic growth by defining an intrinsic machine direction within the material. Comparisons with experiments and volumetric finite elements show that our simulations achieve excellent qualitative and quantitative agreement. By combining the reduced-order shell theory with appropriate physical models, our approach accurately captures all the physical phenomena while avoiding expensive volumetric discretization of the shell volume.
References:
1. Iggesund Paperboard AB. 1993. Paperboard reference manual. Iggesund Paperboard AB.Google Scholar
2. Kosala Bandara and Fehmi Cirak. 2018. Isogeometric shape optimisation of shell structures using multiresolution subdivision surfaces. Computer-Aided Design 95, Supplement C (2018), 62 — 71. Google ScholarDigital Library
3. David Baraff and Andrew Witkin. 1998. Large Steps in Cloth Simulation. In Proceedings of the 25th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH ’98). ACM, New York, NY, USA, 43–54. Google ScholarDigital Library
4. Jernej Barbič, Fun Shing Sin, and Daniel Schroeder. 2012. Vega FEM Library. (2012). http://www.jernejbarbic.com/vega.Google Scholar
5. Klaus Jürgen Bathe, Eduardo Dvorkin, and Lee W. Ho. 1983. Our discrete-Kirchhoff and isoparametric shell elements for nonlinear analysis – An assessment. Computers & Structures 16, 1 (1983), 89 — 98.Google ScholarCross Ref
6. Jean-Louis Batoz, Klaus-Jürgen Bathe, and Lee-Wing Ho. 1980. A study of three-node triangular plate bending elements. Internat. J. Numer. Methods Engrg. 15, 12 (1980), 1771–1812.Google ScholarCross Ref
7. D.J. Benson, Y. Bazilevs, M.C. Hsu, and T.J.R. Hughes. 2010. Isogeometric shell analysis: The Reissner-Mindlin shell. Computer Methods in Applied Mechanics and Engineering 199, 5 (2010), 276 — 289. Computational Geometry and Analysis.Google ScholarCross Ref
8. Miklos Bergou, Max Wardetzky, David Harmon, Denis Zorin, and Eitan Grinspun. 2006. A Quadratic Bending Model for Inextensible Surfaces. In Proceedings of the Fourth Eurographics Symposium on Geometry Processing (SGP ’06). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 227–230. Google ScholarDigital Library
9. Alexander I. Bobenko, Helmut Pottmann, and Johannes Wallner. 2010. A curvature theory for discrete surfaces based on mesh parallelity. Math. Ann. 348, 1 (01 Sep 2010), 1–24.Google Scholar
10. Alexander I. Bobenko and Peter Schröder. 2005. Discrete Willmore Flow. In Proceedings of the Third Eurographics Symposium on Geometry Processing (SGP ’05). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, Article 101. Google ScholarDigital Library
11. Sergey Bochkanov. 1999. ALGLIB. (1999). www.alglib.netGoogle Scholar
12. Robert Bridson, Ronald Fedkiw, and John Anderson. 2002. Robust Treatment of Collisions, Contact and Friction for Cloth Animation. ACM Trans. Graph. 21, 3 (July 2002), 594–603. Google ScholarDigital Library
13. Yanqing Chen, Timothy A. Davis, William W. Hager, and Sivasankaran Rajamanickam. 2008. Algorithm 887: CHOLMOD, Supernodal Sparse Cholesky Factorization and Update/Downdate. ACM Trans. Math. Softw. 35, 3, Article 22 (Oct. 2008), 14 pages. Google ScholarDigital Library
14. Philippe G. Ciarlet. 2000. Theory of Shells, Volume 3 (Mathematical Elasticity). North Holland.Google Scholar
15. Fehmi Cirak, Michael Ortiz, and Peter Schröder. 2000. Subdivision surfaces: a new paradigm for thin-shell finite-element analysis. Internat. J. Numer. Methods Engrg. 47, 12 (2000), 2039–2072.Google ScholarCross Ref
16. Julien Dervaux and Martine Ben Amar. 2008. Morphogenesis of Growing Soft Tissues. Phys. Rev. Lett. 101 (Aug 2008), 068101. Issue 6.Google ScholarCross Ref
17. Efi Efrati, Eran Sharon, and Raz Kupferman. 2009a. Buckling transition and boundary layer in non-Euclidean plates. Physical Review E 80, 1 (Jul 2009).Google ScholarCross Ref
18. E. Efrati, E. Sharon, and R. Kupferman. 2009b. Elastic theory of unconstrained non-Euclidean plates. Journal of the Mechanics and Physics of Solids 57, 4 (2009), 762 — 775.Google ScholarCross Ref
19. Elliot English and Robert Bridson. 2008. Animating Developable Surfaces Using Non-conforming Elements. ACM Trans. Graph. 27, 3, Article 66 (Aug. 2008), 5 pages. Google ScholarDigital Library
20. Yotam Gingold, Adrian Secord, Jefferson H. Han, Eitan Grinspun, and Denis Zorin. 2004. Poster: A Discrete Model for Inelastic Deformation of Thin Shells. In ACM/Eurographics Symposium on Computer Animation ’04.Google Scholar
21. Alain Goriely and Martine Ben Amar. 2005. Differential Growth and Instability in Elastic Shells. Phys. Rev. Lett. 94 (May 2005), 198103. Issue 19.Google ScholarCross Ref
22. Eitan Grinspun, Yotam Gingold, Jason Reisman, and Denis Zorin. 2006. Computing discrete shape operators on general meshes. Computer Graphics Forum 25, 3 (2006), 547–556.Google ScholarCross Ref
23. Eitan Grinspun, Anil N. Hirani, Mathieu Desbrun, and Peter Schröder. 2003. Discrete Shells. In Proceedings of the 2003 ACM SIGGRAPH/Eurographics Symposium on Computer Animation (SCA ’03). Eurographics Association, Aire-la-Ville, Switzerland, Switzerland, 62–67. Google ScholarDigital Library
24. Christophe Guberan. 2012. Hydro-Fold. (2012). http://www.christopheguberan.ch/hydro-fold/Google Scholar
25. Ruslan Guseinov, Eder Miguel, and Bernd Bickel. 2017. CurveUps: Shaping Objects from Flat Plates with Tension-actuated Curvature. ACM Trans. Graph. 36, 4, Article 64 (July 2017), 12 pages. Google ScholarDigital Library
26. SoHyeon Jeong, Tae-hyeong Kim, and Chang-Hun Kim. 2011. Shrinkage, Wrinkling and Ablation of Burning Cloth and Paper. Vis. Comput. 27, 6–8 (June 2011), 417–427. Google ScholarDigital Library
27. SoHyeon Jeong, Si-Hyung Park, and Chang-Hun Kim. 2013. Simulation of Morphology Changes in Drying Leaves. Computer Graphics Forum 32, 1 (2013), 204–215.Google ScholarCross Ref
28. J. Kiendl, K.-U. Bletzinger, J. Linhard, and R. Wüchner. 2009. Isogeometric shell analysis with Kirchhoff-Love elements. Computer Methods in Applied Mechanics and Engineering 198, 49 (2009), 3902 — 3914.Google ScholarCross Ref
29. J. Kim, J.A. Hanna, M. Byun, C.D. Santangelo, and R.C. Hayward. 2012. Designing responsive buckled surfaces by halftone gel lithography. Science 335, 6073 (2012), 1201–1205.Google ScholarCross Ref
30. Yael Klein, Efi Efrati, and Eran Sharon. 2007. Shaping of Elastic Sheets by Prescription of Non-Euclidean Metrics. Science 315, 5815 (2007), 1116–1120.Google Scholar
31. Caroline Larboulette, Pablo Quesada, and Olivier Dumas. 2013. Burning Paper: Simulation at the Fiber’s Level. In Proceedings of Motion on Games (MIG ’13). ACM, New York, NY, USA, Article 25, 6 pages. Google ScholarDigital Library
32. Shiguang Liu, Qiguang Liu, Tai An, Jizhou Sun, and Qunsheng Peng. 2009. Physically based simulation of thin-shell objects’ burning. The Visual Computer 25, 5 (01 May 2009), 687–696. Google ScholarDigital Library
33. Frank Losasso, Geoffrey Irving, Eran Guendelman, and Ron Fedkiw. 2006. Melting and Burning Solids into Liquids and Gases. IEEE Transactions on Visualization and Computer Graphics 12, 3 (May 2006), 343–352. Google ScholarDigital Library
34. Zeki Melek and John Keyser. 2003. Interactive Simulation of Burning Objects. In Proceedings of the 11th Pacific Conference on Computer Graphics and Applications (PG ’03). IEEE Computer Society, Washington, DC, USA, 462–. Google ScholarDigital Library
35. Zeki Melek and John Keyser. 2005. Multi-representation Interaction for Physically Based Modeling. In Proceedings of the 2005 ACM Symposium on Solid and Physical Modeling (SPM ’05). ACM, New York, NY, USA, 187–196. Google ScholarDigital Library
36. Zeki Melek and John Keyser. 2007. Driving Object Deformations from Internal Physical Processes. In Proceedings of the 2007 ACM Symposium on Solid and Physical Modeling (SPM ’07). ACM, New York, NY, USA, 51–59. Google ScholarDigital Library
37. Rahul Narain, Tobias Pfaff, and James F. O’Brien. 2013. Folding and Crumpling Adaptive Sheets. ACM Transactions on Graphics 32, 4 (July 2013), 51:1–8. Proceedings of ACM SIGGRAPH 2013, Anaheim. Google ScholarDigital Library
38. Rahul Narain, Armin Samii, and James F. O’Brien. 2012. Adaptive Anisotropic Remeshing for Cloth Simulation. ACM Trans. Graph. 31, 6, Article 152 (Nov. 2012), 10 pages. Google ScholarDigital Library
39. P. Neff. 2004. A geometrically exact Cosserat shell-model including size effects, avoiding degeneracy in the thin shell limit. Part I: Formal dimensional reduction for elastic plates and existence of minimizers for positive Cosserat couple modulus. Continuum Mechanics and Thermodynamics 16, 6 (01 Oct 2004), 577–628.Google Scholar
40. Jesus Perez, Miguel A. Otaduy, and Bernhard Thomaszewski. 2017. Computational Design and Automated Fabrication of Kirchhoff-Plateau Surfaces. ACM Trans. on Graphics (Proc. of ACM SIGGRAPH) 36, 4 (2017), 62.1–62.12. Google ScholarDigital Library
41. Jessica Rosenkrantz and Jesse Louis-Rosenberg. 2018. Nervous Systems. (2018). https://n-e-r-v-o-u-s.com/Google Scholar
42. Eran Sharon and Efi Efrati. 2010. The mechanics of non-Euclidean plates. Soft Matter 6 (2010), 5693–5704. Issue 22.Google ScholarCross Ref
43. J.C. Simo and D.D. Fox. 1989. On a stress resultant geometrically exact shell model. Part I: Formulation and optimal parametrization. Computer Methods in Applied Mechanics and Engineering 72, 3 (1989), 267 — 304. Google ScholarDigital Library
44. John M. Sullivan. 2008. Curvatures of Smooth and Discrete Surfaces. Birkhäuser Basel. Basel, 175–188.Google Scholar
45. Rasmus Tamstorf and Eitan Grinspun. 2013. Discrete bending forces and their Jacobians. Graphical Models 75, 6 (2013), 362 — 370. Google ScholarDigital Library
46. Wim M. van Rees, Etienne Vouga, and L. Mahadevan. 2017. Growth patterns for shape-shifting elastic bilayers. Proceedings of the National Academy of Sciences 114, 44 (2017), 11597–11602.Google ScholarCross Ref
47. Roman Vetter, Norbert Stoop, Thomas Jenni, Falk K. Wittel, and Hans J. Herrmann. 2013. Subdivision shell elements with anisotropic growth. Internat. J. Numer. Methods Engrg. 95, 9 (2013), 791–810.Google ScholarCross Ref
48. Wen Wang, Lining Yao, Teng Zhang, Chin-Yi Cheng, Daniel Levine, and Hiroshi Ishii. 2017. Transformative Appetite: Shape-Changing Food Transforms from 2D to 3D by Water Interaction Through Cooking. In Proceedings of the 2017 CHI Conference on Human Factors in Computing Systems (CHI ’17). ACM, New York, NY, USA. 6123–6132. Google ScholarDigital Library
49. Max Wardetzky, Miklós Bergou, David Harmon, Denis Zorin, and Eitan Grinspun. 2007. Discrete Quadratic Curvature Energies. Comput. Aided Geom. Des. 24, 8–9 (Nov. 2007), 499–518. Google ScholarDigital Library
50. Anna Wawrzinek, Klaus Hildebrandt, and Konrad Polthier. 2011. Koiter’s Thin Shells on Catmull-Clark Limit Surfaces. In Vision, Modeling, and Visualization (2011), Peter Eisert, Joachim Hornegger, and Konrad Polthier (Eds.). The Eurographics Association.Google Scholar
51. Clarisse Weischedel. 2012. A discrete geometric view on shear-deformable shell models. Ph.D. Dissertation. Georg-August-Universität Göttingen.Google Scholar
52. Hang Xiao and Xi Chen. 2011. Modeling and simulation of curled dry leaves. Soft Matter 7, 22 (2011), 10794.Google ScholarCross Ref
